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For the special case of using the standard uniform distribution as a non-informative prior, formula_68, the posterior mean estimator becomes: (A posterior mode should just lead to the standard estimator.) This method is called the rule of succession, which was introduced in the 18th century by Pierre-Simon Laplace. When relying on Jeffreys prior, the prior is formula_70, which leads to the estimator: When estimating with very rare events and a small (e.g.: if ), then using the standard estimator leads to formula_72 which sometimes is unrealistic and undesirable. In such cases there are various alternative estimators. One way is to use the Bayes estimator formula_73, leading to: Another method is to use the upper bound of the confidence interval obtained using the rule of three: Confidence intervals for the parameter p. Even for quite large values of "n", the actual distribution of the mean is significantly nonnormal. Because of this problem several methods to estimate confidence intervals have been proposed.
In the equations for confidence intervals below, the variables have the following meaning: Wald method. A continuity correction of may be added. Agresti–Coull method. Here the estimate of is modified to This method works well for and . See here for formula_86. For use the Wilson (score) method below. Wilson (score) method. The notation in the formula below differs from the previous formulas in two respects: Comparison. The so-called "exact" (Clopper–Pearson) method is the most conservative. ("Exact" does not mean perfectly accurate; rather, it indicates that the estimates will not be less conservative than the true value.) The Wald method, although commonly recommended in textbooks, is the most biased. Related distributions. Sums of binomials. If and are independent binomial variables with the same probability , then is again a binomial variable; its distribution is : A Binomial distributed random variable can be considered as the sum of Bernoulli distributed random variables. So the sum of two Binomial distributed random variables and is equivalent to the sum of Bernoulli distributed random variables, which means . This can also be proven directly using the addition rule.
However, if and do not have the same probability , then the variance of the sum will be smaller than the variance of a binomial variable distributed as . Poisson binomial distribution. The binomial distribution is a special case of the Poisson binomial distribution, which is the distribution of a sum of independent non-identical Bernoulli trials . Ratio of two binomial distributions. This result was first derived by Katz and coauthors in 1978. Let and be independent. Let . Then log("T") is approximately normally distributed with mean log("p"1/"p"2) and variance . Conditional binomials. If "X" ~ B("n", "p") and "Y" \| "X" ~ B("X", "q") (the conditional distribution of "Y", given "X"), then "Y" is a simple binomial random variable with distribution "Y" ~ B("n", "pq"). For example, imagine throwing "n" balls to a basket "UX" and taking the balls that hit and throwing them to another basket "UY". If "p" is the probability to hit "UX" then "X" ~ B("n", "p") is the number of balls that hit "UX". If "q" is the probability to hit "UY" then the number of balls that hit "UY" is "Y" ~ B("X", "q") and therefore "Y" ~ B("n", "pq").
Since formula_95 and formula_96, by the law of total probability, Since formula_98 the equation above can be expressed as Factoring formula_100 and pulling all the terms that don't depend on formula_101 out of the sum now yields After substituting formula_103 in the expression above, we get Notice that the sum (in the parentheses) above equals formula_105 by the binomial theorem. Substituting this in finally yields and thus formula_107 as desired. Bernoulli distribution. The Bernoulli distribution is a special case of the binomial distribution, where . Symbolically, has the same meaning as . Conversely, any binomial distribution, , is the distribution of the sum of independent Bernoulli trials, , each with the same probability . Normal approximation. If is large enough, then the skew of the distribution is not too great. In this case a reasonable approximation to is given by the normal distribution and this basic approximation can be improved in a simple way by using a suitable continuity correction. The basic approximation generally improves as increases (at least 20) and is better when is not near to 0 or 1. Various rules of thumb may be used to decide whether is large enough, and is far enough from the extremes of zero or one:
This can be made precise using the Berry–Esseen theorem. The rule formula_112 is totally equivalent to request that Moving terms around yields: Since formula_115 and formula_116, to obtain the desired conditions: Notice that these conditions automatically imply that formula_118. On the other hand, apply again the square root and divide by 3, Subtracting the second set of inequalities from the first one yields: and so, the desired first rule is satisfied, Assume that both values formula_122 and formula_123 are greater than 9. Since formula_124, we easily have that We only have to divide now by the respective factors formula_126 and formula_127, to deduce the alternative form of the 3-standard-deviation rule: The following is an example of applying a continuity correction. Suppose one wishes to calculate for a binomial random variable . If has a distribution given by the normal approximation, then is approximated by . The addition of 0.5 is the continuity correction; the uncorrected normal approximation gives considerably less accurate results.
This approximation, known as de Moivre–Laplace theorem, is a huge time-saver when undertaking calculations by hand (exact calculations with large are very onerous); historically, it was the first use of the normal distribution, introduced in Abraham de Moivre's book "The Doctrine of Chances" in 1738. Nowadays, it can be seen as a consequence of the central limit theorem since is a sum of independent, identically distributed Bernoulli variables with parameter . This fact is the basis of a hypothesis test, a "proportion z-test", for the value of using , the sample proportion and estimator of , in a common test statistic. For example, suppose one randomly samples people out of a large population and ask them whether they agree with a certain statement. The proportion of people who agree will of course depend on the sample. If groups of "n" people were sampled repeatedly and truly randomly, the proportions would follow an approximate normal distribution with mean equal to the true proportion "p" of agreement in the population and with standard deviation
Poisson approximation. The binomial distribution converges towards the Poisson distribution as the number of trials goes to infinity while the product converges to a finite limit. Therefore, the Poisson distribution with parameter can be used as an approximation to of the binomial distribution if is sufficiently large and is sufficiently small. According to rules of thumb, this approximation is good if and such that , or if and such that , or if and . Concerning the accuracy of Poisson approximation, see Novak, ch. 4, and references therein. Beta distribution. The binomial distribution and beta distribution are different views of the same model of repeated Bernoulli trials. The binomial distribution is the PMF of successes given independent events each with a probability of success. Mathematically, when and , the beta distribution and the binomial distribution are related by a factor of : Beta distributions also provide a family of prior probability distributions for binomial distributions in Bayesian inference:
Given a uniform prior, the posterior distribution for the probability of success given independent events with observed successes is a beta distribution. Computational methods. Random number generation. Methods for random number generation where the marginal distribution is a binomial distribution are well-established. One way to generate random variates samples from a binomial distribution is to use an inversion algorithm. To do so, one must calculate the probability that for all values from through . (These probabilities should sum to a value close to one, in order to encompass the entire sample space.) Then by using a pseudorandom number generator to generate samples uniformly between 0 and 1, one can transform the calculated samples into discrete numbers by using the probabilities calculated in the first step. History. This distribution was derived by Jacob Bernoulli. He considered the case where where is the probability of success and and are positive integers. Blaise Pascal had earlier considered the case where , tabulating the corresponding binomial coefficients in what is now recognized as Pascal's triangle.
Biostatistics Biostatistics (also known as biometry) is a branch of statistics that applies statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experiments and the interpretation of the results. History. Biostatistics and genetics. Biostatistical modeling forms an important part of numerous modern biological theories. Genetics studies, since its beginning, used statistical concepts to understand observed experimental results. Some genetics scientists even contributed with statistical advances with the development of methods and tools. Gregor Mendel started the genetics studies investigating genetics segregation patterns in families of peas and used statistics to explain the collected data. In the early 1900s, after the rediscovery of Mendel's Mendelian inheritance work, there were gaps in understanding between genetics and evolutionary Darwinism. Francis Galton tried to expand Mendel's discoveries with human data and proposed a different model with fractions of the heredity coming from each ancestral composing an infinite series. He called this the theory of "Law of Ancestral Heredity". His ideas were strongly disagreed by William Bateson, who followed Mendel's conclusions, that genetic inheritance were exclusively from the parents, half from each of them. This led to a vigorous debate between the biometricians, who supported Galton's ideas, as Raphael Weldon, Arthur Dukinfield Darbishire and Karl Pearson, and Mendelians, who supported Bateson's (and Mendel's) ideas, such as Charles Davenport and Wilhelm Johannsen. Later, biometricians could not reproduce Galton conclusions in different experiments, and Mendel's ideas prevailed. By the 1930s, models built on statistical reasoning had helped to resolve these differences and to produce the neo-Darwinian modern evolutionary synthesis.
Solving these differences also allowed to define the concept of population genetics and brought together genetics and evolution. The three leading figures in the establishment of population genetics and this synthesis all relied on statistics and developed its use in biology. These and other biostatisticians, mathematical biologists, and statistically inclined geneticists helped bring together evolutionary biology and genetics into a consistent, coherent whole that could begin to be quantitatively modeled. In parallel to this overall development, the pioneering work of D'Arcy Thompson in "On Growth and Form" also helped to add quantitative discipline to biological study. Despite the fundamental importance and frequent necessity of statistical reasoning, there may nonetheless have been a tendency among biologists to distrust or deprecate results which are not qualitatively apparent. One anecdote describes Thomas Hunt Morgan banning the Friden calculator from his department at Caltech, saying "Well, I am like a guy who is prospecting for gold along the banks of the Sacramento River in 1849. With a little intelligence, I can reach down and pick up big nuggets of gold. And as long as I can do that, I'm not going to let any people in my department waste scarce resources in placer mining."
Research planning. Any research in life sciences is proposed to answer a scientific question we might have. To answer this question with a high certainty, we need accurate results. The correct definition of the main hypothesis and the research plan will reduce errors while taking a decision in understanding a phenomenon. The research plan might include the research question, the hypothesis to be tested, the experimental design, data collection methods, data analysis perspectives and costs involved. It is essential to carry the study based on the three basic principles of experimental statistics: randomization, replication, and local control. Research question. The research question will define the objective of a study. The research will be headed by the question, so it needs to be concise, at the same time it is focused on interesting and novel topics that may improve science and knowledge and that field. To define the way to ask the scientific question, an exhaustive literature review might be necessary. So the research can be useful to add value to the scientific community.
Hypothesis definition. Once the aim of the study is defined, the possible answers to the research question can be proposed, transforming this question into a hypothesis. The main propose is called null hypothesis (H0) and is usually based on a permanent knowledge about the topic or an obvious occurrence of the phenomena, sustained by a deep literature review. We can say it is the standard expected answer for the data under the situation in test. In general, HO assumes no association between treatments. On the other hand, the alternative hypothesis is the denial of HO. It assumes some degree of association between the treatment and the outcome. Although, the hypothesis is sustained by question research and its expected and unexpected answers. As an example, consider groups of similar animals (mice, for example) under two different diet systems. The research question would be: what is the best diet? In this case, H0 would be that there is no difference between the two diets in mice metabolism (H0: μ1 = μ2) and the alternative hypothesis would be that the diets have different effects over animals metabolism (H1: μ1 ≠ μ2).
The hypothesis is defined by the researcher, according to his/her interests in answering the main question. Besides that, the alternative hypothesis can be more than one hypothesis. It can assume not only differences across observed parameters, but their degree of differences ("i.e." higher or shorter). Sampling. Usually, a study aims to understand an effect of a phenomenon over a population. In biology, a population is defined as all the individuals of a given species, in a specific area at a given time. In biostatistics, this concept is extended to a variety of collections possible of study. Although, in biostatistics, a population is not only the individuals, but the total of one specific component of their organisms, as the whole genome, or all the sperm cells, for animals, or the total leaf area, for a plant, for example. It is not possible to take the measures from all the elements of a population. Because of that, the sampling process is very important for statistical inference. Sampling is defined as to randomly get a representative part of the entire population, to make posterior inferences about the population. So, the sample might catch the most variability across a population. The sample size is determined by several things, since the scope of the research to the resources available. In clinical research, the trial type, as inferiority, equivalence, and superiority is a key in determining sample size.
Experimental design. Experimental designs sustain those basic principles of experimental statistics. There are three basic experimental designs to randomly allocate treatments in all plots of the experiment. They are completely randomized design, randomized block design, and factorial designs. Treatments can be arranged in many ways inside the experiment. In agriculture, the correct experimental design is the root of a good study and the arrangement of treatments within the study is essential because environment largely affects the plots (plants, livestock, microorganisms). These main arrangements can be found in the literature under the names of "lattices", "incomplete blocks", "split plot", "augmented blocks", and many others. All of the designs might include control plots, determined by the researcher, to provide an error estimation during inference. In clinical studies, the samples are usually smaller than in other biological studies, and in most cases, the environment effect can be controlled or measured. It is common to use randomized controlled clinical trials, where results are usually compared with observational study designs such as case–control or cohort.
