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hypothesis testing | Hypothesis testing for equivalence of two arrangements | https://stats.stackexchange.com/questions/79380/hypothesis-testing-for-equivalence-of-two-arrangements | <p>I have two arrangements(i.e. permutations) of numbers. First one is the target/real arrangement. Second, is the observed arrangement.</p>
<blockquote>
<p>e.g.</p>
<p>Target := 1,2,3,4,5,6,7</p>
<p>Observed := 4,1,7,3,2,5,6</p>
</blockquote>
<p>Any two elements in an arrangement is not equal. What kind of test should... | <p>First of all, I would suggest to reconsider the names you chose for your data. In most places 'Observed' is used for the actual observed/measured/real value of your data, so in your case I would expect it to be used for the sequence of real world events.</p>
<p>I would also suggest to switch 'Targeted' for 'predict... | 300 |
hypothesis testing | Dependent vs Independent sample | https://stats.stackexchange.com/questions/276323/dependent-vs-independent-sample | <p>I am quite confused about a question that came up in my exam.</p>
<p><strong>Question:</strong> <em>The travel times on two alternative routes through a network are recorded on 20 working days during a month. The results of this are given in Table 4.
Perform an appropriate hypothesis test to investigate the differen... | <p>If it is the same driver in the same car on the travelling both routes over 20 days then the samples are dependent. If there are different drivers in different cars on the two routes then the samples are independent. Samples can only be dependent if there is some common factor, like a single driver, otherwise the sa... | 301 |
hypothesis testing | Comparing a proportion to a 'mean' proportion. Which test? | https://stats.stackexchange.com/questions/473018/comparing-a-proportion-to-a-mean-proportion-which-test | <p>Suppose there are 24 factories who all fabricate the same product with a certain percentage of that product being faulty. We have a table of data:</p>
<p>Factory, Produced, Faulty</p>
<p>F1, 212, 31</p>
<p>F2, 1021, 145</p>
<p>…, …, …</p>
<p>F24, 480, 40</p>
<p>Now I want to check factory F1 has a different proporti... | <p>The question is not clarifying whether the data arises from random sampling or not.</p>
<p>You can check out the following images for a more detail description.</p>
<p><a href="https://i.sstatic.net/XY9FE.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/XY9FE.png" alt="Chi-Square Test" /></a></p>
<p><a... | 302 |
hypothesis testing | Question about p.adjust in R and BH correction | https://stats.stackexchange.com/questions/473580/question-about-p-adjust-in-r-and-bh-correction | <p>In multiple test we adjust the significant level by BH. I used p.adjust in R and adjust my p value after that when I print those out it has some 0 and 1, I don’t get what it means .Also, does p.adjust default 0.05 significant level? In my knowledge, BH should change the significant level instead of p value, so I am ... | <p>In the documentation for p.adjust there is this for "value"</p>
<blockquote>
<p>A numeric vector of corrected p-values (of the same length as p, with
names copied from p).</p>
</blockquote>
<p>So, it is doing what it says it should. Of course, p values can't be below 0 or above 1. The 0's are probably some... | 303 |
hypothesis testing | How can I show that the hypothesis $\mu = \mu_0$ is true exactly if $\mathbf a'\mu = \mathbf a'\mu_0$ for all vectors $\mathbf a \in \mathbb R^p$? | https://stats.stackexchange.com/questions/473620/how-can-i-show-that-the-hypothesis-mu-mu-0-is-true-exactly-if-mathbf-a | <p>How can I show that the hypothesis <span class="math-container">$\mu = \mu_0$</span> is true exactly if <span class="math-container">$\mathbf a'\mu = \mathbf a'\mu_0$</span> for all vectors <span class="math-container">$\mathbf a \in \mathbb R^p$</span>?</p>
| <p>Consider that <span class="math-container">$A \implies B \iff B^c \implies A^c$</span>.</p>
<p>You can prove your statement by contrapositive: suppose <span class="math-container">$\mu \neq \mu_0$</span>, then it is enough to show that there exists one <span class="math-container">$a \in \mathbb{R}^p$</span> such th... | 304 |
hypothesis testing | What does it mean to fail to reject in a one-sided hypothesis test? | https://stats.stackexchange.com/questions/475402/what-does-it-mean-to-fail-to-reject-in-a-one-sided-hypothesis-test | <p>Let's say we want to test the following hypotheses:</p>
<p><span class="math-container">$H_0: \mu = 0$</span> <span class="math-container">$H_1: \mu > 0$</span></p>
<p>for a random sample <span class="math-container">$\{X_1, \dots , X_n\}$</span> that is normally distributed <span class="math-container">$X... | 305 | |
hypothesis testing | Alpha error vs Beta error | https://stats.stackexchange.com/questions/475535/alpha-error-vs-beta-error | <p>If my main hypothesis is that there will be no difference between two different designs in an experiment, should I be more concerned about the alpha error (rejecting H0 when it is true) or beta error (accepting H0 when it is false)?
Also, would my null hypothesis in this experiment be that there is a difference betw... | <p>It depends on the situation. For example, if you work in the medical field and you want to check if the patient has a critical disease like cancer, the false-negative would be terrible. Because if you pass on the sick patient, the patient might die. In this case, you want to reduce the false-negative as much as poss... | 306 |
hypothesis testing | Hypothesises testing | https://stats.stackexchange.com/questions/476733/hypothesises-testing | <p>I want to test a hypothesis saying 50% of employees in a company are happy. A survey of 100 people has been made and 41 say that they are happy.
My questions: I can't understand what I am given.
(1) Is the hypothesis <span class="math-container">$H_0: \mu_0 = 50$</span> <span class="math-container">$H_1:\mu_1 \ne 5... | <ol>
<li><p>The null and alternative would be <span class="math-container">$H_0: p = 0.5$</span> and <span class="math-container">$H_A: p \neq 0.5$</span>. Here, <span class="math-container">$p$</span> is the proportion of the population which are happy.</p>
</li>
<li><p>The standard deviation is a function of the sa... | 307 |
hypothesis testing | Can you create an example showing when the p-value $P(D|H_0)$ does not imply probability of $H_0$ being true given the observed data $P(H_0|D)$? | https://stats.stackexchange.com/questions/487928/can-you-create-an-example-showing-when-the-p-value-pdh-0-does-not-imply-pro | <p>I'm reading <a href="https://journals.sagepub.com/doi/abs/10.1177/106591299905200309" rel="nofollow noreferrer">The Insignificance of Null Hypothesis Significance Testing</a> and on page 654, the author states that most people incorrectly think that the null hypothesis significance test produces <span class="math-co... | <p>Is not possible to create the example that you looking for. The problem here is that <span class="math-container">$P(H_0|D)$</span> is a meaningless writing. The last because, even if in practice case you do not known if <span class="math-container">$H_0$</span> is true or false, we have to remember that, under the ... | 308 |
hypothesis testing | Is a hypothesis test useful if our null hypothesis is not the true value? | https://stats.stackexchange.com/questions/487972/is-a-hypothesis-test-useful-if-our-null-hypothesis-is-not-the-true-value | <p>Assume we are testing if the true average weight of milk cartons is 100g. We may specify <span class="math-container">$H_0: \mu = 100$</span> and <span class="math-container">$H_1: \mu \ne 100$</span>.
