Questions tagged [hypothesis-testing]

Hypothesis testing assesses whether data are inconsistent with a given hypothesis rather than being an effect of random fluctuations.

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353
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16answers
125k views

Is normality testing 'essentially useless'?

A former colleague once argued to me as follows: We usually apply normality tests to the results of processes that, under the null, generate random variables that are only asymptotically or ...
278
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What is the meaning of p values and t values in statistical tests?

After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests. It ...
168
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16answers
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Are large data sets inappropriate for hypothesis testing?

In a recent article of Amstat News, the authors (Mark van der Laan and Sherri Rose) stated that "We know that for large enough sample sizes, every study—including ones in which the null hypothesis of ...
141
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8answers
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Is Facebook coming to an end?

Recently, this paper has received a lot of attention (e.g. from WSJ). Basically, the authors conclude that Facebook will lose 80% of its members by 2017. They base their claims on an extrapolation ...
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7answers
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How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples

Certain hypotheses can be tested using Student's t-test (maybe using Welch's correction for unequal variances in the two-sample case), or by a non-parametric test like the Wilcoxon paired signed rank ...
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10answers
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ASA discusses limitations of $p$-values - what are the alternatives?

We already have multiple threads tagged as p-values that reveal lots of misunderstandings about them. Ten months ago we had a thread about psychological journal that "banned" $p$-values, now American ...
106
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7answers
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T-test for non normal when N>50?

Long ago I learnt that normal distribution was necessary to use a two sample T-test. Today a colleague told me that she learnt that for N>50 normal distribution was not necessary. Is that true? If ...
102
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9answers
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Is this really how p-values work? Can a million research papers per year be based on pure randomness?

I'm very new to statistics, and I'm just learning to understand the basics, including $p$-values. But there is a huge question mark in my mind right now, and I kind of hope my understanding is wrong. ...
100
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3answers
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What are examples where a "naive bootstrap" fails?

Suppose I have a set of sample data from an unknown or complex distribution, and I want to perform some inference on a statistic $T$ of the data. My default inclination is to just generate a bunch of ...
95
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2answers
13k views

How much do we know about p-hacking "in the wild"?

The phrase p-hacking (also: "data dredging", "snooping" or "fishing") refers to various kinds of statistical malpractice in which results become artificially statistically significant. There are many ...
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4answers
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When to use Fisher and Neyman-Pearson framework?

I've been reading a lot lately about the differences between Fisher's method of hypothesis testing and the Neyman-Pearson school of thought. My question is, ignoring philosophical objections for a ...
84
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9answers
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Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?

In a multiple linear regression, why is it possible to have a highly significant F statistic (p<.001) but have very high p-values on all the regressor's t tests? In my model, there are 10 ...
81
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9answers
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Regarding p-values, why 1% and 5%? Why not 6% or 10%?

Regarding p-values, I am wondering why $1$% and $5$% seem to be the gold standard for "statistical significance". Why not other values, like $6$% or $10$%? Is ...
80
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191k views

How to obtain the p-value (check significance) of an effect in a lme4 mixed model?

I use lme4 in R to fit the mixed model lmer(value~status+(1|experiment))) where value is continuous, status and experiment are factors, and I get ...
73
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15answers
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Why would parametric statistics ever be preferred over nonparametric?

Can someone explain to me why would anyone choose a parametric over a nonparametric statistical method for hypothesis testing or regression analysis? In my mind, it's like going for rafting and ...
73
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4answers
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A psychology journal banned p-values and confidence intervals; is it indeed wise to stop using them?

On 25 February 2015, the journal Basic and Applied Social Psychology issued an editorial banning $p$-values and confidence intervals from all future papers. Specifically, they say (formatting and ...
71
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3answers
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Is this the solution to the p-value problem?

In February 2016, the American Statistical Association released a formal statement on statistical significance and p-values. Our thread about it discusses these issues extensively. However, no ...
69
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8answers
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What is a good, convincing example in which p-values are useful?