Data collection. Data collection methods must be considered in research planning, because it highly influences the sample size and experimental design. Data collection varies according to type of data. For qualitative data, collection can be done with structured questionnaires or by observation, considering presence or intensity of disease, using score criterion to categorize levels of occurrence. For quantitative data, collection is done by measuring numerical information using instruments. In agriculture and biology studies, yield data and its components can be obtained by metric measures. However, pest and disease injuries in plats are obtained by observation, considering score scales for levels of damage. Especially, in genetic studies, modern methods for data collection in field and laboratory should be considered, as high-throughput platforms for phenotyping and genotyping. These tools allow bigger experiments, while turn possible evaluate many plots in lower time than a human-based only method for data collection.
Finally, all data collected of interest must be stored in an organized data frame for further analysis. Analysis and data interpretation. Descriptive tools. Data can be represented through tables or graphical representation, such as line charts, bar charts, histograms, scatter plot. Also, measures of central tendency and variability can be very useful to describe an overview of the data. Follow some examples: Frequency tables. One type of table is the frequency table, which consists of data arranged in rows and columns, where the frequency is the number of occurrences or repetitions of data. Frequency can be: Absolute: represents the number of times that a determined value appear; formula_1 Relative: obtained by the division of the absolute frequency by the total number; formula_2 In the next example, we have the number of genes in ten operons of the same organism. Line graph. Line graphs represent the variation of a value over another metric, such as time. In general, values are represented in the vertical axis, while the time variation is represented in the horizontal axis.
Bar chart. A bar chart is a graph that shows categorical data as bars presenting heights (vertical bar) or widths (horizontal bar) proportional to represent values. Bar charts provide an image that could also be represented in a tabular format. In the bar chart example, we have the birth rate in Brazil for the December months from 2010 to 2016. The sharp fall in December 2016 reflects the outbreak of Zika virus in the birth rate in Brazil. Histograms. The histogram (or frequency distribution) is a graphical representation of a dataset tabulated and divided into uniform or non-uniform classes. It was first introduced by Karl Pearson. Scatter plot. A scatter plot is a mathematical diagram that uses Cartesian coordinates to display values of a dataset. A scatter plot shows the data as a set of points, each one presenting the value of one variable determining the position on the horizontal axis and another variable on the vertical axis. They are also called scatter graph, scatter chart, scattergram, or scatter diagram.
Mean. The arithmetic mean is the sum of a collection of values (formula_3) divided by the number of items of this collection (formula_4). Median. The median is the value in the middle of a dataset. Mode. The mode is the value of a set of data that appears most often. Box plot. Box plot is a method for graphically depicting groups of numerical data. The maximum and minimum values are represented by the lines, and the interquartile range (IQR) represent 25–75% of the data. Outliers may be plotted as circles. Correlation coefficients. Although correlations between two different kinds of data could be inferred by graphs, such as scatter plot, it is necessary validate this though numerical information. For this reason, correlation coefficients are required. They provide a numerical value that reflects the strength of an association. Pearson correlation coefficient. Pearson correlation coefficient is a measure of association between two variables, X and Y. This coefficient, usually represented by "ρ" (rho) for the population and "r" for the sample, assumes values between −1 and 1, where "ρ" = 1 represents a perfect positive correlation, "ρ" = −1 represents a perfect negative correlation, and "ρ" = 0 is no linear correlation.
Inferential statistics. It is used to make inferences about an unknown population, by estimation and/or hypothesis testing. In other words, it is desirable to obtain parameters to describe the population of interest, but since the data is limited, it is necessary to make use of a representative sample in order to estimate them. With that, it is possible to test previously defined hypotheses and apply the conclusions to the entire population. The standard error of the mean is a measure of variability that is crucial to do inferences. Hypothesis testing is essential to make inferences about populations aiming to answer research questions, as settled in "Research planning" section. Authors defined four steps to be set: A confidence interval is a range of values that can contain the true real parameter value in given a certain level of confidence. The first step is to estimate the best-unbiased estimate of the population parameter. The upper value of the interval is obtained by the sum of this estimate with the multiplication between the standard error of the mean and the confidence level. The calculation of lower value is similar, but instead of a sum, a subtraction must be applied.
Statistical considerations. Power and statistical error. When testing a hypothesis, there are two types of statistic errors possible: Type I error and Type II error. The significance level denoted by α is the type I error rate and should be chosen before performing the test. The type II error rate is denoted by β and statistical power of the test is 1 − β. p-value. The p-value is the probability of obtaining results as extreme as or more extreme than those observed, assuming the null hypothesis (H0) is true. It is also called the calculated probability. It is common to confuse the p-value with the significance level (α), but, the α is a predefined threshold for calling significant results. If p is less than α, the null hypothesis (H0) is rejected. Multiple testing. In multiple tests of the same hypothesis, the probability of the occurrence of false positives (familywise error rate) increase and a strategy is needed to account for this occurrence. This is commonly achieved by using a more stringent threshold to reject null hypotheses. The Bonferroni correction defines an acceptable global significance level, denoted by α* and each test is individually compared with a value of α = α/m. This ensures that the familywise error rate in all m tests, is less than or equal to α. When m is large, the Bonferroni correction may be overly conservative. An alternative to the Bonferroni correction is to control the false discovery rate (FDR). The FDR controls the expected proportion of the rejected null hypotheses (the so-called discoveries) that are false (incorrect rejections). This procedure ensures that, for independent tests, the false discovery rate is at most q*. Thus, the FDR is less conservative than the Bonferroni correction and have more power, at the cost of more false positives.
Mis-specification and robustness checks. The main hypothesis being tested (e.g., no association between treatments and outcomes) is often accompanied by other technical assumptions (e.g., about the form of the probability distribution of the outcomes) that are also part of the null hypothesis. When the technical assumptions are violated in practice, then the null may be frequently rejected even if the main hypothesis is true. Such rejections are said to be due to model mis-specification. Verifying whether the outcome of a statistical test does not change when the technical assumptions are slightly altered (so-called robustness checks) is the main way of combating mis-specification. Model selection criteria. Model criteria selection will select or model that more approximate true model. The Akaike's Information Criterion (AIC) and The Bayesian Information Criterion (BIC) are examples of asymptotically efficient criteria. Developments and big data. Recent developments have made a large impact on biostatistics. Two important changes have been the ability to collect data on a high-throughput scale, and the ability to perform much more complex analysis using computational techniques. This comes from the development in areas as sequencing technologies, Bioinformatics and Machine learning (Machine learning in bioinformatics).
Use in high-throughput data. New biomedical technologies like microarrays, next-generation sequencers (for genomics) and mass spectrometry (for proteomics) generate enormous amounts of data, allowing many tests to be performed simultaneously. Careful analysis with biostatistical methods is required to separate the signal from the noise. For example, a microarray could be used to measure many thousands of genes simultaneously, determining which of them have different expression in diseased cells compared to normal cells. However, only a fraction of genes will be differentially expressed. Multicollinearity often occurs in high-throughput biostatistical settings. Due to high intercorrelation between the predictors (such as gene expression levels), the information of one predictor might be contained in another one. It could be that only 5% of the predictors are responsible for 90% of the variability of the response. In such a case, one could apply the biostatistical technique of dimension reduction (for example via principal component analysis). Classical statistical techniques like linear or logistic regression and linear discriminant analysis do not work well for high dimensional data (i.e. when the number of observations n is smaller than the number of features or predictors p: n < p). As a matter of fact, one can get quite high R2-values despite very low predictive power of the statistical model. These classical statistical techniques (esp. least squares linear regression) were developed for low dimensional data (i.e. where the number of observations n is much larger than the number of predictors p: n » p). In cases of high dimensionality, one should always consider an independent validation test set and the corresponding residual sum of squares (RSS) and R2 of the validation test set, not those of the training set.
Often, it is useful to pool information from multiple predictors together. For example, Gene Set Enrichment Analysis (GSEA) considers the perturbation of whole (functionally related) gene sets rather than of single genes. These gene sets might be known biochemical pathways or otherwise functionally related genes. The advantage of this approach is that it is more robust: It is more likely that a single gene is found to be falsely perturbed than it is that a whole pathway is falsely perturbed. Furthermore, one can integrate the accumulated knowledge about biochemical pathways (like the JAK-STAT signaling pathway) using this approach. Bioinformatics advances in databases, data mining, and biological interpretation.
Nowadays, increase in size and complexity of molecular datasets leads to use of powerful statistical methods provided by computer science algorithms which are developed by machine learning area. Therefore, data mining and machine learning allow detection of patterns in data with a complex structure, as biological ones, by using methods of supervised and unsupervised learning, regression, detection of clusters and association rule mining, among others. To indicate some of them, self-organizing maps and "k"-means are examples of cluster algorithms; neural networks implementation and support vector machines models are examples of common machine learning algorithms. Collaborative work among molecular biologists, bioinformaticians, statisticians and computer scientists is important to perform an experiment correctly, going from planning, passing through data generation and analysis, and ending with biological interpretation of the results. Use of computationally intensive methods. On the other hand, the advent of modern computer technology and relatively cheap computing resources have enabled computer-intensive biostatistical methods like bootstrapping and re-sampling methods.
In recent times, random forests have gained popularity as a method for performing statistical classification. Random forest techniques generate a panel of decision trees. Decision trees have the advantage that you can draw them and interpret them (even with a basic understanding of mathematics and statistics). Random Forests have thus been used for clinical decision support systems. Applications. Public health. Public health, including epidemiology, health services research, nutrition, environmental health and health care policy & management. In these medicine contents, it's important to consider the design and analysis of the clinical trials. As one example, there is the assessment of severity state of a patient with a prognosis of an outcome of a disease. With new technologies and genetics knowledge, biostatistics are now also used for Systems medicine, which consists in a more personalized medicine. For this, is made an integration of data from different sources, including conventional patient data, clinico-pathological parameters, molecular and genetic data as well as data generated by additional new-omics technologies.
Quantitative genetics. The study of population genetics and statistical genetics in order to link variation in genotype with a variation in phenotype. In other words, it is desirable to discover the genetic basis of a measurable trait, a quantitative trait, that is under polygenic control. A genome region that is responsible for a continuous trait is called a quantitative trait locus (QTL). The study of QTLs become feasible by using molecular markers and measuring traits in populations, but their mapping needs the obtaining of a population from an experimental crossing, like an F2 or recombinant inbred strains/lines (RILs). To scan for QTLs regions in a genome, a gene map based on linkage have to be built. Some of the best-known QTL mapping algorithms are Interval Mapping, Composite Interval Mapping, and Multiple Interval Mapping. However, QTL mapping resolution is impaired by the amount of recombination assayed, a problem for species in which it is difficult to obtain large offspring. Furthermore, allele diversity is restricted to individuals originated from contrasting parents, which limit studies of allele diversity when we have a panel of individuals representing a natural population. For this reason, the genome-wide association study was proposed in order to identify QTLs based on linkage disequilibrium, that is the non-random association between traits and molecular markers. It was leveraged by the development of high-throughput SNP genotyping.
In animal and plant breeding, the use of markers in selection aiming for breeding, mainly the molecular ones, collaborated to the development of marker-assisted selection. While QTL mapping is limited due resolution, GWAS does not have enough power when rare variants of small effect that are also influenced by environment. So, the concept of Genomic Selection (GS) arises in order to use all molecular markers in the selection and allow the prediction of the performance of candidates in this selection. The proposal is to genotype and phenotype a training population, develop a model that can obtain the genomic estimated breeding values (GEBVs) of individuals belonging to a genotype and but not phenotype population, called testing population. This kind of study could also include a validation population, thinking in the concept of cross-validation, in which the real phenotype results measured in this population are compared with the phenotype results based on the prediction, what used to check the accuracy of the model.