Let's assume the true weight is 102.</p>
<p>In the course of testing we may calculate metrics, such as the type 1 e... | <p>If the power of your test of <span class="math-container">$H_0: \mu=100$</span> against <span class="math-container">$H_a: \mu\ne 100$</span> is sufficient, you will likely reject <span class="math-container">$H_0.$</span> So the test has not been useless. Furthermore, it is
good statistical practice to accompany th... | 309 |
hypothesis testing | interdependence of type 1 error and type 2 error in p-Value based hypothesis tests | https://stats.stackexchange.com/questions/225183/interdependence-of-type-1-error-and-type-2-error-in-p-value-based-hypothesis-tes | <p>Investigating a t-Test, I ran some "experiments", generating randomly distributed values around a given mean, and running a whole bunch of t-test (always with new data) for conditions where the null-hypothesis is true, and I indeed found, that the type 1 error, the ratio of the number of times the t-test incorrectly... | <p>To summarize, you find that if you use a lower p-value as threshold to reject hypotheses, the type I error goes down and the type II error goes up.</p>
<p>This should make sense; if you use a lower threshold (in terms of p-values) for rejecting a null hypothesis, you will be rejecting fewer hypotheses. For one, tha... | 310 |
hypothesis testing | Hypothesis testing options on non-normal populations | https://stats.stackexchange.com/questions/226282/hypothesis-testing-options-on-non-normal-populations | <p>Can a hypothesis test be performed if I have a non-normal population, small sample size, but population standard deviation is known? We are testing if the mean differs from the given mean.</p>
| <p>The <a href="https://en.wikipedia.org/wiki/Student%27s_t-test" rel="nofollow">t-test</a> is <a href="http://thestatsgeek.com/2013/09/28/the-t-test-and-robustness-to-non-normality/" rel="nofollow">quite robust</a> to departures from the assumption of normality. Intuitively, the reason for this is that the T statistic... | 311 |
hypothesis testing | How can I test whether the mean return of stock indices is 0? | https://stats.stackexchange.com/questions/229270/how-can-i-test-whether-the-mean-return-of-stock-indices-is-0 | <p>I have daily return data for SPX over 50 years. And I calculate the mean return by just taking arithmetic average. I want to test the hypothesis whether the mean is 0.</p>
<p>Can I use the t statistic, which is (mean-0)/sample varirance, to test whether the mean return is 0? If not, what statistic should I use? Tha... | <p><strong>Can I use the t statistic to test whether the mean return is 0? If not, what statistic should I use? Thanks.</strong></p>
<p>Two factoids: Yes you can, but probably no you shouldn't. Stock prices cannot be negative, consequently, the differences between stock prices are limited below by what you paid for th... | 312 |
hypothesis testing | setting up hypothesis testing problems | https://stats.stackexchange.com/questions/230891/setting-up-hypothesis-testing-problems | <p>I'm trying to do some hypothesis testing for work, but I have to admit that it's a bit trickier when you have to formulate the question yourself.</p>
<p>I have some data of the number of errors in a software we provide in the first 3 months after going live. I also have the number of those errors that are "critical... | <p>pnuts' comment is correct. </p>
<p>If the true rate of critical errors is actually zero, you won't see a single one. (Even then, you can't <em>prove</em> the rate is zero, you can at best give an upper bound -- in a confidence interval sense -- on the rate.)</p>
<p>Conversely if you observe <em>any</em> critical f... | 313 |
hypothesis testing | What to compare - means or variances? | https://stats.stackexchange.com/questions/233648/what-to-compare-means-or-variances | <p>I have dataset about vehicles that crossed a certain singalized intersection (each record is vehicle). I want to model the relationship between the entrance time relative to the yellow onset (independent variable) and the number of vehicles (dependent variable). To this end, I use the following logistic model:</p>
... | <p>Let us look at a simple possible example. Suppose you divide your sample of patients into two groups and give one group your new experimental treatment and the other your old boring control treatment. Even the new exciting treatment will not work equally well for everybody so it may well be that when you measure ser... | 314 |
hypothesis testing | Measuring Difference when AB Testing is not ideal | https://stats.stackexchange.com/questions/234213/measuring-difference-when-ab-testing-is-not-ideal | <p>Normally it is best to be able to set up a randomized AB test to measure if some change is actually better than the original. What about in situations where it is not ideal to AB test? </p>
<p>For example, we are a ride sharing company operating in an area where the amount of drivers are much lower than the amoun... | <p><strong>Edited to reflect revised interpretation of question</strong></p>
<p>If the algorithms were selected based on some mathematical model of consumer behavior, that same model might be used to evaluate the new algorithm and compare its projections directly to the old algorithm. If no model currently exists, one... | 315 |
hypothesis testing | I have to compare pre and post training effectiveness for group of Managers statistically | https://stats.stackexchange.com/questions/234287/i-have-to-compare-pre-and-post-training-effectiveness-for-group-of-managers-stat | <p>I have to compare pre and post training effectiveness for group of Managers who have undergone training programme. I have data based on rank order from 1 to 4 where 1 being the most preferred and 4 being the least preferred . Based on the pre and post data i have to give the percentage improvement in the mangers . W... | <p>If you are just checking only if there are differences between the same group such as before test and after test to see if there are improvements you can use ANOVA. </p>
<p>If you are looking at how much improvement from the test I would use t-test.</p>
<p>This source may interest you for looking at which test to ... | 316 |
hypothesis testing | Hypothesis testing Type I and Type II with erroneous error | https://stats.stackexchange.com/questions/245745/hypothesis-testing-type-i-and-type-ii-with-erroneous-error | <p>I am in a Stats class with a brilliant Professor that I unfortunately do not get everything they say and or do. I have a question of theirs that I would like to see how others address the answer to it. The question is below. I am having trouble connecting how to decipher a Type I and a Type II and how it should be s... | <p>A Type I means to postulate a non existing effect. The manufacturer claims there is an effect of pain relief. So when the error of agreeing with the manufacturer is of type 1, the null hypothesis must be that there isn't an effect.</p>
<p>B The manufacturer still claims pain relief and she is still wrong in agreein... | 317 |
hypothesis testing | Hypothesis Testing of means | https://stats.stackexchange.com/questions/245929/hypothesis-testing-of-means | <p>Can anyone help me out with this question? My notes & textbooks just aren't giving me the explanations I need.</p>
<p>The average household size in a certain region several years ago was 3.14 persons. A sociologist wishes to test, at the 5% level of significance, whether it is decreased now. Preform the test us... | <ol>
<li><p>This would actually be A since the alternative hypothesis is that the household size has decreased. </p></li>
<li><p>Test statistic = (observed-expected)/(standard deviation/sqrt(75).
This is (2.98-3.14)/(0.82/8.66) which = -1.69</p></li>
</ol>
<p>check your parentheses with this calculation. </p>
<ol st... | 318 |
hypothesis testing | Design/invention of Statistical Tests | https://stats.stackexchange.com/questions/246253/design-invention-of-statistical-tests | <p>I was wondering how the statisticians come up with the statistical tests for hypothesis testings and the corresponding tables/distribution? Let's say Wilcoxon Rank Sum Test. Any references with concrete examples would be appreciated.</p>
| 319 | |
hypothesis testing | Which statistical test should I apply? | https://stats.stackexchange.com/questions/248544/which-statistical-test-should-i-apply | <p>I have 2 sets of data.</p>
<p>First set is historical data and samples are taken up to a date. It has 3000 samples.</p>
<p>Second set of new samples are taken after that particular date. It has 400 samples.</p>
<p>I want to compare these two sets of data statistically.</p>
<p>Which test should I apply? Student-T... | <p>You can perform Welch's $t$-test in MATLAB using the function <a href="https://ch.mathworks.com/help/stats/ttest2.html" rel="nofollow noreferrer"><code>ttest2</code></a>. Welch's $t$-test is a version of Student's $t$-test adapted to the case where variances and/or sample sizes may not be equal (both populations sho... | 320 |
hypothesis testing | probability of data ratio increasing | https://stats.stackexchange.com/questions/251393/probability-of-data-ratio-increasing | <p>I have a data set of control and paired test values in which the control variability can be relatively high. I'd like to answer whether or not the the test values have increased relative to controls. Specifically, I wanted to examine the increase as a function (percentage/ratio) of the control value (i.e. divide obs... | <p>The ratio can't differ from 1 without the difference differing from 0. Whether you would have more statistical power to detect differences or ratios will depend on the nature of the distributions of those quantities. A $t$-test would be appropriate if they are normal, or sufficiently close and you have a lot of da... | 321 |
hypothesis testing | Choosing the right regression model | https://stats.stackexchange.com/questions/252302/choosing-the-right-regression-model | <p>I'm trying to see whether the number of salesman per customer entering the store affect the sales amount using a simple OLS regression. Which one is a better model to test the hypothesis? Can you also tell me why?</p>
<p>Model 1:sales= B1+ B2(salesman/customers entering the store). </p>
<p>Model 2:sales=B1 + B2 *s... | <p>Split your sample in two: training and validation. Estimate both models on the training and pick the model that performs the best (in mean squares error) on the validation dataset. </p>
| 322 |
hypothesis testing | Are significance level and critical value the same thing in hypothesis testing? | https://stats.stackexchange.com/questions/252655/are-significance-level-and-critical-value-the-same-thing-in-hypothesis-testing | <p>It seems to me that the alpha value is used behind both concepts. It is the cut off point where you determine whether to reject the null hypothesis or not.</p>
<p>So why are there two names for the same concept?</p>
| <p>They are not the same concept. They are, however, related.</p>
<p>For a simple null hypothesis, your significance level is the type I error rate that you choose, which is the long-run proportion of times you would reject the null hypothesis when the null hypothesis was true (and the other assumptions all held true)... | 323 |
hypothesis testing | Why aren't cox regression models validated against independent test sets in medical literature | https://stats.stackexchange.com/questions/254620/why-arent-cox-regression-models-validated-against-independent-test-sets-in-medi | <p>It has been the standard in many machine learning journals for very many years that models should be evaluated against a test set that's identically distributed but has independently samples from training data, and authors report averages of many iterations of random train/test partitions of a full dataset.</p>
<p>... | <p>Finding independent survival datasets in the public domain for validation is often quite difficult. In addition to requiring all the same features, you need to find a dataset with time and event information. Many studies don't collect this information, and if they do, they probably already did the survival analysi... | 324 |
hypothesis testing | Interpreting hypothesis testing result (assuming that the null hypothesis is true) | https://stats.stackexchange.com/questions/255169/interpreting-hypothesis-testing-result-assuming-that-the-null-hypothesis-is-tru | <p>I have a doubt on how to interpret a result of a hypothesis test. For example, a scenario where I have an existing configuration and also a new configuration. I am trying to check if with the new configuration the program is faster.</p>
<p>The execution of the program in the existing configuration is 70.20 and in t... | 325 | |
hypothesis testing | hypothesis testing for this simple problem | https://stats.stackexchange.com/questions/257413/hypothesis-testing-for-this-simple-problem | <p>I want to know if my system is functional or not base on 30 trials. so what i did is, I have 1 group with 30 trials. the variable for the group is categorical success or fail.
