text stringlengths 0 131k |
|---|
. |
Regional |
Britain and Ireland |
Australia |
New Zealand |
Europe |
Arctic |
Greenland |
Faroe Islands |
. |
Canary Islands |
Morocco |
South Africa |
North America |
External links |
– a database of all algal names including images, nomenclature, taxonomy, distribution, bibliography, uses, extracts |
EnAlgae |
Endosymbiotic events |
Polyphyletic groups Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total vari... |
History |
While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to Stigler. These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was performing hypothesis testing in the 1770s. Around 180... |
from reaction times (the "personal equation") and had developed methods of reducing the errors. The experimental methods used in the study of the personal equation were later accepted by the emerging field of psychology which developed strong (full factorial) experimental methods to which randomization and blinding w... |
Ronald Fisher introduced the term variance and proposed its formal analysis in a 1918 article The Correlation Between Relatives on the Supposition of Mendelian Inheritance. His first application of the analysis of variance was published in 1921. Analysis of variance became widely known after being included in Fisher's... |
Randomization models were developed by several researchers. The first was published in Polish by Jerzy Neyman in 1923. |
Example |
The analysis of variance can be used to describe otherwise complex relations among variables. A dog show provides an example. A dog show is not a random sampling of the breed: it is typically limited to dogs that are adult, pure-bred, and exemplary. A histogram of dog weights from a show might plausibly be rather co... |
In the illustrations to the right, groups are identified as X1, X2, etc. In the first illustration, the dogs are divided according to the product (interaction) of two binary groupings: young vs old, and short-haired vs long-haired (e.g., group 1 is young, short-haired dogs, group 2 is young, long-haired dogs, etc.). Si... |
An attempt to explain the weight distribution by grouping dogs as pet vs working breed and less athletic vs more athletic would probably be somewhat more successful (fair fit). The heaviest show dogs are likely to be big, strong, working breeds, while breeds kept as pets tend to be smaller and thus lighter. As shown ... |
An attempt to explain weight by breed is likely to produce a very good fit. All Chihuahuas are light and all St Bernards are heavy. The difference in weights between Setters and Pointers does not justify separate breeds. The analysis of variance provides the formal tools to justify these intuitive judgments. A comm... |
Classes of models |
There are three classes of models used in the analysis of variance, and these are outlined here. |
Fixed-effects models |
The fixed-effects model (class I) of analysis of variance applies to situations in which the experimenter applies one or more treatments to the subjects of the experiment to see whether the response variable values change. This allows the experimenter to estimate the ranges of response variable values that the treatmen... |
Random-effects models |
Random-effects model (class II) is used when the treatments are not fixed. This occurs when the various factor levels are sampled from a larger population. Because the levels themselves are random variables, some assumptions and the method of contrasting the treatments (a multi-variable generalization of simple differe... |
Mixed-effects models |
A mixed-effects model (class III) contains experimental factors of both fixed and random-effects types, with appropriately different interpretations and analysis for the two types. |
Example: |
Teaching experiments could be performed by a college or university department to find a good introductory textbook, with each text considered a treatment. The fixed-effects model would compare a list of candidate texts. The random-effects model would determine whether important differences exist among a list of rando... |
Defining fixed and random effects has proven elusive, with competing definitions arguably leading toward a linguistic quagmire. |
Assumptions |
The analysis of variance has been studied from several approaches, the most common of which uses a linear model that relates the response to the treatments and blocks. Note that the model is linear in parameters but may be nonlinear across factor levels. Interpretation is easy when data is balanced across factors but m... |
Textbook analysis using a normal distribution |
The analysis of variance can be presented in terms of a linear model, which makes the following assumptions about the probability distribution of the responses: |
Independence of observations – this is an assumption of the model that simplifies the statistical analysis. |
Normality – the distributions of the residuals are normal. |
Equality (or "homogeneity") of variances, called homoscedasticity — the variance of data in groups should be the same. |
The separate assumptions of the textbook model imply that the errors are independently, identically, and normally distributed for fixed effects models, that is, that the errors () are independent and |
Randomization-based analysis |
In a randomized controlled experiment, the treatments are randomly assigned to experimental units, following the experimental protocol. This randomization is objective and declared before the experiment is carried out. The objective random-assignment is used to test the significance of the null hypothesis, following th... |
Unit-treatment additivity |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.