As a summary, some points about the application of quantitative genetics are: Expression data. Studies for differential expression of genes from RNA-Seq data, as for RT-qPCR and microarrays, demands comparison of conditions. The goal is to identify genes which have a significant change in abundance between different conditions. Then, experiments are designed appropriately, with replicates for each condition/treatment, randomization and blocking, when necessary. In RNA-Seq, the quantification of expression uses the information of mapped reads that are summarized in some genetic unit, as exons that are part of a gene sequence. As microarray results can be approximated by a normal distribution, RNA-Seq counts data are better explained by other distributions. The first used distribution was the Poisson one, but it underestimate the sample error, leading to false positives. Currently, biological variation is considered by methods that estimate a dispersion parameter of a negative binomial distribution. Generalized linear models are used to perform the tests for statistical significance and as the number of genes is high, multiple tests correction have to be considered. Some examples of other analysis on genomics data comes from microarray or proteomics experiments. Often concerning diseases or disease stages.
Tools. There are a lot of tools that can be used to do statistical analysis in biological data. Most of them are useful in other areas of knowledge, covering a large number of applications (alphabetical). Here are brief descriptions of some of them: Scope and training programs. Almost all educational programmes in biostatistics are at postgraduate level. They are most often found in schools of public health, affiliated with schools of medicine, forestry, or agriculture, or as a focus of application in departments of statistics. In the United States, where several universities have dedicated biostatistics departments, many other top-tier universities integrate biostatistics faculty into statistics or other departments, such as epidemiology. Thus, departments carrying the name "biostatistics" may exist under quite different structures. For instance, relatively new biostatistics departments have been founded with a focus on bioinformatics and computational biology, whereas older departments, typically affiliated with schools of public health, will have more traditional lines of research involving epidemiological studies and clinical trials as well as bioinformatics. In larger universities around the world, where both a statistics and a biostatistics department exist, the degree of integration between the two departments may range from the bare minimum to very close collaboration. In general, the difference between a statistics program and a biostatistics program is twofold: (i) statistics departments will often host theoretical/methodological research which are less common in biostatistics programs and (ii) statistics departments have lines of research that may include biomedical applications but also other areas such as industry (quality control), business and economics and biological areas other than medicine.
List of major biblical figures The Bible is a collection of canonical sacred texts of Judaism and Christianity. Different religious groups include different books within their canons, in different orders, and sometimes divide or combine books, or incorporate additional material into canonical books. Christian Bibles range from the sixty-six books of the Protestant canon to the eighty-one books of the Ethiopian Orthodox Church canon. Hebrew Bible. Tribes of Israel. According to the Book of Genesis, the Israelites were descendants of the sons of Jacob, who was renamed Israel after wrestling with an angel. His twelve male children become the ancestors of the Twelve Tribes of Israel. New Testament. Apostles of Jesus. The Thirteen: Others:
British & Irish Lions The British & Irish Lions is a rugby union team selected from players eligible for the national teams of England, Ireland, Scotland, and Wales. The Lions are a test side and most often select players who have already played for their national team, although they can pick uncapped players who are eligible for any of the four unions. The team tours every four years, with these rotating between Australia, New Zealand and South Africa in order. The most recent test series, the 2021 series against South Africa, was won 2–1 by South Africa. From 1888 onwards, combined British rugby sides toured the Southern Hemisphere. The first tour was a commercial venture, undertaken without official backing. The six subsequent visits enjoyed a growing degree of support from the authorities, before the 1910 South Africa tour, which was the first tour representative of the four Home Unions. In 1949 the four Home Unions formally created a Tours Committee and for the first time, every player of the 1950 Lions squad had played internationally before the tour. The 1950s tours saw high win rates in provincial games, but the Test series were typically lost or drawn. The series wins in 1971 (New Zealand) and 1974 (South Africa) interrupted this pattern. The last tour of the amateur age took place in 1993. The Lions have also played occasional matches in the Northern Hemisphere either as one-off exhibitions or before a Southern Hemisphere tour.
Naming and symbols. Name. The Shaw and Shrewsbury team first played in 1888 and is considered the precursor of the British & Irish Lions. It was then primarily English in composition but also contained players from Scotland and Wales. Later the team used the name British Isles. On their 1950 tour of New Zealand and Australia they officially adopted the name British Lions, the nickname first used by British and South African journalists on the 1924 South African tour after the lion emblem on their ties, the emblem on their jerseys having been dropped in favour of the four-quartered badge with the symbols of the four represented unions. When the team first emerged in the 19th century, the United Kingdom of Great Britain and Ireland was one single state. The team continued after the Irish Free State was set up in 1922, but was still known as the British Lions or British Isles. The name "British & Irish Lions" has been used since the 2001 tour of Australia. The team is often referred to simply as the Lions.
Anthem. As the Lions represent four rugby unions, which cover two sovereign states, they do not currently have a national anthem. For the 1989 tour, the British national anthem "God Save the Queen" was used. For the 2005 tour to New Zealand, the Lions management commissioned a song, "The Power of Four", although it was met with little support among Lions fans at the matches and has not been used since. Colours and strip. For more than half a century, the Lions have worn a red jersey that sports the amalgamated crests of the four unions. Prior to 1950 the strip went through a number of significantly different formats. Unsanctioned tours. In 1888, the promoter of the first expedition to Australia and New Zealand, Arthur Shrewsbury, demanded "something that would be good material and yet take them by storm out here". The result was a jersey in thick red, white and blue hoops, worn above white shorts and dark socks. The tours to South Africa in 1891 and 1896 retained the red, white and blue theme but this time as red and white hooped jerseys and dark blue shorts and socks.
The tours to South Africa in 1891 and 1896 retained the red, white and blue theme but this time as red and white hooped jerseys and dark blue shorts and socks. The 1899 trip to Australia saw a reversion to red, white and blue jerseys, but with the blue used in thick hoops and the red and white in thin bands. The shorts remained blue, as did the socks although a white flash was added to the latter. The one-off test in 1999 between England and Australia that was played to commemorate Australia's first test against Reverend Matthew Mullineux's British side saw England wear an updated version of this jersey. In 1903, the South Africa tour followed on from the 1896 tour, with red and white hooped jerseys. The slight differences were that the red hoops were slightly thicker than the white (the opposite was true in 1896), and the white flash on the socks introduced in 1899 was partially retained. The Australia tour of 1904 saw exactly the same kit as in 1899. In 1908, with the Scottish and Irish unions not taking part, the Anglo-Welsh side sported red jerseys with a thick white band on tour to Australia and New Zealand. The Australia tour of 1904 saw exactly the same kit as in 1899. In 1908, with the Scottish and Irish unions not taking part, the Anglo-Welsh side sported red jerseys with a thick white band on tour to Australia and New Zealand. Blue shorts were retained, but the socks were for the first time red, with a white flash.
Blue jerseys, the Lions named and the crest adopted. The Scots were once again involved in Tom Smyth's 1910 team to South Africa. Thus, dark blue jerseys were introduced with white shorts and the red socks of 1908. The jerseys also had a single lion-rampant crest. The 1924 tour returned to South Africa, retaining the blue jerseys but now with shorts to match. It is the 1924 tour that is credited as being the first in which the team were referred to as "the Lions", the irony being that it was on this tour that the single lion-rampant crest was replaced with the forerunner of the four-quartered badge with the symbols of the four represented unions, that is still worn today. Although the lion had been dropped from the jersey, the players had worn the lion motif on their ties as they arrived in South Africa, which led the press and public referring to them as "the Lions".
Red jerseys. The adoption of the red jersey happened in the 1950 tour. A return to New Zealand was accompanied by a desire to avoid the controversy of 1930 and so red replaced blue for the jersey with the resultant kit being that which is still worn today, the combination of red jersey, white shorts and green and blue socks, representing the four unions. The only additions to the strip since 1950 began appearing in 1993, with the addition of kit suppliers logos in prominent positions. Umbro had in 1989 asked for "maximum brand exposure whenever possible" but this did not affect the kit's appearance. Since then, Nike, Adidas and Canterbury have had more overt branding on the shirts, with sponsors Scottish Provident (1997), (2001), Zurich (2005), HSBC (2009 and 2013), Standard Life Investments (2017) and Vodafone (2021). History. 1888–1909. The earliest tours date back to 1888, when a 21-man squad visited Australia and New Zealand. The squad drew players from England, Scotland and Wales, though English players predominated. The 35-match tour of two host nations included no tests, but the side played provincial, city and academic sides, winning 27 matches. They played 19 games of Australian rules football, against prominent clubs in Victoria and South Australia, winning six and drawing one of these (see Australian rules football in England).
The first tour, although unsanctioned by rugby bodies, established the concept of Northern Hemisphere sporting sides touring to the Southern Hemisphere. Three years after the first tour, the Western Province union invited rugby bodies in Britain to tour South Africa. Some saw the 1891 team – the first sanctioned by the Rugby Football Union – as the England national team, though others referred to it as "the British Isles". The tourists played a total of twenty matches, three of them tests. The team also played the regional side of South Africa (South Africa did not exist as a political unit in 1891), winning all three matches. In a notable event of the tour, the touring side presented the Currie Cup to Griqualand West, the province they thought produced the best performance on the tour. Five years later a British Isles side returned to South Africa. They played one extra match on this tour, making the total of 21 games, including four tests against South Africa, with the British Isles winning three of them. The squad had a notable Irish orientation, with the Ireland national team contributing six players to the 21-man squad.
In 1899 the British Isles touring side returned to Australia for the first time since the unofficial tour of 1888. The squad of 23 for the first time ever had players from each of the home nations. The team again participated in 21 matches, playing state teams as well as northern Queensland sides and Victorian teams. A four-test series took place against Australia, the tourists winning three out of the four. The team returned via Hawaii and Canada playing additional games en route. Four years later, in 1903, the British Isles team returned to South Africa. The opening performance of the side proved disappointing from the tourists' point of view, with defeats in its opening three matches by Western Province sides in Cape Town. From then on the team experienced mixed results, though more wins than losses. The side lost the test series to South Africa, drawing twice, but with the South Africans winning the decider 8 to nil. No more than twelve months passed before the British Isles team ventured to Australia and New Zealand in 1904. The tourists devastated the Australian teams, winning every single game. Australia also lost all three tests to the visitors, even getting held to a standstill in two of the three games. Though the New Zealand leg of the tour did not take long in comparison to the number of Australian games, the British Isles experienced considerable difficulty across the Tasman after whitewashing the Australians. The team managed two early wins before losing the test to New Zealand and only winning one more game as well as drawing once. Despite their difficulties in New Zealand, the tour proved a raging success on-field for the British Isles.
In 1908, another tour took place to Australia and New Zealand. In a reversal of previous practice, the planners allocated more matches in New Zealand rather than in Australia: perhaps the strength of the New Zealand teams and the heavy defeats of all Australian teams on the previous tour influenced this decision. Some commentators thought that this tour hoped to reach out to rugby communities in Australia, as rugby league (infamously) started in Australia in 1908. The Anglo-Welsh side (Irish and Scottish unions did not participate) performed well in all the non-test matches, but drew a test against New Zealand and lost the other two. 1910–1949. Visits that took place before the 1910 South Africa tour (the first selected by a committee from the four Home Unions) had enjoyed a growing degree of support from the authorities, although only one of these included representatives of all four nations. The 1910 tour to South Africa marked the official beginning of British Isles rugby tours: the inaugural tour operating under all four unions. The team performed moderately against the non-test teams, claiming victories in just over half their matches, and the test series went to South Africa, who won two of the three games. A side managed by Oxford University — supposedly the England rugby team, but actually including three Scottish players — toured Argentina at the time: the people of Argentina termed it the "Combined British".
The next British Isles team tour did not take place until 1924, again in South Africa. The team, led by Ronald Cove-Smith, struggled with injuries and lost three of the four test matches, drawing the other 3–3. In total, 21 games were played, with the touring side winning 9, drawing 3 and losing 9. In 1927 a short, nine-game series took place in Argentina, with the British isles winning all nine encounters, and the tour was a financial success for Argentine rugby. The Lions returned to New Zealand in 1930 with some success. The Lions won all of their games that did not have test status except for the matches against Auckland, Wellington and Canterbury, but they lost three of their four test matches against New Zealand, winning the first test 6–3. The side also visited Australia, losing a test but winning five out of the six non-test games. In 1936 the British Isles visited Argentina for the third time, winning all ten of their matches and only conceding nine points in the whole tour. Two years later in 1938 the British Isles toured in South Africa, winning more than half of their normal matches. Despite having lost the test series to South Africa by game three, they won the final test. This is when they were named THE LIONS by their then Captain Sam Walker. 1950–1969.