for 30 trials, the system has 30 successes.</p>
<p>how to do the hypothesis testing? i feel like im very wrong. </p>
<p>can i say this?... | <p>Under H0, which assumes that in each run probability of success equals the probability of fails. The probability to obtain N successes is $0.5^N$. In your case p-value= $9.3^{-10}$. </p>
| 326 |
hypothesis testing | Negative t-value | https://stats.stackexchange.com/questions/258169/negative-t-value | <p>I have run a test on a treatment where the mean (of particular performance) after treatment is greater than that before and standard deviation has decreased. My t value is in the -22 area and I have not found a negative t value before. Should I just use the absolute value and check this agains the t-table, as in com... | <p>The t distribution is two-sided and centered around 0, so it is possible to have a negative t statistics. What was the null hypothesis?</p>
| 327 |
hypothesis testing | Can we use t-test for large sample..?? | https://stats.stackexchange.com/questions/260270/can-we-use-t-test-for-large-sample | <p>How can I use t-test, my sample size is 368, my sample is dependent in nature as it is collected from same population over two period of time, population s.d is unknown.</p>
| <p>This is a <a href="https://en.wikipedia.org/wiki/Student's_t-test#Paired_samples" rel="nofollow noreferrer">paired t-test (ref Wikipedia)</a>. It forms one sample by examining the before-and-after differences.</p>
<p>To implement this in Excel, use the code <code>=TTEST()</code> with the <code>type</code> optio... | 328 |
hypothesis testing | What is the right hypothesis test for this problem? | https://stats.stackexchange.com/questions/259126/what-is-the-right-hypothesis-test-for-this-problem | <p>I would like to discuss and analyze what is the best hypothesis test for this problem: </p>
<blockquote>
<p>We have data with the distance that each football player of each team runs in a match. Now we want to find two teams with the most similar pattern (by comparing any combination of teams). </p>
</blockquote>... | <p>"<em>Now we want to find two teams with the most similar pattern</em>" doesn't seem to be a hypothesis testing problem.</p>
<p>Once you define what "most similar" among pairs of patterns for teams is (or conversely, what most dissimilar is), it seems to be a matter of calculation to find the most (or least, if you ... | 329 |
hypothesis testing | statistical test for 3 response answer satisfied , not satisfied , can't say | https://stats.stackexchange.com/questions/264122/statistical-test-for-3-response-answer-satisfied-not-satisfied-cant-say | <p>the survey is for different online payment methods from which replies for which different methods they are satisfied, not satisfied , can't say.which test is to be done in this question.</p>
| <p>It's not completely clear what you are trying to do, but if your dependent variable is the satisfaction measure, then I think ordinal logistic regression would be a good starting point. Or perhaps classification trees. Or multinomial logistic. Or random forests. Or a neural network might work best. </p>
| 330 |
hypothesis testing | Understanding statistical hypothesis tests in paper | https://stats.stackexchange.com/questions/264696/understanding-statistical-hypothesis-tests-in-paper | <p>I'm a stats noob, so I don't really understand the statistic tests that the authors Ross, Greene, and House use to justify their results in their paper <a href="http://web.mit.edu/curhan/www/docs/Articles/biases/13_J_Experimental_Social_Psychology_279_%28Ross%29.pdf" rel="nofollow noreferrer">"The 'false consensus e... | <p>The paper includes the phrase "F-ratio". This is almost certainly the <a href="http://www.statisticshowto.com/f-statistic/" rel="nofollow noreferrer">F-statistic</a> produced during analysis of variance <a href="https://en.wikipedia.org/wiki/Analysis_of_variance" rel="nofollow noreferrer">(ANOVA)</a>. The <a href="h... | 331 |
hypothesis testing | What kind of Non-parametric test to use when huge difference between two sample sizes? | https://stats.stackexchange.com/questions/265360/what-kind-of-non-parametric-test-to-use-when-huge-difference-between-two-sample | <p>I have Type I CD protein data which consists of 27 Enzymes and 217 non-enzymes. I want to determine if there is a significant difference in the length of enzymes versus non-enzyme. What type of non-parametric test should I use if there is a huge difference between the sample size of enzymes versus non-enzyme?</p>
| <p>Use whichever nonparametric test is suited for your particular null and alternative. </p>
<p>None of the usual tests suitable for two independent samples will care that one sample is larger than the other.</p>
<p>Note that "difference in the length" is sort of vague -- if that's as specific as you can be, I'd lean... | 332 |
hypothesis testing | If $p\text{-value}<\alpha$ does the observed test statistic always belongs to critical region? | https://stats.stackexchange.com/questions/265584/if-p-text-value-alpha-does-the-observed-test-statistic-always-belongs-to-cr | <p>Assume we carry out a hypothesis test at the 5% significance level. We have an observed test statistics $t$ with calculated p-value $0.03$. Does that imply that the observation has to lie in the critical region? I mean $3\%$ of the distribution is at least as extreme and the critical region is the most extreme 5% of... | <blockquote>
<p>If p-value<α
does the observed test statistics always belongs to critical region?</p>
</blockquote>
<p>Yes, that's right. </p>
<p>(It doesn't depend on whether the t-test is appropriate as suggested in comments -- the appropriateness of the assumptions doesn't come into this at all; this is a q... | 333 |
hypothesis testing | Which test to use for generalizations | https://stats.stackexchange.com/questions/267033/which-test-to-use-for-generalizations | <p>I'm currently conducting a research in linguistics. The goal is to show the audience preference when it comes to different translation strategies in subtitling. The experiment design has one independent variable with two levels (2 different translations of the same clip), and the dependent variable is the reception ... | <p>You will get a 2x2 table as a result of the experiment. If each person in your sample sees only one version, you could use the chi-square test.</p>
<p>If you get the same 100 people watch both translations and rate them, you might use McNemar's test.</p>
<p>You could read more here: <a href="https://stats.stackexc... | 334 |
hypothesis testing | hypotheses testing | https://stats.stackexchange.com/questions/188433/hypotheses-testing | <p>so I'm new to statistics and am not very comfortable with it yet. It may be a very simple question, but I'm finding this very difficult to understand
In research papers the hypotheses are mostly in a particular direction.
Like "satisfaction is positively related to customer retention"
If this particular hypothesis ... | <p>then satisfaction is not positively related to customer retention. that's all we know .This implies that in statistical hypothesis testing you are unable to find evidence for H0. If one rejects H0 then the only conclusion you can draw is 'We can not prove H0' or 'it is probable that H0 is false and so we accept H1 (... | 335 |
hypothesis testing | How to test whether the average return on S(USD/AUD) of the last 30 days is significantly different from zero at the 5% level of significance? | https://stats.stackexchange.com/questions/188948/how-to-test-whether-the-average-return-on-susd-aud-of-the-last-30-days-is-sign | <p>I have daily returns on S(USD/AUD). Now how to test whether average return of last 30 days is significantly different from zero at 5% level of significance ?</p>
| <p>You may be looking for a so-called "HAC"-test, a "heteroskedasticity and autocorrelation consistent" test for $\mu=\mu_0$:
$$
t_{HAC}=\frac{\bar{Y}_T-\mu_0}{\sqrt{\frac{\sum_{j=-\infty}^{\infty}\gamma_j}{T}}}
$$
We can then approximately (i.e. for $T$ sufficiently large) argue that, under $H_0:\mu=\mu_0$
$$
t_{HAC}\... | 336 |
hypothesis testing | How to Compare Mortality Rates Among 5 Groups | https://stats.stackexchange.com/questions/189639/how-to-compare-mortality-rates-among-5-groups | <p>What statistical test would I use to compare differences in mortality among 5 independent groups? I know chi square can be used for comparing 2 groups.</p>
| <p>You want to see whether the distribution in frequencies among the five groups is consistent with a discrete uniform distribution (null hypothesis) or they are instead different enough to reject the null. To do so, you can use a goodness-of-fit test chi squared test.</p>
<p>If you are using R, you can do something l... | 337 |
hypothesis testing | Proper way to test hypothesis of random selection? | https://stats.stackexchange.com/questions/193301/proper-way-to-test-hypothesis-of-random-selection | <p>Suppose I have $N$ urns, each containing various mixes of red and green balls.