The first post-war tour went to New Zealand and Australia in 1950. The Lions, sporting newly redesigned jerseys and displaying a fresh style of play, managed to win 22 and draw one of 29 matches over the two nations. The Lions won the opening four fixtures before losing to Otago and Southland, but succeeded in holding New Zealand to a 9–9 draw. The Lions performed well in the remaining All Black tests though they lost all three, the team did not lose another non-test in the New Zealand leg of the tour. The Lions won all their games in Australia except for their final fixture against a New South Wales XV in Newcastle. They won both tests against Australia, in Brisbane, Queensland and in Sydney. In 1955 the Lions toured South Africa and left with another imposing record, one draw and 19 wins from the 25 fixtures. The four-test series against South Africa, a thrilling affair, ended in a drawn series. The 1959 tour to Australia and New Zealand marked once again a very successful tour for the Lions, who only lost six of their 35 fixtures. The Lions easily won both tests against Australia and lost the first three tests against New Zealand, but did find victory (9–6) in the final test.
After the glittering decade of the 1950s, the first tour of the 1960s proved not nearly as successful as previous ones. The 1962 tour to South Africa saw the Lions still win 16 of their 25 games, but did not fare well against the Springboks, losing three of the four tests. For the 1966 tour to Australia and New Zealand John Robins became the first Lions coach, and the trip started off very well for the Lions, who stormed through Australia, winning five non-tests and drawing one, and defeating Australia in two tests. The Lions experienced mixed results during the New Zealand leg of the tour, as well as losing all of the tests against New Zealand. The Lions also played a test against Canada on their way home, winning 19 to 8 in Toronto. The 1968 tour of South Africa saw the Lions win 15 of their 16 provincial matches, but the team actually lost three tests against the Springboks and drew one. 1970–1979. The 1970s saw a renaissance for the Lions. The 1971 British Lions tour to New Zealand and Australia, centred around the skilled Welsh half-back pairing of Gareth Edwards and Barry John, secured a series win over New Zealand. The tour started with a loss to Queensland but proceeded to storm through the next provincial fixtures, winning 11 games in a row. The Lions then went on to defeat New Zealand in Dunedin. The Lions only lost one match on the rest of the tour and won the test series against New Zealand, winning and drawing the last two games, to take the series two wins to one.
The 1974 British Lions tour to South Africa was one of the best-known and most successful Lions teams. Apartheid concerns meant some players declined the tour. Nonetheless, led by the esteemed Irish forward Willie John McBride, the tour went through 22 games unbeaten and triumphed 3–0 (with one drawn) in the test series. The series featured a lot of violence. The management of the Lions concluded that the Springboks dominated their opponents with physical aggression. At that time, test match referees came from the home nation, substitutions took place only if a doctor found a player unable to continue and there were no video cameras or sideline officials to prevent violent play. The Lions decided "to get their retaliation in first" with the infamous "99 call". The Lions postulated that a South African referee would probably not send off all of the Lions if they all retaliated against "blatant thuggery". Famous video footage of the 'battle of Boet Erasmus Stadium' shows J. P. R. Williams running over half of the pitch and launching himself at Van Heerden after such a call.
The 1977 British Lions tour to New Zealand saw the Lions drop only one non-test out of 21 games, a loss to a Universities side. The team did not win the test series though, winning one game but losing the other three. In August 1977 the British Lions made a stopover in Fiji on the way home from their tour of New Zealand. Fiji beat them 25–21 at Buckhurst Park, Suva. 1980–1989. The Lions toured South Africa in 1980, and completed a flawless non-test record, winning 14 out of 14 matches. The Lions lost the first three tests to South Africa, only winning the last one once the Springboks were guaranteed to win the series. The 1983 tour to New Zealand saw the team successful in the non-test games, winning all but two games, but being whitewashed in the test series against New Zealand. A tour to South Africa by the Lions was anticipated in 1986, but the invitation for the Lions to tour was never accepted because of controversy surrounding Apartheid and the tour did not go ahead. The Lions did not return to South Africa until 1997, after the Apartheid era. A Lions team was selected in April 1986 for the International Rugby Board centenary match against 'The Rest'. The team was organised by the Four Home Unions Committee and the players were given the status of official British Lions.
The Lions tour to Australia in 1989 was a shorter affair, being only 12 matches in total. The tour was very successful for the Lions, who won all eight non-test matches and won the test series against Australia, two to one. 1990–1999. The tour to New Zealand in 1993 was the last of the amateur era. The Lions won six and lost four non-test matches, and lost the test series 2–1. The tour to South Africa in 1997 was a success for the Lions, who completed the tour with only two losses, and won the test series 2–1. 2000–2009. In 2001, the ten-game tour to Australia saw the Wallabies win the test series 2–1. This series saw the first award of the Tom Richards Trophy. In the Lions' 2005 tour to New Zealand, coached by Clive Woodward, the Lions won seven games against provincial teams, were defeated by the New Zealand Maori team, and suffered heavy defeats in all three tests. In 2009, the Lions toured South Africa. There they faced the World Cup winners South Africa, with Ian McGeechan leading a coaching team including Warren Gatland, Shaun Edwards and Rob Howley. The Lions were captained by Irish lock Paul O'Connell. The initial Lions selection consisted of fourteen Irish players, thirteen Welsh, eight English and two Scots in the 37-man squad. In the first Test on 20 June, they lost 26–21, and lost the series in the second 28–25 in a tightly fought game at Loftus Versfeld on 27 June. The Lions won the third Test 28–9 at Ellis Park, and the series finished 2–1 to South Africa. 2010–2019.
During June 2013 the British & Irish Lions toured Australia. Former Scotland and Lions full-back Andy Irvine was appointed as tour manager in 2010. Wales head coach Warren Gatland was the Lions' head coach, and their tour captain was Sam Warburton. The tour started in Hong Kong with a match against the Barbarians before moving on to Australia for the main tour featuring six provincial matches and three tests. The Lions won all but one non-test matches, losing to the Brumbies 14–12 on 18 June. The first test was followed shortly after this, which saw the Lions go 1-up over Australia winning 23–21. Australia did have a chance to take the win in the final moments of the game, but a missed penalty by Kurtley Beale saw the Lions take the win. The Wallabies drew the series in the second test winning 16–15, though the Lions had a chance to steal the win had it not been because of a missed penalty by Leigh Halfpenny. With tour captain Warburton out of the final test due to injury, Alun Wyn Jones took over the captaincy in the final test in Sydney. The final test was won by the Lions in what was a record win, winning 41–16 to earn their first series win since 1997 and their first over Australia since 1989.
Following his winning tour of Australia in 2013, Warren Gatland was reappointed as Lions Head Coach for the tour to New Zealand in June and July 2017. In April 2016, it was announced that the side would again be captained again by Sam Warburton. The touring schedule included 10 games: an opening game against the Provincial Barbarians, challenge matches against all five of New Zealand's Super Rugby sides, a match against the Māori All Blacks and three tests against . The Lions defeated the Provincial Barbarians in the first game of the tour, before being beaten by the Blues three days later. The team recovered to beat the Crusaders but this was followed up with another midweek loss, this time against the Highlanders. The Lions then faced the Māori All Blacks, winning comfortably to restore optimism and followed up with their first midweek victory of the tour against the Chiefs. On 24 June, the Lions, captained by Peter O'Mahony, faced New Zealand in Eden Park in the first Test and were beaten 30–15. This was followed by the final midweek game of the tour, a draw against the Hurricanes. For the second Test, Gatland recalled Warburton to the starting team as captain. In Wellington Regional Stadium, the Lions beat a 14-man New Zealand side 24–21 after Sonny Bill Williams was red-carded at the 24-minute mark after a shoulder charge on Anthony Watson. This tied the series going into the final game, ending the side's 47-game winning run at home. In the final test at Eden Park the following week, the teams were tied at 15 points apiece with 78 minutes gone. Romain Poite signaled a penalty to New Zealand for an offside infringement after Ken Owens received the ball in front of his teammate Liam Williams, giving New Zealand the opportunity to kick for goal and potentially win the series. Poite, however, decided to downgrade the penalty to a free-kick after discussing with assistant referee Jérôme Garcès and Lions captain Sam Warburton. The match finished as a draw and the series was tied. 2020–present.
Warren Gatland was Lions head coach again for the tour to South Africa in 2021. In December 2019, the Lions' Test venues were announced, but the tour was significantly disrupted by the COVID-19 pandemic, and all the games were played behind closed doors. South Africa won the test series by two games to one. In the deciding third test, Morne Steyn again kicked a late penalty to win the series. In 2024, it was announced that Andy Farrell would succeed Gatland as the Lions head coach. A women's Lions team was established in 2024, with their inaugural tour to New Zealand to take place in 2027. Overall test match record. Overall test series results Tours. Format. The Lions now regularly tour three Southern Hemisphere countries; Australia, South Africa and New Zealand. They also toured Argentina three times before the Second World War. Since 1989 tours have been held every four years. The most recent tour was to South Africa in 2021. In a break with tradition, the 2005 tour of New Zealand was preceded by a "home" fixture against Argentina at the Millennium Stadium in Cardiff on 23 May 2005. It finished in a 25–25 draw. A similar fixture was held against Japan before the 2021 tour of South Africa at Murrayfield, with the Lions winning 28–10.
On tour, games take place against local provinces, clubs or representative sides as well as test matches against the host's national team. The Lions and their predecessor teams have also played games against other nearby countries on tour. For example, they played Rhodesia in 1910, 1924, 1938, 1955, 1962, 1968 and 1974 during their tours to South Africa. They were also beaten by Fiji on their 1977 tour to New Zealand. In addition, they visited pre-independence Namibia (then South West Africa), in 1955, 1962, 1968 and 1974. There have also been games in other countries on the way home. These include games in in 1959 and 1966, East Africa (then mostly Kenya, and held in Nairobi), and an unofficial game against Ceylon (future Sri Lanka) in 1950. Lions non-tour and home matches. The Lions have played a number of other matches against international opposition. With the exception of the matches against Argentina in 2005 and Japan in 2021, which were preparation matches for Lions tours, these matches have been one-offs to mark special occasions.
The Lions played an unofficial international match in 1955 at Cardiff Arms Park against a Welsh XV to mark the 75th anniversary of the Welsh Rugby Union. The Lions won 20–17 but did not include all the big names of the 1955 tour, such as Tony O'Reilly, Jeff Butterfield, Phil Davies, Dickie Jeeps, Bryn Meredith and Jim Greenwood. In 1977, the Lions played their first official home game, against the Barbarians as a charity fund-raiser held as part of the Queen's silver jubilee celebrations. The Barbarians line-up featured J. P. R. Williams, Gerald Davies, Gareth Edwards, Jean-Pierre Rives and Jean-Claude Skrela. The Lions included 13 of the team who played in the fourth test against New Zealand three weeks before and won 23–14. In 1986, a match was organised against The Rest as a warm-up to the 1986 South Africa tour, and as a celebration to mark the International Rugby Board's centenary. The Lions lost 15–7 and the planned tour was subsequently cancelled. In 1989, the Lions played against France in Paris. The game formed part of the celebrations of the bi-centennial of the French Revolution. The Lions, captained by Rob Andrew, won 29–27.
In 1990, a Four Home Unions team played against the Rest of Europe in a match to raise money for the rebuilding of Romania following the overthrow of Nicolae Ceaușescu in December 1989. The team used the Lions' logo, while the Rest of Europe played under the symbol of the Romanian Rugby Federation. Player records. Most caps. "Updated 7 August 2021" Most points. "Updated 31 July 2021" Most tries. "Updated 31 July 2021"
Bass guitar The bass guitar, electric bass () is the lowest-pitched member of the guitar family. It is similar in appearance and construction to an electric but with a longer neck and scale length. The electric bass guitar most commonly has four strings, though five- and six-stringed models are also built. Since the mid-1950s, the bass guitar has replaced the double bass in popular music due to its lighter weight, smaller size, most models' inclusion of frets for easier intonation, and electromagnetic pickups for amplification. The bass guitar is usually tuned the same as the double bass, corresponding to pitches one octave lower than the four lowest-pitched strings of a guitar (typically E, A, D, and G). It is played with the fingers and thumb or with a pick. Because the electric bass guitar is acoustically a quiet instrument, it requires external amplification, generally via electromagnetic or piezo-electric pickups. It can also be used with direct input boxes, audio interfaces, mixing consoles, computers, or bass-effects processors which offer headphone jacks.
Terminology. The "New Grove Dictionary of Music and Musicians" refers to this instrument as an "Electric bass guitar, usually with four heavy strings tuned E1'–A1'–D2–G2." It also defines "bass" as "Bass (iv). A contraction of Double bass or Electric bass guitar." "Mottola's Cyclopedic Dictionary of Lutherie Terms" begins its definition of the instrument as "A bass guitar that produces sound primarily with the aid of electronic devices." According to some authors the proper term is "electric bass". Common names for the instrument are "bass guitar", "electric bass guitar","electric bass", and simply "bass". and some authors claim that they are historically accurate. A bass guitar whose neck lacks frets is termed a fretless bass. Scale. The scale of a bass is defined as the length of the vibrating strings between the nut and the bridge saddles. On a modern 4-string bass guitar, 30" (76 cm) or less is considered short scale, 32" (81 cm) medium scale, 34" (86 cm) standard scale and 35" (89 cm) long scale. Pickup.
Bass pickups are attached to the body of the guitar and located beneath the strings. They are responsible for converting the vibrations of the strings into analogous electrical voltage sent as input to an instrument amplifier. Strings. Bass guitar strings are composed of a core and winding. The core is a wire which runs through the center of the string and is made of steel, nickel, or an alloy. The winding is a smaller gauge wire wrapped around the core. Bass guitar strings vary by the material and cross-sectional shape of the winding. Common string variants include roundwound, flatwound, halfwound (groundwound), coated, tapewound and taperwound strings. Roundwound and flatwound strings feature windings with circular and rounded-square cross-sections, respectively, with half-round strings being a hybrid between the two. Coated strings have their surface coated with a synthetic layer while tapewound strings feature a metal core with a plastic winding. Taperwound strings have a tapered end where the exposed core sits on the bridge saddle without windings. The choice of winding has considerable impact on the sound of the instrument, with certain winding styles often being preferred for certain musical genres.
History. 1930s. In the 1930s, musician and inventor Paul Tutmarc of Seattle, Washington, developed the first electric bass guitar in its modern form, a fretted instrument designed to be played horizontally. The 1935 sales catalog for Tutmarc's company Audiovox featured the "Model 736 Bass Fiddle", a solid body electric bass guitar with four strings, a scale length, and a single pickup. Around 100 were made during this period. Audiovox also sold their "Model 236" bass amplifier. 1950s. In the 1950s, Leo Fender and George Fullerton developed the first mass-produced electric bass guitar. The Fender Electric Instrument Manufacturing Company began producing the Precision Bass, or P-Bass, in October 1951. The design featured a simple uncontoured "slab" body design (with no edge contours) and a single coil pickup, both features similar to a Telecaster. By 1957, the Precision Bass began to resemble the Fender Stratocaster with the body edges beveled for comfort and the pickup changed to a separate halves split coil design.
The Fender Bass was a revolutionary instrument for working musicians. In comparison to the upright bass, the bass guitar could be easily transported. When amplified, the bass guitar was also much less prone than acoustic basses to audio feedback. The addition of frets enabled bassists to play in tune more easily than on upright basses, and allowed guitarists to more easily play the instrument. In 1953, Monk Montgomery became the first bassist to tour with the Fender bass, in Lionel Hampton's postwar big band. Montgomery was also possibly the first to record with the electric bass, on July 2, 1953, with the Art Farmer Septet. Roy Johnson (with Lionel Hampton), and Shifty Henry (with Louis Jordan and His Tympany Five), were other early Fender bass pioneers. Bill Black, who played with Elvis Presley and James Jamerson switched from upright bass to the Fender Precision Bass around 1957. The bass guitar was intended to appeal to guitarists as well as upright bass players, and many early pioneers of the instrument, such as Joe Osborn, and Paul McCartney were originally guitarists.
Also in 1953, Gibson released the first short-scale violin-shaped electric bass, the EB-1, with an extendable end pin so a bassist could play it upright or horizontally. In 1958, Gibson released the maple arched-top EB-2 described in the Gibson catalog as a "hollow-body electric bass that features a Bass/Baritone pushbutton for two different tonal characteristics". In 1959, these were followed by the more conventional-looking EB-0 Bass. The EB-0 was very similar to a Gibson SG in appearance (although the earliest examples have a slab-sided body shape closer to that of the double-cutaway Les Paul Special). The Fender and Gibson versions used bolt-on and set necks. Several other companies also began manufacturing bass guitars during the 1950s. Kay Musical Instrument Company began production of the K162 in 1952. Also in 1956, at the German trade fair "Musikmesse Frankfurt", the distinctive Höfner 500/1 viola-shaped bass first appeared, constructed using violin techniques by Walter Höfner, a second-generation violin luthier. Due to its use by Paul McCartney, it became known as the "Beatle bass". In 1957, Rickenbacker introduced the model 4000, the first bass to feature a neck-through-body design in which the neck is part of the body wood. The Burns London Supersound was introduced in 1958. 1960s.
With the explosion in popularity of rock music in the 1960s, many more manufacturers began making electric basses, including Yamaha, Teisco and Guyatone. Introduced in 1960, the Fender Jazz Bass, initially known as the "Deluxe Bass", used a body design known as an offset waist which was first seen on the Jazzmaster guitar in an effort to improve comfort while playing seated. The Jazz bass, or J-Bass, features two single-coil pickups. Providing a more "Gibson-scale" instrument, rather than the Jazz and Precision, Fender produced the Mustang Bass, a scale-length instrument. The Fender VI, a 6-string bass, was tuned one octave lower than standard guitar tuning. It was released in 1961, and was briefly favored by Jack Bruce of Cream. Gibson introduced its short-scale EB-3 in 1961, also used by Bruce. The EB-3 had a "mini-humbucker" at the bridge position. Gibson basses tended to be instruments with a shorter 30.5" scale length than the Precision. Gibson did not produce a -scale bass until 1963 with the release of the Thunderbird.
The first commercial fretless bass guitar was the Ampeg AUB-1, introduced in 1966. In the late 1960s, eight-string basses, with four octave paired courses (similar to a 12 string guitar), were introduced, such as the Hagström H8. 1970s. In 1972, Alembic established what became known as "boutique" or "high-end" electric bass guitars. These expensive, custom-tailored instruments, as used by Phil Lesh, Jack Casady, and Stanley Clarke, featured unique designs, premium hand-finished wood bodies, and innovative construction techniques such as multi-laminate neck-through-body construction and graphite necks. Alembic also pioneered the use of onboard electronics for pre-amplification and equalization. Active electronics increase the output of the instrument, and allow more options for controlling tonal flexibility, giving the player the ability to amplify as well as to attenuate certain frequency ranges while improving the overall frequency response (including more low-register and high-register sounds). 1976 saw the UK company Wal begin production of their own range of active basses. In 1974 Music Man Instruments, founded by Tom Walker, Forrest White and Leo Fender, introduced the StingRay, the first widely produced bass with active (powered) electronics built into the instrument. Basses with active electronics can include a preamplifier and knobs for boosting and cutting the low and high frequencies. In the mid-1970s, five-string basses, with a very low "B" string, were introduced. In 1975, bassist Anthony Jackson commissioned luthier Carl Thompson to build a six-string bass tuned (low to high) B0, E1, A1, D2, G2, C3, adding a low B string and a high C string.
Basketball Basketball is a team sport in which two teams, most commonly of five players each, opposing one another on a rectangular court, compete with the primary objective of shooting a basketball (approximately in diameter) through the defender's hoop (a basket in diameter mounted high to a backboard at each end of the court), while preventing the opposing team from shooting through their own hoop. A field goal is worth two points, unless made from behind the three-point line, when it is worth three. After a foul, timed play stops and the player fouled or designated to shoot a technical foul is given one, two or three one-point free throws. The team with the most points at the end of the game wins, but if regulation play expires with the score tied, an additional period of play (overtime) is mandated. Players advance the ball by bouncing it while walking or running (dribbling) or by passing it to a teammate, both of which require considerable skill. On offense, players may use a variety of shotsthe layup, the jump shot, or a dunk; on defense, they may steal the ball from a dribbler, intercept passes, or block shots; either offense or defense may collect a rebound, that is, a missed shot that bounces from rim or backboard. It is a violation to lift or drag one's pivot foot without dribbling the ball, to carry it, or to hold the ball with both hands then resume dribbling.
The five players on each side fall into five playing positions. The tallest player is usually the center, the second-tallest and strongest is the power forward, a slightly shorter but more agile player is the small forward, and the shortest players or the best ball handlers are the shooting guard and the point guard, who implement the coach's game plan by managing the execution of offensive and defensive plays (player positioning). Informally, players may play three-on-three, two-on-two, and one-on-one. Invented in 1891 by Canadian-American gym teacher James Naismith in Springfield, Massachusetts, in the United States, basketball has evolved to become one of the world's most popular and widely viewed sports. The National Basketball Association (NBA) is the most significant professional basketball league in the world in terms of popularity, salaries, talent, and level of competition (drawing most of its talent from U.S. college basketball). Outside North America, the top clubs from national leagues qualify to continental championships such as the EuroLeague and the Basketball Champions League Americas. The FIBA Basketball World Cup and Men's Olympic Basketball Tournament are the major international events of the sport and attract top national teams from around the world. Each continent hosts regional competitions for national teams, like EuroBasket and FIBA AmeriCup.
The FIBA Women's Basketball World Cup and women's Olympic basketball tournament feature top national teams from continental championships. The main North American league is the WNBA (NCAA Women's Division I Basketball Championship is also popular), whereas the strongest European clubs participate in the EuroLeague Women. History. Early history. A game similar to basketball is mentioned in a 1591 book published in Frankfurt am Main that reports on the lifestyles and customs of coastal North American residents, (German; translates as "Truthful Depictions of the Savages": "Among other things, a game of skill is described in which balls must be thrown against a target woven from twigs, mounted high on a pole. There's a small reward for the player if the target is being hit." Creation. In December 1891, James Naismith, a Canadian-American professor of physical education and instructor at the International Young Men's Christian Association Training School (now Springfield College) in Springfield, Massachusetts, was trying to keep his gym class active on a rainy day. He sought a vigorous indoor game to keep his students occupied and at proper levels of fitness during the long New England winters. After rejecting other ideas as either too rough or poorly suited to walled-in gymnasiums, he invented a new game in which players would pass a ball to teammates and try to score points by tossing the ball into a basket mounted on a wall.
Naismith wrote the basic rules and nailed a peach basket onto an elevated track. Naismith initially set up the peach basket with its bottom intact, which meant that the ball had to be retrieved manually after each "basket" or point scored. This quickly proved tedious, so Naismith removed the bottom of the basket to allow the balls to be poked out with a long dowel after each scored basket. Shortly after, Senda Berenson, instructor of physical culture at the nearby Smith College, went to Naismith to learn more about the game. Fascinated by the new sport and the values it could teach, she started to organize games with her pupils, following adjusted rules. The first official women's interinstitutional game was played barely 11 months later, between the University of California and the Miss Head's School. In 1899, a committee was established at the Conference of Physical Training in Springfield to draw up general rules for women's basketball. Thus, the sport quickly spread throughout America's schools, colleges and universities with uniform rules for both sexes.