A subject is to make a random selection without replacement of $M$ balls from each of the urns, whereupon a count is made of the red and green for that urn, resulting in a count of these for each urn.</p>
<p>The hypothesis is the selecti... | <p>Summing over all the probabilities that are as or more extreme is perfectly sufficient here, but there are a few things to keep in mind. First, you have to be careful about what you mean by "as or more extreme" here. If you have a particular reason to believe a cheater would prefer picking green over red, then the p... | 338 |
hypothesis testing | How to determine Uniformly most powerful test? | https://stats.stackexchange.com/questions/199027/how-to-determine-uniformly-most-powerful-test | <p>In practice, how do you find the uniformly most powerful test? Would you essentially brute-force all possible hypothesis tests?</p>
<p>Could we prove that there exists a uniformly most powerful test and the one that we are using is sub-optimal?</p>
| <p>For a case of testing simple hypothese, there's a <a href="https://en.wikipedia.org/wiki/Neyman%E2%80%93Pearson_lemma" rel="nofollow">Neyman–Pearson lemma</a> whereas for case of composite hypotheses we've got Karlin–Rubin theorem, which is a bit limiting (to scalar parameters and scalar measurements). Probably ther... | 339 |
hypothesis testing | Why we also consider the opposite signed value of test statistic in two tailed test to calculate P value? | https://stats.stackexchange.com/questions/200768/why-we-also-consider-the-opposite-signed-value-of-test-statistic-in-two-tailed-t | <p>Why P value of a 2 tailed test is multiplied by 2 [=2 X P(Z>tcal)? I am looking for a answer which may explain the underlying reason except the answer 'because it is a two tailed test'. Why we also consider the opposite signed value of test statistic in two tailed test to calculate P value?</p>
| <blockquote>
<p>why the P value of a two tailed test is multiplied by 2?</p>
</blockquote>
<p>Not all two-tailed tests have the property that a p-value of a two-tailed test should be double the p-value of a one-tailed test.</p>
<p>However, tests where </p>
<p>i. being in either of the tails are mutually exclusive ... | 340 |
hypothesis testing | Is the choice of test statistics in hypothesis testing a completely philosophical one? | https://stats.stackexchange.com/questions/203868/is-the-choice-of-test-statistics-in-hypothesis-testing-a-completely-philosophica | <p>Is the choice of test statistic in hypothesis testing a completely philosophical one? In other words, is the choice of test statistic and rejection/acceptance region a completely judgement call and is not bounded by any requirment?</p>
| <p>I am assuming that you are asking about the choice of test statistic within a specific statistical model rather than asking about the choice of statistical model. I am also assuming that you are asking about the test statistic to be used in a classical hypothesis test in the accept/reject manner.</p>
<p>The choice ... | 341 |
hypothesis testing | To use the right model and analysis | https://stats.stackexchange.com/questions/204690/to-use-the-right-model-and-analysis | <p>I have a dataset, <code>data</code>, that contains <code>user</code>, <code>game_played</code>, <code>amount_spent</code> and <code>amount_won</code>. So <code>head(data)</code> gives</p>
<pre><code>user game amount_spent amount_won
14 4 186 120
14 2 200 80
10 2 65 ... | <p>It is worth noting that a statistician should not look for "causation" as much as "association." There is no statistical method for identifying causation. In addition, the data set does not appear to have a variable that indicates when the user begins playing a game and when he stops playing a game. A user is always... | 342 |
hypothesis testing | One Sided Null Hypothesis - 2 Interpretations | https://stats.stackexchange.com/questions/205958/one-sided-null-hypothesis-2-interpretations | <p>I've been reading around about hypothesis testing. I don't understand why the following one sided tests are equivalent:</p>
<p>$H_0:\mu \leq \mu_0$; $H_a:\mu > \mu_0$</p>
<p>and</p>
<p>$H_0:\mu = \mu_0$; $H_a:\mu > \mu_0$</p>
<p>Any thoughts?</p>
<p>Edit:
I think I understand why they are equivalent. Anyt... | <p>I do not think those are equivalent and in fact I believe one of them </p>
<blockquote>
<p>H0:μ=μ0; Ha:μ>μ0
is incorrect. </p>
</blockquote>
<p>Philosophically, the 'rules' for forming the Ho and the Ha are that they be
a-mutually exclusive and b-exhaustive, and so I think technically that form of the null is... | 343 |
hypothesis testing | Which Hypothesis Test should I apply in this case? | https://stats.stackexchange.com/questions/206240/which-hypothesis-test-should-i-apply-in-this-case | <p>A system produces samples. I have historical data as thousands of samples. I know the number of samples, their mean and their standard deviation. This data was collected by using the same system.</p>
<p>But recently the system was modified. And I have around 30 new samples after the system update. I know the number... | <p>I think that a single sample Z-test would be appropriate as you suggest that the samples that you are in possession of have a mean and standard deviation. Conceptually, you would be treating the population of samples which you have as a true population. It's mean would be equal to the mean of all the samples' means.... | 344 |
hypothesis testing | What is p-value in simple words and good non-mathematical examples? | https://stats.stackexchange.com/questions/205653/what-is-p-value-in-simple-words-and-good-non-mathematical-examples | <p>Can someone explain in simple words and with many good down-to-earth examples what is the p-value and how do we find it? </p>
<p>Is it true that it shows what is the probability that the sample we have tested is true not simply by chance? Isn't that the point of the alpha level to guarantee that for an instance, fo... | 345 | |
hypothesis testing | hypothesis test_ determine null and alternative | https://stats.stackexchange.com/questions/208622/hypothesis-test-determine-null-and-alternative | <p>What is the most suitable null and alternative hypothesis for following problem? </p>
<blockquote>
<p>It is believed that the average level of Prothrombin in a normal
population s 20 mg/100 ml of blood plasma with a standard deviation
of 4 mg /100 ml. To verify this, a sample is taken from 40
individuals in... | <p>The answer sheet seems to suggest an answer that I think is wrong for several reason:</p>
<ol>
<li>the tested hypotheses depend on the observed data, </li>
<li>the tested hypotheses include the sample size (why?!!) and </li>
<li>are seemingly unrelated to hypothesized value that is to be verified (20 mg/100 ml).</l... | 346 |
hypothesis testing | Comparing difference between two subsets | https://stats.stackexchange.com/questions/213652/comparing-difference-between-two-subsets | <p>I have a large sample of 800 participants who completed a measure of relationship at 2 time points. The result of a paired-samples t-test indicates that there was no statistically significant difference between both time points. I then split the group into high risk and low risk subsets of participants likely to dev... | <blockquote>
<p>I feel that one subset should be significant relative to the other?</p>
</blockquote>
<p>From what you posted it doesn't sound like that's the comparison you were making but rather that you were comparing time t1 with time t2 in both subgroups. If that is the case I don't see any reason why the subgr... | 347 |
hypothesis testing | a hypothesis test for evidence that one thing is dependant on another | https://stats.stackexchange.com/questions/215070/a-hypothesis-test-for-evidence-that-one-thing-is-dependant-on-another | <p>I'm not sure what the null hypothesis for this would be/ what the correct symbols are.
the data is unpaired and I'm needing to find if there evidence ( at 5% level of significance) that one thing is dependant on another. </p>
<p>for example, is there evidence that the size of the banana is dependant on the plantati... | <p>You might use Chi-Square Test for Independence.</p>
<p>Considering the independence of size of banana and the plantation its grown in.