Basketball was originally played with a soccer ball. These round balls from "association football" were made, at the time, with a set of laces to close off the hole needed for inserting the inflatable bladder after the other sewn-together segments of the ball's cover had been flipped outside-in. These laces could cause bounce passes and dribbling to be unpredictable. Eventually a lace-free ball construction method was invented, and this change to the game was endorsed by Naismith (whereas in American football, the lace construction proved to be advantageous for gripping and remains to this day). The first balls made specifically for basketball were brown, and it was only in the late 1950s that Tony Hinkle, searching for a ball that would be more visible to players and spectators alike, introduced the orange ball that is now in common use. Dribbling was not part of the original game except for the "bounce pass" to teammates. Passing the ball was the primary means of ball movement. Dribbling was eventually introduced but limited by the asymmetric shape of early balls. Dribbling was common by 1896, with a rule against the double dribble by 1898.
The peach baskets were used until 1906 when they were finally replaced by metal hoops with backboards. A further change was soon made, so the ball merely passed through. Whenever a person got the ball in the basket, their team would gain a point. Whichever team got the most points won the game. The baskets were originally nailed to the mezzanine balcony of the playing court, but this proved impractical when spectators in the balcony began to interfere with shots. The backboard was introduced to prevent this interference; it had the additional effect of allowing rebound shots. Naismith's handwritten diaries, discovered by his granddaughter in early 2006, indicate that he was nervous about the new game he had invented, which incorporated rules from a children's game called duck on a rock, as many had failed before it. Frank Mahan, one of the players from the original first game, approached Naismith after the Christmas break, in early 1892, asking him what he intended to call his new game. Naismith replied that he had not thought of it because he had been focused on just getting the game started. Mahan suggested that it be called "Naismith ball", at which he laughed, saying that a name like that would kill any game. Mahan then said, "Why not call it basketball?" Naismith replied, "We have a basket and a ball, and it seems to me that would be a good name for it." The first official game was played in the YMCA gymnasium in Albany, New York, on January 20, 1892, with nine players. The game ended at 1–0; the shot was made from , on a court just half the size of a present-day Streetball or National Basketball Association (NBA) court.
At the time, soccer was being played with 10 to a team (which was increased to 11). When winter weather got too icy to play soccer, teams were taken indoors, and it was convenient to have them split in half and play basketball with five on each side. By 1897–98, teams of five became standard. College basketball. Basketball's early adherents were dispatched to YMCAs throughout the United States, and it quickly spread through the United States and Canada. By 1895, it was well established at several women's high schools. While YMCA was responsible for initially developing and spreading the game, within a decade it discouraged the new sport, as rough play and rowdy crowds began to detract from YMCA's primary mission. However, other amateur sports clubs, colleges, and professional clubs quickly filled the void. In the years before World War I, the Amateur Athletic Union and the Intercollegiate Athletic Association of the United States (forerunner of the NCAA) vied for control over the rules for the game. The first pro league, the National Basketball League, was formed in 1898 to protect players from exploitation and to promote a less rough game. This league only lasted five years.
James Naismith was instrumental in establishing college basketball. His colleague C. O. Beamis fielded the first college basketball team just a year after the Springfield YMCA game at the suburban Pittsburgh Geneva College. Naismith himself later coached at the University of Kansas for six years, before handing the reins to renowned coach Forrest "Phog" Allen. Naismith's disciple Amos Alonzo Stagg brought basketball to the University of Chicago, while Adolph Rupp, a student of Naismith's at Kansas, enjoyed great success as coach at the University of Kentucky. On February 9, 1895, the first intercollegiate 5-on-5 game was played at Hamline University between Hamline and the School of Agriculture, which was affiliated with the University of Minnesota. The School of Agriculture won in a 9–3 game. In 1901, colleges, including the University of Chicago, Columbia University, Cornell University, Dartmouth College, the University of Minnesota, the U.S. Naval Academy, the University of Colorado and Yale University began sponsoring men's games. In 1905, frequent injuries on the football field prompted President Theodore Roosevelt to suggest that colleges form a governing body, resulting in the creation of the Intercollegiate Athletic Association of the United States (IAAUS). In 1910, that body changed its name to the National Collegiate Athletic Association (NCAA). The first Canadian interuniversity basketball game was played at YMCA in Kingston, Ontario on February 6, 1904, when McGill UniversityNaismith's alma matervisited Queen's University. McGill won 9–7 in overtime; the score was 7–7 at the end of regulation play, and a ten-minute overtime period settled the outcome. A good turnout of spectators watched the game.
The first men's national championship tournament, the National Association of Intercollegiate Basketball tournament, which still exists as the National Association of Intercollegiate Athletics (NAIA) tournament, was organized in 1937. The first national championship for NCAA teams, the National Invitation Tournament (NIT) in New York, was organized in 1938; the NCAA national tournament began one year later. College basketball was rocked by gambling scandals from 1948 to 1951, when dozens of players from top teams were implicated in game-fixing and point shaving. Partially spurred by an association with cheating, the NIT lost support to the NCAA tournament. High school basketball. Before widespread school district consolidation, most American high schools were far smaller than their present-day counterparts. During the first decades of the 20th century, basketball quickly became the ideal interscholastic sport due to its modest equipment and personnel requirements. In the days before widespread television coverage of professional and college sports, the popularity of high school basketball was unrivaled in many parts of America. Perhaps the most legendary of high school teams was Indiana's Franklin Wonder Five, which took the nation by storm during the 1920s, dominating Indiana basketball and earning national recognition.
Today virtually every high school in the United States fields a basketball team in varsity competition. Basketball's popularity remains high, both in rural areas where they carry the identification of the entire community, as well as at some larger schools known for their basketball teams where many players go on to participate at higher levels of competition after graduation. In the 2016–17 season, 980,673 boys and girls represented their schools in interscholastic basketball competition, according to the National Federation of State High School Associations. The states of Illinois, Indiana and Kentucky are particularly well known for their residents' devotion to high school basketball, commonly called Hoosier Hysteria in Indiana; the critically acclaimed film "Hoosiers" shows high school basketball's depth of meaning to these communities. ⁣There is currently no tournament to determine a national high school champion. The most serious effort was the National Interscholastic Basketball Tournament at the University of Chicago from 1917 to 1930. The event was organized by Amos Alonzo Stagg and sent invitations to state champion teams. The tournament started out as a mostly Midwest affair but grew. In 1929 it had 29 state champions. Faced with opposition from the National Federation of State High School Associations and North Central Association of Colleges and Schools that bore a threat of the schools losing their accreditation the last tournament was in 1930. The organizations said they were concerned that the tournament was being used to recruit professional players from the prep ranks. The tournament did not invite minority schools or private/parochial schools.
The National Catholic Interscholastic Basketball Tournament ran from 1924 to 1941 at Loyola University. The National Catholic Invitational Basketball Tournament from 1954 to 1978 played at a series of venues, including Catholic University, Georgetown and George Mason. The National Interscholastic Basketball Tournament for Black High Schools was held from 1929 to 1942 at Hampton Institute. The National Invitational Interscholastic Basketball Tournament was held from 1941 to 1967 starting out at Tuskegee Institute. Following a pause during World War II it resumed at Tennessee State College in Nashville. The basis for the champion dwindled after 1954 when "Brown v. Board of Education" began an integration of schools. The last tournaments were held at Alabama State College from 1964 to 1967. Professional basketball. Teams abounded throughout the 1920s. There were hundreds of men's professional basketball teams in towns and cities all over the United States, and little organization of the professional game. Players jumped from team to team and teams played in armories and smoky dance halls. Leagues came and went. Barnstorming squads such as the Original Celtics and two all-African American teams, the New York Renaissance Five ("Rens") and the (still existing) Harlem Globetrotters played up to two hundred games a year on their national tours.
In 1946, the Basketball Association of America (BAA) was formed. The first game was played in Toronto, Ontario, Canada between the Toronto Huskies and New York Knickerbockers on November 1, 1946. Three seasons later, in 1949, the BAA merged with the National Basketball League (NBL) to form the National Basketball Association (NBA). By the 1950s, basketball had become a major college sport, thus paving the way for a growth of interest in professional basketball. In 1959, a basketball hall of fame was founded in Springfield, Massachusetts, site of the first game. Its rosters include the names of great players, coaches, referees and people who have contributed significantly to the development of the game. The hall of fame has people who have accomplished many goals in their career in basketball. An upstart organization, the American Basketball Association, emerged in 1967 and briefly threatened the NBA's dominance until the ABA-NBA merger in 1976. Today the NBA is the top professional basketball league in the world in terms of popularity, salaries, talent, and level of competition.
The NBA has featured many famous players, including George Mikan, the first dominating "big man"; ball-handling wizard Bob Cousy and defensive genius Bill Russell of the Boston Celtics; charismatic center Wilt Chamberlain, who originally played for the barnstorming Harlem Globetrotters; all-around stars Oscar Robertson and Jerry West; more recent big men Kareem Abdul-Jabbar, Shaquille O'Neal, Hakeem Olajuwon and Karl Malone; playmakers John Stockton, Isiah Thomas and Steve Nash; crowd-pleasing forwards Julius Erving and Charles Barkley; European stars Dirk Nowitzki, Pau Gasol, Nikola Jokić and Tony Parker; Latin American stars Manu Ginobili, more recent superstars, Allen Iverson, Kobe Bryant, Tim Duncan, LeBron James, Stephen Curry, Giannis Antetokounmpo, etc.; and the three players who many credit with ushering the professional game to its highest level of popularity during the 1980s and 1990s: Larry Bird, Earvin "Magic" Johnson, and Michael Jordan. In 2001, the NBA formed a developmental league, the National Basketball Development League (later known as the NBA D-League and then the NBA G League after a branding deal with Gatorade). As of the 2023–24 season, the G League has 31 teams.
International basketball. FIBA (International Basketball Federation) was formed in 1932 by eight founding nations: Argentina, Czechoslovakia, Greece, Italy, Latvia, Portugal, Romania and Switzerland. At this time, the organization only oversaw amateur players. Its acronym, derived from the French "Fédération Internationale de Basket-ball Amateur", was thus "FIBA". Men's basketball was first included at the Berlin 1936 Summer Olympics, although a demonstration tournament was held in 1904. The United States defeated Canada in the first final, played outdoors. This competition has usually been dominated by the United States, whose team has won all but three titles. The first of these came in a controversial final game in Munich in 1972 against the Soviet Union, in which the ending of the game was replayed three times until the Soviet Union finally came out on top. In 1950 the first FIBA World Championship for men, now known as the FIBA Basketball World Cup, was held in Argentina. Three years later, the first FIBA World Championship for women, now known as the FIBA Women's Basketball World Cup, was held in Chile. Women's basketball was added to the Olympics in 1976, which were held in Montreal, Quebec, Canada with teams such as the Soviet Union, Brazil and Australia rivaling the American squads.
In 1989, FIBA allowed professional NBA players to participate in the Olympics for the first time. Prior to the 1992 Summer Olympics, only European and South American teams were allowed to field professionals in the Olympics. The United States' dominance continued with the introduction of the original Dream Team. In the 2004 Athens Olympics, the United States suffered its first Olympic loss while using professional players, falling to Puerto Rico (in a 19-point loss) and Lithuania in group games, and being eliminated in the semifinals by Argentina. It eventually won the bronze medal defeating Lithuania, finishing behind Argentina and Italy. The Redeem Team, won gold at the 2008 Olympics, and the B-Team, won gold at the 2010 FIBA World Championship in Turkey despite featuring no players from the 2008 squad. The United States continued its dominance as they won gold at the 2012 Olympics, 2014 FIBA World Cup and the 2016 Olympics. Worldwide, basketball tournaments are held for boys and girls of all age levels. The global popularity of the sport is reflected in the nationalities represented in the NBA. Players from all six inhabited continents currently play in the NBA. Top international players began coming into the NBA in the mid-1990s, including Croatians Dražen Petrović and Toni Kukoč, Serbian Vlade Divac, Lithuanians Arvydas Sabonis and Šarūnas Marčiulionis, Dutchman Rik Smits and German Detlef Schrempf.