For simplification, let's assume that those bananas are dividing into $r$ groups according to its size and are grown in $s$ plantations. Denote $A_1, A_2..A_r$ for size level, $B_1... | 348 |
hypothesis testing | Basic Hypothesis Testing | https://stats.stackexchange.com/questions/220246/basic-hypothesis-testing | <p>I'm having trouble with a basic hypothesis testing question that I just thought of. The question is the following: suppose you know that a certain lawnmower manufacturing company (called Company A) makes lawnmowers that run on average 300 minutes before running out of gas with a standard deviation of 30 minutes. Sup... | <p>Regarding your approach:
Confidence interval is a <em>random</em> interval $I$ constructed from the data that contains the unknown parameter of interest $\theta$ with specified probability $1-\alpha$, $\mathbb{P}(\theta\in I)=1-\alpha$. Your interval $(300−1.96∗30,300+1.96∗30)$ is not random, it is constructed from ... | 349 |
hypothesis testing | What is appropriate statistical test for one condition? | https://stats.stackexchange.com/questions/144265/what-is-appropriate-statistical-test-for-one-condition | <p>There is one chemical for plants; in absence of it (control) all 3 of them live. In presence 5 of 6 die, only 1 lives. So how can we show if it is significant or not? It may be basic but I appreciate your help. </p>
| <p>I suggest to use the Fisher's Exact test in order to test if there is a statistically significant difference between the proportions of survivors in the two samples (treatment and control).</p>
<p>Check <a href="http://en.wikipedia.org/wiki/Fisher%27s_exact_test" rel="nofollow">http://en.wikipedia.org/wiki/Fisher%2... | 350 |
hypothesis testing | Why do different statistical tests differ? | https://stats.stackexchange.com/questions/145803/why-do-different-statistical-tests-differ | <p>I heard from the grapevine that when somebody has statistics, some tests may indicate one type of significance, while others do not. The tests themselves may be inconsistent. My question is, what is the fundamental problem that causes the tests to break down? </p>
<p>My answer, which I am not sure if correct or not... | <p>[Beware using the term 'inconsistent' in this context, as <em>inconsistency</em> has a particular technical meaning when applied to hypothesis tests. I'll use it because you did, but with the clear stipulation that it's not taking its technical meaning in this discussion.]</p>
<p>Different test statistics - even wh... | 351 |
hypothesis testing | Interpretation of empirical frequency of null hypothesis rejections | https://stats.stackexchange.com/questions/145286/interpretation-of-empirical-frequency-of-null-hypothesis-rejections | <p>assume I know a theoretical distribution that is quite non-normal.</p>
<p>I simulate many (N) samples of given size (T).</p>
<p>Then for each sample I test if the sample average is equal to the theoretical one (t-test).</p>
<p>Then I look at the frequency of rejections as a function of T.</p>
<p>Let T* the small... | <p>Sounds like you want to do a <a href="http://en.wikipedia.org/wiki/Statistical_power" rel="nofollow">power analysis</a>. There is a large literature on that, so you may want to read that first. However, if you worry about non-normality, then I would start with worrying whether a t-test is appropriate in the first pl... | 352 |
hypothesis testing | A basic question on hypothesis testing | https://stats.stackexchange.com/questions/145293/a-basic-question-on-hypothesis-testing | <p>In hypothesis testing a hypothesis is generally defined to be "a statement about the value of a population parameter". For example the mean value of the height of people living in a certain city.</p>
<p>I do not understand how this applies to the classical example of coin tossing. In coin tossing we test the hypoth... | <p>Let's say you toss your coin 100 times. Then you count how often you've got heads. </p>
<p>Doing this very often you may draw a graph that shows how often you've got one head, two heads, three heads ...up to 100 heads. Your x-axis is 1 to 100 heads, your y-axis is how often you've got it tossing very very often 100... | 353 |
hypothesis testing | Would a t-test apply? Statistical Test Suggestion | https://stats.stackexchange.com/questions/146175/would-a-t-test-apply-statistical-test-suggestion | <p>Given two lists of characters. For example </p>
<p>List #1</p>
<p>A
C
O
P</p>
<p>List #2</p>
<p>A
O
R
T</p>
<p>How would you test whether the two lists differ significantly or not. I feel like a t-test can be applied, but I'm not sure how given I have character values as opposed to numerical values (i.e. I cant... | <p>Your answer makes little sense. You're <strong>NOT</strong> comparing directly the ammio acid or nucleotides. You're trying to conduct a differential expression test of two experiments. The dependent variable is the abundance of each RNA sample and the values are integers.</p>
<p>Comparing directly the ammio acid o... | 354 |
hypothesis testing | Which test to use to compare calculated percentages? | https://stats.stackexchange.com/questions/146479/which-test-to-use-to-compare-calculated-percentages | <p>I have data in the following form:</p>
<pre><code>subject PercA PercB PercC PercD
A1 0.12 0.33 0.40 0.15
A2 0.14 0.31 0.38 0.17
...
B1 0.18 0.30 0.35 0.17
B2 0.17 0.29 0.39 0.15
...
</code></pre>
<p>The percentages in each row sum up to 1 because the percentages ar... | <p>You can possibly rearrange the data and use regression like this: </p>
<pre><code>> mydf
subject num PercA PercB PercC PercD
A 1 0.12 0.33 0.40 0.15
A 2 0.14 0.31 0.38 0.17
B 1 0.18 0.30 0.35 0.17
B 2 0.17 0.29 0.39 0.15
> mm = melt(mydf, id=c('subject','num'))
> mm
subject num variable value
1 ... | 355 |
hypothesis testing | How to estimate relative risk for a small group which has 0 members with the outcome? | https://stats.stackexchange.com/questions/148406/how-to-estimate-relative-risk-for-a-small-group-which-has-0-members-with-the-out | <p>I have a contingency table that looks like this:</p>
<pre><code> Disease Not Disease
Exposed 372 870
Not Exposed 0 23
</code></pre>
<p>What methods would I use to estimate if there is a statistically significant difference between the exposed and... | <p>Expected:-</p>
<pre><code> Disease Not Disease
Exposed 365.24 876.76
Not Exposed 6.76 16.24
</code></pre>
<p>as expected cell values is big enough you can test by Chi-square contingency test.</p>
| 356 |
hypothesis testing | Testing Hypothesis | https://stats.stackexchange.com/questions/148562/testing-hypothesis | <p>I have a sample of 40 data, that shows the average of time a person waits in a gas station line.</p>
<p>Descriptive statistics of this sample are as follow:
N= 40, mean= 115sec, std.dev.=11sec, min=90sec, max=147sec.</p>
<p>I decided to test the following hypothesis:
H0: waiting time = 115sec
H1: waiting time is n... | <p>You can test that hypothesis with the standard t-test. Simply compute:</p>
<p>$$
\frac{t_0 - t_1}{se(t_0)}
$$</p>
<p>Where $t_1$ is the value under the null (that value you think $t$ should have). And $t_0$ is the value of $t$ estimated from your data (the sample mean of 115). $se(t_0)$ is the sample standard dev... | 357 |
hypothesis testing | Test two 1-10 ranking processes on same data and test for statistical significance in the two processes | https://stats.stackexchange.com/questions/149089/test-two-1-10-ranking-processes-on-same-data-and-test-for-statistical-significan | <p>I have one set of data. I have two procedures for making 1-10 ranking of the data (one was used previously and one is a new procedure). I want to do a hypothesis test to see if the ranking is the same or not.</p>
| <p>I would advise you to have a look at one of the follow tests:</p>
<ul>
<li>Wilcoxon signed-rank test </li>
<li>Mann–Whitney U test </li>
<li>Kruskal–Wallis test</li>
</ul>
<p>These tests are generally used when testing with rankings. </p>
<p>I'm pretty sure one of them matches your data and does everything you as... | 358 |
hypothesis testing | Hypothesis test null hypothesis equality | https://stats.stackexchange.com/questions/152928/hypothesis-test-null-hypothesis-equality | <p>If we want to test whether the sample mean is at least 5 meters, how should we state the null hypothesis and alternative hypothesis? Here is what I think:
H0: µ>=5
H1: µ<5
But when determining the p value, I will be looking at a left tail probability isn't it? It just feels weird. So is my H0 and H1 correct?</p>
| <p>You do not want to take H0 as µ>5 because it can't yield assumptions that allows you to draw a distribution to test it. This is the point of null hypothesis testing. <strong>Only H0:µ=5 allows you to do that</strong>. Moreover, in null hypothesis testing, <strong>you want to reject H0</strong> (not accept it), then ... | 359 |
hypothesis testing | Test that a group of probabilities is different from chance - in either direction | https://stats.stackexchange.com/questions/153877/test-that-a-group-of-probabilities-is-different-from-chance-in-either-directio | <p>Suppose I have subjects sort 10 images into the categories "Group A" or "Group B". I want the null hypothesis to be that subjects are randomly assigning the images, and the alternate hypothesis that certain images tend to be assigned to certain categories. Importantly, I do not have an a priori hypothesis about the ... | <p>Conducting a $\chi^2$ test is totally appropriate. Your last sentence:</p>
<blockquote>
<p>My initial thought was to do a chi squared test of homogeneity, but such a test would be punished as the number of images increases, whereas it seems intuitively that my chosen test should become more powerful the more imag... | 360 |
hypothesis testing | Is power always associated with hypothesis testing? | https://stats.stackexchange.com/questions/157296/is-power-always-associated-with-hypothesis-testing | <p>Suppose I know that the true population proportion of a mutation is p = 0.3493119. I want to know that given power = 0.8, what's the proportion of of mutation in my sample of n = 30? Here's what I have so far: </p>
<p>1 - cdf((x-p)/sqrt(p*(1-p)/30) = 0.8
Since p = 0.3493119, I can solve for x and I get x = 0.276055... | <p>I would say "Yes"power is alway associated with hypothesis testing it relates to sample size, type I error and both H1 and H0. </p>
<p>The followings are R code to show the power curve for OP's cases (one tailed at 0.05 level, by approximate a normal distribution. </p>
<pre><code>mu<-30*0.35
sd<-sqrt(30*0.3... | 361 |
hypothesis testing | hypothesis test one-sample vs two-sample | https://stats.stackexchange.com/questions/163543/hypothesis-test-one-sample-vs-two-sample | <p>An industrial process is in place that increases the strength of a metal component. We are tuning a couple of settings on the system to optimize the strength. There are already some settings in place, but I have found some new settings that I would like to make a recommendation to change the system to. The new setti... | <p>You should do a two sample test since you are comparing two samples, each of which has variability that should be modeled. A one sample test would be if you were comparing the mean of a sample to some fixed value.</p>
| 362 |
hypothesis testing | Measure the performance of this year | https://stats.stackexchange.com/questions/164740/measure-the-performance-of-this-year | <p>I am going to measure the performance of this year. The average of the past year records (e.g. 5 years) and this year record will be used to judge how many standard deviation it is and if this year performance has improved or not. However, I have a doubt if the average should also include this year record for calcul... | <p>From a practical standpoint, by including the current year in whatever calculation you want to do, you are probably reducing the chance that the current year's value deviates from whatever baseline expectation you have. </p>
| 363 |
hypothesis testing | Which type of analysis to use? | https://stats.stackexchange.com/questions/166375/which-type-of-analysis-to-use | <p>I'm trying to predict my DV based on IV (predictor variable) scores.
I have a sample size of 62.
DV is categorical (addicted or not addicted).
8 IVs are all continuous (at a push I can lose 3 IVs)
I only have access to SPSS.
Could you help me decide, please, the most appropriate and correct statistical analysis to u... | <ul>
<li>Use continuous data for DV as forcing it to categorical (2 categories -addicted or not addicted) leads to information loss</li>
<li>For 8 (or even 5) predictors, sample size is very less (You may need more sophisticated techniques to handle such data)</li>
<li>Either try to gather more data (recommended)</li>
... | 364 |
hypothesis testing | consequences of rejected/accepted hypothesis | https://stats.stackexchange.com/questions/166934/consequences-of-rejected-accepted-hypothesis | <p>A and B are some statements such that A implies B. I test the null hypothesis that A is true. If my test fails to reject A, does that result say anything about B? Analogously, if instead I test the null hypothesis that B is true, and my test rejects B, can I conclude that A is rejected as well?</p>
| <p>A implies B, understood as <em>logical implication</em>, means that if A is true, then B is true. However if A is false, this says nothing about B, and if B is true, this says nothing about A.</p>
<p>According to that definition, concluding that B is true will shed no light over A. Also, concluding that A is false ... | 365 |
hypothesis testing | Test if the difference is statistically significant in A/B test | https://stats.stackexchange.com/questions/174787/test-if-the-difference-is-statistically-significant-in-a-b-test | <p>Let's say we did an A/B testing, and the click rate for 1 group was 0.4 and for the other group, it was 0.3.</p>
<p>How can we go about testing whether this difference is statistically significant?
I'm thinking getting a p-value from t-test, but what would the null and alternative hypothesis be?</p>
| <p>You can do a test for difference of binomial proportions. You will need to know how many people were presented with A and with B.</p>
<p>For example, if there were 50 shown each, Stata gives the following result:</p>
<pre><code>. prtesti 50 .4 50 .3
Two-sample test of proportions x: Number of ... | 366 |
hypothesis testing | test if two Binomial distribution are significantly different | https://stats.stackexchange.com/questions/179148/test-if-two-binomial-distribution-are-significantly-different | <p>I have two groups of people.<br>
Group one with 16 choosing 1 and 33 choosing 2.<br>
Group two with 10 choosing 1 and 49 choosing 2.<br>
I assume they both follows Binomial distribution. So how can I found out if they are significant different from each other?<br>
(I have used nonparametric method to see they are ne... | <p>You can use a likelihood-ratio test.</p>
<p>There is an example which corresponds exactly to your problem on the wikipedia page :
<a href="https://en.wikipedia.org/wiki/Likelihood-ratio_test" rel="nofollow">https://en.wikipedia.org/wiki/Likelihood-ratio_test</a></p>
<p>The correspondance with your question is: Gro... | 367 |
hypothesis testing | p value in one-sided test | https://stats.stackexchange.com/questions/177792/p-value-in-one-sided-test | <p>$$H_0:\mu=0 \quad\quad H_1:\mu>0 $$
we assume the distribution of the sample is Gaussian.<br>
If $p$-value is very big, sample mean very small, we still accept null hypothesis.<br>
Isn't it counterintuitive? Why are we still using it?</p>
<p>E.g. $x_1,x_2,\ldots,x_n$, sample mean is $-5$, variance is known as... | <p>You have written the null hypothesis incorrectly. For a one sided test its'</p>
<p>$H_0 \mu \le 0 \\
H_1 \mu > 0$</p>
<p>So, in your example, where $\bar{X} = -5$ it is clearly much less than 0 and the null cannot be rejected. That's the price of a one tailed test. </p>
<p>Also, you don't <em>accept</em> th... | 368 |
hypothesis testing | What test should I use for hypothesis with many variables? | https://stats.stackexchange.com/questions/56435/what-test-should-i-use-for-hypothesis-with-many-variables | <p>I have a survey with a list of questions in which respondents can pick their perceived personality traits. Then I have a question that asks respondents about their favorite in-game character's perceived personality and a question that asks respondents about their least favorite in-game character's perceived personal... | <p>There are many ways to approach this problem. One simple and flexible approach is as follows:</p>
<p>1) Come up with a way of computing a coefficient c for each user, such that this coefficient should usually be bigger if your hypothesis is true than if not. For example, you could use</p>
<p>c = sum_{feature in {E... | 369 |
hypothesis testing | Rejection regions nested or not? | https://stats.stackexchange.com/questions/59122/rejection-regions-nested-or-not | <p>When varying the significance level, the rejection regions can be chosen to be nested or not nested. I was wondering what some theoretical and practical considerations are in using either nested or non-nested rejection regions? Thanks and regards!</p>
| <p>It is not quite true that the rejection regions can be "chosen" to be nested or not. For simple hypotheses, and a continuous test statistic, the rejections regions of maximal power tests are surely nested via the Neyman-Pearson Lemma. The same goes for composite hypotheses and UMP tests.</p>
<p>GLR tests do not gua... | 370 |
hypothesis testing | Seeking to understand asymmetry in hypothesis testing | https://stats.stackexchange.com/questions/21967/seeking-to-understand-asymmetry-in-hypothesis-testing | <p>I need to have one understanding on statistical hypothesis testing. In a typical hypothesis test, we have 2 opposite hypotheses; namely Null and Alternative. Here my textbook says that "those 2 hypotheses are not symmetrical in the sense that if we swap the hypotheses then the result will alter".</p>
<p>Here I am u... | <p>I suspect it means that if you perform a test for H1 with null H0 and are not able to reject the null hypothesis, that does not imply that if you performed a test for H0 with H1 as the null that you would be able to reject H1.</p>
<p>The reason is that failing to reject the null hypothesis does not mean that the nu... | 371 |
hypothesis testing | Hypothesis tests for exponential growth? | https://stats.stackexchange.com/questions/649267/hypothesis-tests-for-exponential-growth | <p>Is a standard test applicable for situations involving exponential growth? I don't have a 'problem on my desk' that I need to solve. This is just a curiosity. Examples might include mitosis of bacteria or compounding interest for an investment.</p>
<p>In this context, we would have panel data for two different group... | <p>With hypothesis testing for exponential growth, your proposed approach of using a log-transformed response variable and linear regression seems reasonable to me. What follows is a more detailed explanation and a refined version of the model considering the comments provided in the OP, particularly those of MattF.</p... | 372 |
hypothesis testing | Evaluating total effect on population after conducting a/b test | https://stats.stackexchange.com/questions/659770/evaluating-total-effect-on-population-after-conducting-a-b-test | <p>I conducted an A/B test where the treatment involved offering discounts to customers. However, after the test concluded, I discovered that the discount was not consistently displayed to customers in the test group due to an additional logic layer that determined whether the discount was significant enough to be show... | <p>What actually happened in your experiment is that, instead of the "treatment" being "offer discount to customers", it was "offer discount to customers only if discount is <em>substantial</em>" (I would not use the word <em>significant</em> here on CV, to avoid confusion between colloqui... | 373 |
hypothesis testing | Given big enough sample size, a test will always show significant result unless the true effect size is exactly zero. Why? | https://stats.stackexchange.com/questions/323862/given-big-enough-sample-size-a-test-will-always-show-significant-result-unless | <p>I am curious about a claim made in Wikipedia's article on <a href="https://en.wikipedia.org/wiki/Effect_size#Relationship_to_test_statistics" rel="noreferrer">effect size</a>.