In the Philippines, the Philippine Basketball Association's first game was played on April 9, 1975, at the Araneta Coliseum in Cubao, Quezon City, Philippines. It was founded as a "rebellion" of several teams from the now-defunct Manila Industrial and Commercial Athletic Association, which was tightly controlled by the Basketball Association of the Philippines (now defunct), the then-FIBA recognized national association. Nine teams from the MICAA participated in the league's first season that opened on April 9, 1975. The NBL is Australia's pre-eminent men's professional basketball league. The league commenced in 1979, playing a winter season (April–September) and did so until the completion of the 20th season in 1998. The 1998–99 season, which commenced only months later, was the first season after the shift to the current summer season format (October–April). This shift was an attempt to avoid competing directly against Australia's various football codes. It features 8 teams from around Australia and one in New Zealand. A few players including Luc Longley, Andrew Gaze, Shane Heal, Chris Anstey and Andrew Bogut made it big internationally, becoming poster figures for the sport in Australia. The Women's National Basketball League began in 1981.
Women's basketball. Women began to play basketball in the fall of 1892 at Smith College through Senda Berenson, substitute director of the newly opened gymnasium and physical education teacher, after having modified the rules for women. Shortly after Berenson was hired at Smith, she visited Naismith to learn more about the game. Fascinated by the new sport and the values it could teach, she instantly introduced the game as a class exercise and soon after teams were organized. The first women's collegiate basketball game was played on March 21, 1893, when her Smith freshmen and sophomores played against one another. The first official women's interinstitutional game was played later that year between the University of California and the Miss Head's School. In 1899, a committee was established at the Conference of Physical Training in Springfield to draw up general rules for women's basketball. These rules, designed by Berenson, were published in 1899. In 1902 Berenson became the editor of A. G. Spalding's first Women's Basketball Guide. The same year women of Mount Holyoke and Sophie Newcomb College (coached by Clara Gregory Baer), began playing basketball. By 1895, the game had spread to colleges across the country, including Wellesley, Vassar, and Bryn Mawr. The first intercollegiate women's game was on April 4, 1896. Stanford women played Berkeley, 9-on-9, ending in a 2–1 Stanford victory.
Women's basketball development was more structured than that for men in the early years. In 1905, the executive committee on Basket Ball Rules (National Women's Basketball Committee) was created by the American Physical Education Association. These rules called for six to nine players per team and 11 officials. The International Women's Sports Federation (1924) included a women's basketball competition. 37 women's high school varsity basketball or state tournaments were held by 1925. And in 1926, the Amateur Athletic Union backed the first national women's basketball championship, complete with men's rules. The Edmonton Grads, a touring Canadian women's team based in Edmonton, Alberta, operated between 1915 and 1940. The Grads toured all over North America, and were exceptionally successful. They posted a record of 522 wins and only 20 losses over that span, as they met any team that wanted to challenge them, funding their tours from gate receipts. The Grads also shone on several exhibition trips to Europe, and won four consecutive exhibition Olympics tournaments, in 1924, 1928, 1932, and 1936; however, women's basketball was not an official Olympic sport until 1976. The Grads' players were unpaid, and had to remain single. The Grads' style focused on team play, without overly emphasizing skills of individual players. The first women's AAU All-America team was chosen in 1929. Women's industrial leagues sprang up throughout the United States, producing famous athletes, including Babe Didrikson of the Golden Cyclones, and the All American Red Heads Team, which competed against men's teams, using men's rules. By 1938, the women's national championship changed from a three-court game to two-court game with six players per team.
The NBA-backed Women's National Basketball Association (WNBA) began in 1997. Though it had shaky attendance figures, several marquee players (Lisa Leslie, Diana Taurasi, and Candace Parker among others) have helped the league's popularity and level of competition. Other professional women's basketball leagues in the United States, such as the American Basketball League (1996–98), have folded in part because of the popularity of the WNBA. The WNBA has been looked at by many as a niche league. However, the league has recently taken steps forward. In June 2007, the WNBA signed a contract extension with ESPN. The new television deal ran from 2009 to 2016. Along with this deal, came the first-ever rights fees to be paid to a women's professional sports league. Over the eight years of the contract, "millions and millions of dollars" were "dispersed to the league's teams." In a March 12, 2009, article, NBA commissioner David Stern said that in the bad economy, "the NBA is far less profitable than the WNBA. We're losing a lot of money among a large number of teams. We're budgeting the WNBA to break even this year."
Rules and regulations. Measurements and time limits discussed in this section often vary among tournaments and organizations; international and NBA rules are used in this section. The object of the game is to outscore one's opponents by throwing the ball through the opponents' basket from above while preventing the opponents from doing so on their own. An attempt to score in this way is called a shot. A successful shot is worth two points, or three points if it is taken from beyond the three-point arc from the basket in international games and in NBA games. A one-point shot can be earned when shooting from the foul line after a foul is made. After a team has scored from a field goal or free throw, play is resumed with a throw-in awarded to the non-scoring team taken from a point beyond the endline of the court where the points were scored. Playing regulations. Games are played in four quarters of 10 (FIBA) or 12 minutes (NBA). College men's games use two 20-minute halves, college women's games use 10-minute quarters, and most United States high school varsity games use 8-minute quarters; however, this varies from state to state. 15 minutes are allowed for a half-time break under FIBA, NBA, and NCAA rules and 10 minutes in United States high schools. Overtime periods are five minutes in length except for high school, which is four minutes in length. Teams exchange baskets for the second half. The time allowed is actual playing time; the clock is stopped while the play is not active. Therefore, games generally take much longer to complete than the allotted game time, typically about two hours.
Five players from each team may be on the court at one time. Substitutions are unlimited but can only be done when play is stopped. Teams also have a coach, who oversees the development and strategies of the team, and other team personnel such as assistant coaches, managers, statisticians, doctors and trainers. For both men's and women's teams, a standard uniform consists of a pair of shorts and a jersey with a clearly visible number, unique within the team, printed on both the front and back. Players wear high-top sneakers that provide extra ankle support. Typically, team names, players' names and, outside of North America, sponsors are printed on the uniforms. A limited number of time-outs, clock stoppages requested by a coach (or sometimes mandated in the NBA) for a short meeting with the players, are allowed. They generally last no longer than one minute (100 seconds in the NBA) unless, for televised games, a commercial break is needed. The game is controlled by the officials consisting of the referee (referred to as crew chief in the NBA), one or two umpires (referred to as referees in the NBA) and the table officials. For college, the NBA, and many high schools, there are a total of three referees on the court. The table officials are responsible for keeping track of each team's scoring, timekeeping, individual and team fouls, player substitutions, team possession arrow, and the shot clock.
Equipment. The only essential equipment in a basketball game is the ball and the court: a flat, rectangular surface with baskets at opposite ends. Competitive levels require the use of more equipment such as clocks, score sheets, scoreboards, alternating possession arrows, and whistle-operated stop-clock systems. A regulation basketball court in international games is long and wide. In the NBA and NCAA the court is . Most courts have wood flooring, usually constructed from maple planks running in the same direction as the longer court dimension. The name and logo of the home team is usually painted on or around the center circle. The basket is a steel rim diameter with an attached net affixed to a backboard that measures and one basket is at each end of the court. The white outlined box on the backboard is high and wide. At almost all levels of competition, the top of the rim is exactly above the court and inside the baseline. While variation is possible in the dimensions of the court and backboard, it is considered important for the basket to be of the correct height – a rim that is off by just a few inches can have an adverse effect on shooting. The net must "check the ball momentarily as it passes through the basket" to aid the visual confirmation that the ball went through. The act of checking the ball has the further advantage of slowing down the ball so the rebound does not go as far.
The size of the basketball is also regulated. For men, the official ball is in circumference (size 7, or a "295 ball") and weighs . If women are playing, the official basketball size is in circumference (size 6, or a "285 ball") with a weight of . In 3x3, a formalized version of the halfcourt 3-on-3 game, a dedicated ball with the circumference of a size 6 ball but the weight of a size 7 ball is used in all competitions (men's, women's, and mixed teams). Violations. The ball may be advanced toward the basket by being shot, passed between players, thrown, tapped, rolled or dribbled (bouncing the ball while running). The ball must stay within the court; the last team to touch the ball before it travels out of bounds forfeits possession. The ball is out of bounds if it touches a boundary line, or touches any player or object that is out of bounds. There are limits placed on the steps a player may take without dribbling, which commonly results in an infraction known as traveling. Nor may a player stop their dribble and then resume dribbling. A dribble that touches both hands is considered stopping the dribble, giving this infraction the name double dribble. Within a dribble, the player cannot carry the ball by placing their hand on the bottom of the ball; doing so is known as carrying the ball. A team, once having established ball control in the front half of their court, may not return the ball to the backcourt and be the first to touch it. A violation of these rules results in loss of possession.
The ball may not be kicked, nor be struck with the fist. For the offense, a violation of these rules results in loss of possession; for the defense, most leagues reset the shot clock and the offensive team is given possession of the ball out of bounds. There are limits imposed on the time taken before progressing the ball past halfway (8 seconds in FIBA and the NBA; 10 seconds in NCAA and high school for both sexes), before attempting a shot (24 seconds in FIBA, the NBA, and U Sports (Canadian universities) play for both sexes, and 30 seconds in NCAA play for both sexes), holding the ball while closely guarded (5 seconds), and remaining in the restricted area known as the free-throw lane, (or the "key") (3 seconds). These rules are designed to promote more offense. There are also limits on how players may block an opponent's field goal attempt or help a teammate's field goal attempt. Goaltending is a defender's touching of a ball that is on a downward flight toward the basket, while the related violation of basket interference is the touching of a ball that is on the rim or above the basket, or by a player reaching through the basket from below. Goaltending and basket interference committed by a defender result in awarding the basket to the offense, while basket interference committed by an offensive player results in cancelling the basket if one is scored. The defense gains possession in all cases of goaltending or basket interference.
Fouls. An attempt to unfairly disadvantage an opponent through certain types of physical contact is illegal and is called a personal foul. These are most commonly committed by defensive players; however, they can be committed by offensive players as well. Players who are fouled either receive the ball to pass inbounds again, or receive one or more free throws if they are fouled in the act of shooting, depending on whether the shot was successful. One point is awarded for making a free throw, which is attempted from a line from the basket. The referee is responsible for judging whether contact is illegal, sometimes resulting in controversy. The calling of fouls can vary between games, leagues and referees. There is a second category of fouls called technical fouls, which may be charged for various rules violations including failure to properly record a player in the scorebook, or for unsportsmanlike conduct. These infractions result in one or two free throws, which may be taken by any of the five players on the court at the time. Repeated incidents can result in disqualification. A blatant foul involving physical contact that is either excessive or unnecessary is called an intentional foul (flagrant foul in the NBA). In FIBA and NCAA women's basketball, a foul resulting in ejection is called a disqualifying foul, while in leagues other than the NBA, such a foul is referred to as flagrant.
If a team exceeds a certain limit of team fouls in a given period (quarter or half) – four for NBA, NCAA women's, and international games – the opposing team is awarded one or two free throws on all subsequent non-shooting fouls for that period, the number depending on the league. In the US college men's game and high school games for both sexes, if a team reaches 7 fouls in a half, the opposing team is awarded one free throw, along with a second shot if the first is made. This is called shooting "one-and-one". If a team exceeds 10 fouls in the half, the opposing team is awarded two free throws on all subsequent fouls for the half. When a team shoots foul shots, the opponents may not interfere with the shooter, nor may they try to regain possession until the last or potentially last free throw is in the air. After a team has committed a specified number of fouls, the other team is said to be "in the bonus". On scoreboards, this is usually signified with an indicator light reading "Bonus" or "Penalty" with an illuminated directional arrow or dot indicating that team is to receive free throws when fouled by the opposing team. (Some scoreboards also indicate the number of fouls committed.)