Specifically:</p>
<blockquote>
<p>[...] a non-null statistical comparison will always show a statistically
significant results unless th... | <p>As @Kodiologist points out, this is really about what happens for large sample sizes. For small sample sizes there's no reason why you can't have false positives or false negatives. </p>
<p>I think the $z$-test makes the asymptotic case clearest. Suppose we have $X_1, \dots, X_n \stackrel{\text{iid}}\sim \mathcal N... | 374 |
hypothesis testing | Equivalence test for two multivariate normal distributions? | https://stats.stackexchange.com/questions/55298/equivalence-test-for-two-multivariate-normal-distributions | <p>I'm trying to compare two samples from multivariate normal distributions to see if their distributions are equivalent (within a factor of epsilon).</p>
<p>The standard version of this test is the <a href="http://en.wikipedia.org/wiki/Energy_distance#Testing_for_equal_distributions" rel="nofollow">energy test</a>, b... | <p>If you actually have the confidence interval, your first option is right. It's the TOST. Please remember to take the $1-2\alpha$-confidence interval to get an $\alpha$-level test. If this confidence interval is a subset of your prespecified equivalence region, you may conclude that the distributions are equal up to ... | 375 |
hypothesis testing | Why can't we accept the null hypothesis, but we can accept the alternative hypothesis? | https://stats.stackexchange.com/questions/587383/why-cant-we-accept-the-null-hypothesis-but-we-can-accept-the-alternative-hypot | <p>I understand it's reasonable only to not reject the null hypothesis. But why can we accept the alternative hypothesis?</p>
<p>What's the difference?</p>
| <p>I'll start with a quote for context and to point to a helpful resource that might have an answer for the OP. It's from V. Amrhein, S. Greenland, and B. McShane. Scientists rise up against statistical significance. <em>Nature</em>, 567:305–307, 2019. <a href="https://doi.org/10.1038/d41586-019-00857-9" rel="noreferre... | 376 |
hypothesis testing | Why the probability of rejecting the null hypothesis tends to 1 in this case? | https://stats.stackexchange.com/questions/627209/why-the-probability-of-rejecting-the-null-hypothesis-tends-to-1-in-this-case | <p>Suppose we have an estimator <span class="math-container">$\hat\mu$</span> of population parameter <span class="math-container">$\mu$</span> and we know that</p>
<p><span class="math-container">$$\sqrt{N}(\hat\mu-\mu)\overset{d}{\to}N(0,1).$$</span></p>
<p>We are interested in the following hypothesis scheme:</p>
<p... | <p>Sort of, but not quite: <span class="math-container">$\hat\mu$</span> being exactly zero isn't needed and you've left out some important information.</p>
<p>Consider the distributions. If <span class="math-container">$\mu=\delta$</span>, then <span class="math-container">$$\sqrt{N}(\hat\mu-\delta)\stackrel{d}{\to}N(... | 377 |
hypothesis testing | What if both null hypothesis and alternative hypothesis are wrong? | https://stats.stackexchange.com/questions/365604/what-if-both-null-hypothesis-and-alternative-hypothesis-are-wrong | <p>In hypothesis testing, alternative hypothesis doesn't have to be the opposite of null hypothesis. For example, for $H_0: \mu=0$, $H_a$ is allowed to be $\mu>1$, or $\mu=1$. My question: <em>Why is this allowed</em>? What if in reality, $\mu=-1$ or $\mu=2$, in which case if one applies, say, likelihood ratio test,... | <p>What you've identified is one of the fundamental flaws with this approach to hypothesis testing: namely, that the statistical tests you are doing do not assess the validity of the statement you are actually interested in assessing the truth of.</p>
<p>In this form of hypothesis testing, $H_a$ is <em>never</em> acce... | 378 |
hypothesis testing | Why do we need alternative hypothesis? | https://stats.stackexchange.com/questions/386982/why-do-we-need-alternative-hypothesis | <p>When we do testing we end up with two outcomes.</p>
<p>1) We reject null hypothesis</p>
<p>2) We fail to reject null hypothesis. </p>
<p>We do not talk about accepting alternative hypotheses. If we do not talk about accepting alternative hypothesis, why do we need to have alternative hypothesis at all? </p>
<p><... | <p>There was, historically, disagreement about whether an alternative hypothesis was necessary. Let me explain this point of disagreement by considering the opinions of Fisher and Neyman, within the context of frequentist statistics, and a Bayesian answer.</p>
<ul>
<li><p><em>Fisher</em> - We do not need an alternativ... | 379 |
hypothesis testing | What is the difference between a hypothesis test of $P(|Z|\geq z)$ versus $P(|Z|\geq |z|)$? | https://stats.stackexchange.com/questions/549552/what-is-the-difference-between-a-hypothesis-test-of-pz-geq-z-versus-pz | <p>For a Z test, in say a Normal Z test with known variance, what is the difference between rejection areas being represented by</p>
<p><span class="math-container">$P(|Z|\geq z)$</span></p>
<p>versus</p>
<p><span class="math-container">$P(|Z|\geq |z|)$</span></p>
<p>For <span class="math-container">$P(|Z|\geq z)$</spa... | <p>Well, if you have chosen <span class="math-container">$z$</span> to be a positive number, there is no difference between the two tests and the <em>description</em> of the rejection region as the set
<span class="math-container">$$\{Z \geq z\}\cup \{Z \leq -z\}.\tag{1}$$</span>
Note that what you have <em>stated</em>... | 380 |
hypothesis testing | Why type I error rate is rejection area in hypothesis testing? | https://stats.stackexchange.com/questions/561321/why-type-i-error-rate-is-rejection-area-in-hypothesis-testing | <p>In hypothesis testing, we set up a rejection area for rejecting <span class="math-container">$H_0$</span> in favor of <span class="math-container">$H_1$</span> with <span class="math-container">$\alpha$</span>. I don't understand why type I error (rejecting <span class="math-container">$H_0$</span>, when <span class... | <p>by <a href="https://en.wikipedia.org/wiki/Type_I_and_type_II_errors" rel="nofollow noreferrer">wiki</a>,</p>
<blockquote>
<p>a type I error is the mistaken rejection of an actually true null hypothesis</p>
</blockquote>
<p><span class="math-container">$\alpha$</span> has the same value as type 1 error but you can di... | 381 |
hypothesis testing | Is a test with small effect size and high sensitivity meaningful or useful? | https://stats.stackexchange.com/questions/67676/is-a-test-with-small-effect-size-and-high-sensitivity-meaningful-or-useful | <p>From <a href="https://stats.stackexchange.com/a/2519/1005">a reply by John</a></p>
<blockquote>
<p>What is true is that trivially small effects can be found with very large sample sizes. That does not suggest that you shouldn't have such large sample sizes. What it means is that the way you interpret your finding... | 382 | |
hypothesis testing | Statistical Significance Dependent Populations | https://stats.stackexchange.com/questions/69259/statistical-significance-dependent-populations | <p>I am hoping to understand best way to test statistical significance between 2 dependent population groups. </p>
<p>For example, consider a usability test. When 100 subjects were tested, 50 of them clicked (=50% click rate). However, 50 of the subjects were male, 40 of whom clicked for an 80% click rate for males.</... | <p>You seem to have gone on a convoluted route to asking for how to assess independent count data. You've got 100 independent items. There are 40 males that clicked, 10 males that didn't click, 10 non-males that clicked, and 40 non-males that didn't click. You can easily construct what is called a contingency table (b... | 383 |
hypothesis testing | What statistic procedure to use for analyzing my data? | https://stats.stackexchange.com/questions/74684/what-statistic-procedure-to-use-for-analyzing-my-data | <p>I'm currently a fourth year university student. As part of my studies, I'm taking a class called Capstone, where students design and carry out a research project. An essential part of formulating this research is choosing a statistical procedure with which to analyze and present your results.</p>
<p>My study focuse... | <p>I think you should do a simple pairwise difference comparison (before and after workshop) for each question separately.</p>
<p>Since you will probably use some Likert scale in your questionnaire (such as "Strongly agree", "Agree", etc.) your data will be ordinal.</p>
<p>You can use the Wilcoxon signed rank test, t... | 384 |
hypothesis testing | Testing on non-normal distributed discrete values | https://stats.stackexchange.com/questions/79653/testing-on-non-normal-distributed-discrete-values | <p>I have the following observations</p>
<p>Oberservation ; Count </p>
<p>-1.67 ; 726 </p>
<p>18.33 ; 33</p>
<p>148.33 ; 15</p>
<p>This is obviusly not normal distributed :S</p>
<p>How can I make a test for $H_0: \mu = 0$ or even better is it possible to make a confidence interval for the mean?</p>
| <p>While the original distribution is clearly non-normal, the sample size is so large that the distribution of the mean will be approximately normal:</p>
<p><img src="https://i.sstatic.net/opAdp.png" alt="enter image description here"></p>
<p>(that's the distribution of the sample mean for 10000 samples of the same s... | 385 |
hypothesis testing | Am I doing my quantitative study on GitHub right? | https://stats.stackexchange.com/questions/79957/am-i-doing-my-quantitative-study-on-github-right | <p>I am trying to do a small case study in 24 hours + change.</p>
<p>For a dataset, I'm using <a href="http://ghtorrent.org" rel="nofollow">GHTorrent.org</a>.</p>
<p>A general assumption about virtual work is that richer media leads to greater productivity. I have decided to focus on <a href="http://github.com" rel="... | <p>Seems like an interesting project, and that does seem reasonable, though with some caveats. So here's some thoughts I have.</p>
<p>First, you will encounter right-censoring, that is, there will be reported bugs that are still not resolved past the end of your dataset. You <em>absolutely cannot</em> just use the res... | 386 |
hypothesis testing | Statistical test for a random die roll? | https://stats.stackexchange.com/questions/80555/statistical-test-for-a-random-die-roll | <p>Suppose I roll a six-sided die 1000 times and write down the number of times each face comes up. How do I test whether the die is fair? Can I use a chi-squared test where the expected number of each face is 1000/6=167?</p>
<p>There also appears to be a <a href="http://en.wikipedia.org/wiki/Multinomial_test" rel="... | <p>Apply the chi-square test of goodness of fit with number of possible cases - 1 degrees of freedom and the null hypothesis being the discrete uniform distribution as you pointed out. This is a textbook example for that.</p>
| 387 |
hypothesis testing | Simple Question About Hypothesis Testing | https://stats.stackexchange.com/questions/82752/simple-question-about-hypothesis-testing | <p>I'm trying to test whether or not it's true that people of similar heights tend to marry each other, and I'm a bit confused how exactly to go about it.</p>
<p>I have a data set with 96 pairs of the heights of husband and wife, so I thought I could just take the mean of the differences in height between husband and ... | <p>one questions :
why you set your Null hypothesis like this ? (how you come up to set mean to 15).</p>
<p>Basically, for every statistical testing, the null hypothesis already defined. for example,in your case, you would assume the your Null hypothesis is: μ=o ,then you will calculate the T-test for it and w.r.t th... | 388 |
hypothesis testing | Rejection region or p-value | https://stats.stackexchange.com/questions/82754/rejection-region-or-p-value | <p>I am writing a research paper where I am using an hypothesis test.</p>
<p>Is it better to give a p-value for this test or use a 5% two-tailed rejection region?</p>
<p>Thanks in advance!</p>
| <p>In situations like these - it's best to look at things from the reader's perspective. Would the reader care about the actual value of the test statistic? Do you want the reader to know that the $T$-statistic is $2.79$ or $F = 8.91$? In most cases, the reader would not be interested in these values, so just give the ... | 389 |
hypothesis testing | How can I determine which of two complementary hypotheses should be the null? | https://stats.stackexchange.com/questions/88200/how-can-i-determine-which-of-two-complementary-hypotheses-should-be-the-null | <p>How can you determine the direction of the test by looking at a pair of hypotheses? How can you tell which direction (or no direction) to make the hypothesis by looking at the problem statement (research question)?</p>
| <p>Since we test assuming that the null is true, the null has to include a way to determine a sampling distribution. This means that if one of the hypotheses includes an $=$ and the other does not, then the one with the $=$ is the null. For example if the hypotheses are $\mu \ge 0$ and $\mu < 0$ then the 1st is th... | 390 |
hypothesis testing | Which statistical test? | https://stats.stackexchange.com/questions/90339/which-statistical-test | <p>I am designing my study, but I am a little stuck in which test I eventually should use. I have a between-subject design with 6 conditions (let's say A, B, C, D, E, F), with each having 6 responses (let's call these a, b, c, d, e, f), on a 7-point scale:</p>
<pre><code>IV (condition) -> DV
A -> a, b, c, d, e, ... | <p>Can you please clarify you variable and their measurement scale?</p>
<p><strong>6 conditions (let's say A, B, C, D, E, F)</strong> represents 6 input variables or 6 categories of one input variable.</p>
<p><strong>Each having 6 responses (let's call these a, b, c, d, e, f), on a 7-point scale</strong>. Is it one o... | 391 |
hypothesis testing | How to do this test? | https://stats.stackexchange.com/questions/90859/how-to-do-this-test | <p>Suppose I have a sample $\{(x_{1i}, x_{2i}, \dots, x_{mi}), i=1,\dots, n\}$of $m$ unknown random variables $X_1, X_2,\dots, X_m$. </p>
<p>How can I test if $X_1 = X_2 =\dots = X_m$?</p>
<p>Furthermore, if there is a nonrandom explanatory variable $Y$ such that $Y=y_j$ for $X_j, j=1, \dots, m$, how can I test if $Y... | <p>The first question is addresed by one-way ANOVA (between- or within-subjects, depending on whether your $m$ samples are independent or linked). </p>
<p>Are the values of your explanatory variable pairwise comparable? If they are, you could, for example, reorder your samples in such a way that $y_1\leq\dots\leq y_m$... | 392 |
hypothesis testing | Hypothesis testing with the geometric distribution for dummies | https://stats.stackexchange.com/questions/93244/hypothesis-testing-with-the-geometric-distribution-for-dummies | <p>I'm new to stats and I need some help. Can anybody tell me, in the most "beginner friendly" way, how to perform hypothesis testing with a geometric distribution for 2 samples?
please take into account that, until a month ago, Statistics for me was mean, mode and std dev... </p>
| <p>I'm going to assume you want to test equality of the $p$ parameter against the two sided alternative.</p>
<p>The usual way to construct a test would be to make a test statistic from the likelihood ratio, but it's not the only choice. </p>
<p>The LRT takes the ratio of the likelihood for the null to the likelihood ... | 393 |
hypothesis testing | What kind of test should I use? | https://stats.stackexchange.com/questions/95235/what-kind-of-test-should-i-use | <p>I am designing a study for my project.
I wanted to test if music affects reading comprehension. This study will be a between group design. The independent variable is type of music and the dependent variable is the score on a reading comprehension task. </p>
<p>Half of participants will be randomly assigned to a r... | <p>Your design involves two independent samples, so you will be conducting an <em>unpaired</em> test. An unpaired <em>t</em> test would be appropriate to infer mean difference. You could also use a rank sum test, and if the two groups have similar (univariate) distributions of scores, you could infer median difference.... | 394 |
hypothesis testing | proper statistical test to check differences | https://stats.stackexchange.com/questions/95431/proper-statistical-test-to-check-differences | <p>I have 3 replicas for a value in different individuals. Each of these values are ratios $ab$, and $a$ and $b$ are means from $n=20$ sample pool each. Thus there are 3 times each ratio $ab$ for each individual. When comparing for differences is student t-test correct?</p>
<pre><code> 1st sampling - ... | <p>This question is not clear at all, or what the ratios mean. A sample code/structure of the data would be help provide proper context and definition of the problem.</p>
<p>Generally speaking, when you have more than two means to compare, you should not use the t-test because you are inflating your Type II error. If ... | 395 |
hypothesis testing | How to compare two samples without knowledge of the distribution | https://stats.stackexchange.com/questions/95963/how-to-compare-two-samples-without-knowledge-of-the-distribution | <p>lets say I have the mean of two different measurements of something, a and b. I also have the standard deviation on a, and b, but I do not have access to all the individual measurements of a and b. Is it possible to compare the two values to see if the means are statistically different (i.e., reject the null hypothe... | <p>If, as you now say, you don't know the sample sizes but you have sample means and sample standard deviations, the best you can guarantee is say that the sample sizes are at least two (since if either were smaller than two you couldn't compute standard deviations).</p>
<p>So you can at least test for that 'worst cas... | 396 |
hypothesis testing | What test should I use to see correlations between overlapping groups and a score? | https://stats.stackexchange.com/questions/96381/what-test-should-i-use-to-see-correlations-between-overlapping-groups-and-a-scor | <p>To put it simply, I have the courses students have taken and scores on an exam. The students come from different course backgrounds. (Some have taken only course A some only D some A and D some A and B some B C and D etc etc)</p>
<p>What can test can I use to account for this?</p>
| <p>You want to see if grade relates to previous courses taken. That puts you in the regression group. But some students have taken one earlier course, some more than one. There are a couple options. </p>
<p>If the total number of courses that you are interested in is small and your sample is relatively large, then you... | 397 |
hypothesis testing | Hypothesis testing for non-linearity | https://stats.stackexchange.com/questions/96803/hypothesis-testing-for-non-linearity | <p>I have $n_X$ observations of variable X, $n_Y$ of variable Y, and $n_Z$ of variable Z. I'd like to test the hypothesis that the true mean of $X$ is equal to the sum of the means of Y and Z.
$$H_0: \mu_X - (\mu_Y+\mu_Z) = 0$$</p>
<p><strong>Initial thoughts</strong></p>
<p>I can use the sample means to define an ... | <p>Do you know $\sigma^2$? If not then you will need to estimate it from the data (and assume that all 3 variances are equal). So your final formula will probably be a little more complicated than you show, but it can be reduced to something that is (at least approximately) t distributed (though probably done using $... | 398 |
hypothesis testing | Is a data point significantly larger than a certain distribution average? | https://stats.stackexchange.com/questions/99803/is-a-data-point-significantly-larger-than-a-certain-distribution-average | <p>I have a simulated distribution with mean 12.53% and standard deviation 11.83%. The sample size is big enough (10,000) to assume it is a Normal distribution. </p>
<p>How do I properly test if the value "26.05%" is significantly larger than the mean 12.53%?
Can anyone please help me to write the null hypothesis, as... | <p>One fairly simple way is to create a predictor series (x) and place '0' in it except for the point where the specific value is to be challenged place a "1". Estimate a regression model (OLS) between the y values (profit) and the x series. The t value for the predictor series will test the hypothesis that the challen... | 399 |
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