If a team misses the first shot of a two-shot situation, the opposing team must wait for the completion of the second shot before attempting to reclaim possession of the ball and continuing play. If a player is fouled while attempting a shot and the shot is unsuccessful, the player is awarded a number of free throws equal to the value of the attempted shot. A player fouled while attempting a regular two-point shot thus receives two shots, and a player fouled while attempting a three-point shot receives three shots. If a player is fouled while attempting a shot and the shot is successful, typically the player will be awarded one additional free throw for one point. In combination with a regular shot, this is called a "three-point play" or "four-point play" (or more colloquially, an "and one") because of the basket made at the time of the foul (2 or 3 points) and the additional free throw (1 point). Common techniques and practices. Positions. Although the rules do not specify any positions whatsoever, they have evolved as part of basketball. During the early years of basketball's evolution, two guards, two forwards, and one center were used. In more recent times specific positions evolved, but the current trend, advocated by many top coaches including Mike Krzyzewski, is towards positionless basketball, where big players are free to shoot from outside and dribble if their skill allows it. Popular descriptions of positions include:
Point guard (often called the "1") : usually the fastest player on the team, organizes the team's offense by controlling the ball and making sure that it gets to the right player at the right time. Shooting guard (the "2") : creates a high volume of shots on offense, mainly long-ranged; and guards the opponent's best perimeter player on defense. Small forward (the "3") : often primarily responsible for scoring points via cuts to the basket and dribble penetration; on defense seeks rebounds and steals, but sometimes plays more actively. Power forward (the "4"): plays offensively often with their back to the basket; on defense, plays under the basket (in a zone defense) or against the opposing power forward (in man-to-man defense). Center (the "5"): uses height and size to score (on offense), to protect the basket closely (on defense), or to rebound. The above descriptions are flexible. For most teams today, the shooting guard and small forward have very similar responsibilities and are often called the wings, as do the power forward and center, who are often called post players. While most teams describe two players as guards, two as forwards, and one as a center, on some occasions teams choose to call them by different designations.
Strategy. There are two main defensive strategies: "zone defense" and "man-to-man defense". In a zone defense, each player is assigned to guard a specific area of the court. Zone defenses often allow the defense to double team the ball, a manoeuver known as a trap. In a man-to-man defense, each defensive player guards a specific opponent. Offensive plays are more varied, normally involving planned passes and movement by players without the ball. A quick movement by an offensive player without the ball to gain an advantageous position is known as a "cut". A legal attempt by an offensive player to stop an opponent from guarding a teammate, by standing in the defender's way such that the teammate cuts next to him, is a "screen" or "pick". The two plays are combined in the "pick and roll", in which a player sets a pick and then "rolls" away from the pick towards the basket. Screens and cuts are very important in offensive plays; these allow the quick passes and teamwork, which can lead to a successful basket. Teams almost always have several offensive plays planned to ensure their movement is not predictable. On court, the point guard is usually responsible for indicating which play will occur.
Shooting. Shooting is the act of attempting to score points by throwing the ball through the basket, methods varying with players and situations. Typically, a player faces the basket with both feet facing the basket. A player will rest the ball on the fingertips of the dominant hand (the shooting arm) slightly above the head, with the other hand supporting the side of the ball. The ball is usually shot by jumping (though not always) and extending the shooting arm. The shooting arm, fully extended with the wrist fully bent, is held stationary for a moment following the release of the ball, known as a "follow-through". Players often try to put a steady backspin on the ball to absorb its impact with the rim. The ideal trajectory of the shot is somewhat controversial, but generally a proper arc is recommended. Players may shoot directly into the basket or may use the backboard to redirect the ball into the basket. The two most common shots that use the above described setup are the "set shot" and the "jump shot". Both are preceded by a crouching action which preloads the muscles and increases the power of the shot. In a set shot, the shooter straightens up and throws from a standing position with neither foot leaving the floor; this is typically used for free throws. For a jump shot, the throw is taken in mid-air with the ball being released near the top of the jump. This provides much greater power and range, and it also allows the player to elevate over the defender. Failure to release the ball before the feet return to the floor is considered a traveling violation.
Another common shot is called the "layup". This shot requires the player to be in motion toward the basket, and to "lay" the ball "up" and into the basket, typically off the backboard (the backboard-free, underhand version is called a "finger roll"). The most crowd-pleasing and typically highest-percentage accuracy shot is the "slam dunk", in which the player jumps very high and throws the ball downward, through the basket while touching it. Another shot that is less common than the layup, is the "circus shot". The circus shot is a low-percentage shot that is flipped, heaved, scooped, or flung toward the hoop while the shooter is off-balance, airborne, falling down or facing away from the basket. A back-shot is a shot taken when the player is facing away from the basket, and may be shot with the dominant hand, or both; but there is a very low chance that the shot will be successful. A shot that misses both the rim and the backboard completely is referred to as an "air ball". A particularly bad shot, or one that only hits the backboard, is jocularly called a brick. The "hang time" is the length of time a player stays in the air after jumping, either to make a slam dunk, layup or jump shot.
Rebounding. The objective of rebounding is to successfully gain possession of the basketball after a missed field goal or free throw, as it rebounds from the hoop or backboard. This plays a major role in the game, as most possessions end when a team misses a shot. There are two categories of rebounds: offensive rebounds, in which the ball is recovered by the offensive side and does not change possession, and defensive rebounds, in which the defending team gains possession of the loose ball. The majority of rebounds are defensive, as the team on defense tends to be in better position to recover missed shots; for example, about 75% of rebounds in the NBA are defensive. Passing. A pass is a method of moving the ball between players. Most passes are accompanied by a step forward to increase power and are followed through with the hands to ensure accuracy. A staple pass is the "chest pass". The ball is passed directly from the passer's chest to the receiver's chest. A proper chest pass involves an outward snap of the thumbs to add velocity and leaves the defence little time to react.
Another type of pass is the "bounce pass". Here, the passer bounces the ball crisply about two-thirds of the way from his own chest to the receiver. The ball strikes the court and bounces up toward the receiver. The bounce pass takes longer to complete than the chest pass, but it is also harder for the opposing team to intercept (kicking the ball deliberately is a violation). Thus, players often use the bounce pass in crowded moments, or to pass around a defender. The "overhead pass" is used to pass the ball over a defender. The ball is released while over the passer's head. The "outlet pass" occurs after a team gets a defensive rebound. The next pass after the rebound is the "outlet pass". The crucial aspect of any good pass is it being difficult to intercept. Good passers can pass the ball with great accuracy and they know exactly where each of their other teammates prefers to receive the ball. A special way of doing this is passing the ball without looking at the receiving teammate. This is called a "no-look pass".
Another advanced style of passing is the "behind-the-back pass", which, as the description implies, involves throwing the ball behind the passer's back to a teammate. Although some players can perform such a pass effectively, many coaches discourage no-look or behind-the-back passes, believing them to be difficult to control and more likely to result in turnovers or violations. Dribbling. Dribbling is the act of bouncing the ball continuously with one hand and is a requirement for a player to take steps with the ball. To dribble, a player pushes the ball down towards the ground with the fingertips rather than patting it; this ensures greater control. When dribbling past an opponent, the dribbler should dribble with the hand farthest from the opponent, making it more difficult for the defensive player to get to the ball. It is therefore important for a player to be able to dribble competently with both hands. Good dribblers (or "ball handlers") tend to keep their dribbling hand low to the ground, reducing the distance of travel of the ball from the floor to the hand, making it more difficult for the defender to "steal" the ball. Good ball handlers frequently dribble behind their backs, between their legs, and switch directions suddenly, making a less predictable dribbling pattern that is more difficult to defend against. This is called a crossover, which is the most effective way to move past defenders while dribbling.
A skilled player can dribble without watching the ball, using the dribbling motion or peripheral vision to keep track of the ball's location. By not having to focus on the ball, a player can look for teammates or scoring opportunities, as well as avoid the danger of having someone steal the ball away from him/her. Blocking. A block is performed when, after a shot is attempted, a defender succeeds in altering the shot by touching the ball. In almost all variants of play, it is illegal to touch the ball after it is in the downward path of its arc; this is known as "goaltending". It is also illegal under NBA and Men's NCAA basketball to block a shot after it has touched the backboard, or when any part of the ball is directly above the rim. Under international rules it is illegal to block a shot that is in the downward path of its arc or one that has touched the backboard until the ball has hit the rim. After the ball hits the rim, it is again legal to touch it even though it is no longer considered as a block performed.
To block a shot, a player has to be able to reach a point higher than where the shot is released. Thus, height can be an advantage in blocking. Players who are taller and playing the power forward or center positions generally record more blocks than players who are shorter and playing the guard positions. However, with good timing and a sufficiently high vertical leap, even shorter players can be effective shot blockers. Height. At the professional level, most male players are above and most women above . Guards, for whom physical coordination and ball-handling skills are crucial, tend to be the smallest players. Almost all forwards in the top men's pro leagues are or taller. Most centers are over tall. According to a survey given to all NBA teams, the average height of all NBA players is just under , with the average weight being close to . The tallest players ever in the NBA were Manute Bol and Gheorghe Mureșan, who were both tall. At , Margo Dydek was the tallest player in the history of the WNBA. The shortest player ever to play in the NBA is Muggsy Bogues at . Other average-height or relatively short players have thrived at the pro level, including Anthony "Spud" Webb, who was tall, but had a vertical leap, giving him significant height when jumping, and Temeka Johnson, who won the WNBA Rookie of the Year Award and a championship with the Phoenix Mercury while standing only . While shorter players are often at a disadvantage in certain aspects of the game, their ability to navigate quickly through crowded areas of the court and steal the ball by reaching low are strengths.
Players regularly inflate their height in high school or college. Many prospects exaggerate their height while in high school or college to make themselves more appealing to coaches and scouts, who prefer taller players. Charles Barkley stated; "I've been measured at 6–5, 6-. But I started in college at 6–6." Sam Smith, a former writer from the "Chicago Tribune", said: "We sort of know the heights, because after camp, the sheet comes out. But you use that height, and the player gets mad. And then you hear from his agent. Or you file your story with the right height, and the copy desk changes it because they have the 'official' N.B.A. media guide, which is wrong. So you sort of go along with the joke." Since the 2019–20 NBA season heights of NBA players are recorded definitively by measuring players with their shoes off. Variations and similar games. Variations of basketball are activities based on the game of basketball, using common basketball skills and equipment (primarily the ball and basket). Some variations only have superficial rule changes, while others are distinct games with varying degrees of influence from basketball. Other variations include children's games, contests or activities meant to help players reinforce skills.
An earlier version of basketball, played primarily by women and girls, was six-on-six basketball. Horseball is a game played on horseback where a ball is handled and points are scored by shooting it through a high net (approximately 1.5m×1.5m). The sport is like a combination of polo, rugby, and basketball. There is even a form played on donkeys known as Donkey basketball, which has attracted criticism from animal rights groups. Half-court. Perhaps the single most common variation of basketball is the half-court game, played in informal settings without referees or strict rules. Only one basket is used, and the ball must be "taken back" or "cleared" – passed or dribbled outside the three-point line each time possession of the ball changes from one team to the other. Half-court games require less cardiovascular stamina, since players need not run back and forth a full court. Half-court raises the number of players that can use a court or, conversely, can be played if there is an insufficient number to form full 5-on-5 teams.
Half-court basketball is usually played 1-on-1, 2-on-2 or 3-on-3. The last of these variations is gradually gaining official recognition as 3x3, originally known as FIBA 33. It was first tested at the 2007 Asian Indoor Games in Macau and the first official tournaments were held at the 2009 Asian Youth Games and the 2010 Youth Olympics, both in Singapore. The first FIBA 3x3 Youth World Championships were held in Rimini, Italy in 2011, with the first FIBA 3x3 World Championships for senior teams following a year later in Athens. The sport is highly tipped to become an Olympic sport as early as 2016. In the summer of 2017, the BIG3 basketball league, a professional 3x3 half court basketball league that features former NBA players, began. The BIG3 features several rule variants including a four-point field goal. Other variations. Variations of basketball with their own page or subsection include: Spin-offs from basketball that are now separate sports include: Social forms of basketball. Basketball as a social and communal sport features environments, rules and demographics different from those seen in professional and televised basketball.
Recreational basketball. Basketball is played widely as an extracurricular, intramural or amateur sport in schools and colleges. Notable institutions of recreational basketball include: Fantasy basketball. Fantasy basketball was popularized during the 1990s by ESPN Fantasy Sports, NBA.com, and Yahoo! Fantasy Sports. On the model of fantasy baseball and football, players create fictional teams, select professional basketball players to "play" on these teams through a mock draft or trades, then calculate points based on the players' real-world performance.
Blowfish (disambiguation) Blowfish are species of fish in the family Tetraodontidae. Blowfish may also refer to:

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