My question in the title is self explanatory, but I would like to give it some context. The ASA released a statement earlier this week “on p-values: context, process, and purpose”, outlining various ...
66
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1answer
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40,000 neuroscience papers might be wrong

I saw this article in the Economist about a seemingly devastating paper [1] casting doubt on "something like 40,000 published [fMRI] studies." The error, they say, is because of "erroneous statistical ...
66
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3answers
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References containing arguments against null hypothesis significance testing?

In the last few years I've read a number of papers arguing against the use of null hypothesis significance testing in science, but didn't think to keep a persistent list. A colleague recently asked me ...
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5answers
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What is the difference between a "nested" and a "non-nested" model?

In the literature on hierarchical/multilevel models I have often read about "nested models" and "non-nested models", but what does this mean? Could anyone maybe give me some examples or tell me about ...
63
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Why does collecting data until finding a significant result increase Type I error rate?

I was wondering exactly why collecting data until a significant result (e.g., $p \lt .05$) is obtained (i.e., p-hacking) increases the Type I error rate? I would also highly appreciate an ...
63
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3answers
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Explain the xkcd jelly bean comic: What makes it funny?

I see that one time out of the twenty total tests they run, $p < 0.05$, so they wrongly assume that during one of the twenty tests, the result is significant ($0.05 = 1/20$). xkcd jelly bean ...
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14answers
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If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?

A basic limitation of null hypothesis significance testing is that it does not allow a researcher to gather evidence in favor of the null (Source) I see this claim repeated in multiple places, but I ...
62
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Two-tailed tests... I'm just not convinced. What's the point?

The following excerpt is from the entry, What are the differences between one-tailed and two-tailed tests?, on UCLA's statistics help site. ... consider the consequences of missing an effect in the ...
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1answer
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How to interpret type I, type II, and type III ANOVA and MANOVA?

My primary question is how to interpret the output (coefficients, F, P) when conducting a Type I (sequential) ANOVA? My specific research problem is a bit more complex, so I will break my example ...
61
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6answers
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Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"?

There exists a certain school of thought according to which the most widespread approach to statistical testing is a "hybrid" between two approaches: that of Fisher and that of Neyman-Pearson; these ...
60
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7answers
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Is chi-squared always a one-sided test?

A published article (pdf) contains these 2 sentences: Moreover, misreporting may be caused by the application of incorrect rules or by a lack of knowledge of the statistical test. For example, the ...
59
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How do I test that two continuous variables are independent?

Suppose I have a sample $(X_n,Y_n), n=1..N$ from the joint distribution of $X$ and $Y$. How do I test the hypothesis that $X$ and $Y$ are independent? No assumption is made on the joint or marginal ...
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3answers
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Testing equality of coefficients from two different regressions

This seems to be a basic issue, but I just realized that I actually don't know how to test equality of coefficients from two different regressions. Can anyone shed some light on this? More formally, ...
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8answers
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Why continue to teach and use hypothesis testing (when confidence intervals are available)?

Why continue to teach and use hypothesis testing (with all its difficult concepts and which are among the most statistical sins) for problems where there is an interval estimator (confidence, ...
56
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3answers
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When combining p-values, why not just averaging?

I recently learned about Fisher's method to combine p-values. This is based on the fact that p-value under the null follows a uniform distribution, and that $$-2\sum_{i=1}^n{\log X_i} \sim \chi^2(2n), ...
54
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4answers
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Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis?

Traditional statistical tests, like the two sample t-test, focus on trying to eliminate the hypothesis that there is no difference between a function of two independent samples. Then, we choose a ...
54
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5answers
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Statistical inference when the sample "is" the population

Imagine you have to do reporting on the numbers of candidates who yearly take a given test. It seems rather difficult to infer the observed % of success, for instance, on a wider population due to the ...
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3answers
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Do we have a problem of "pity upvotes"?

I know, this may sound like it is off-topic, but hear me out. At Stack Overflow and here we get votes on posts, this is all stored in a tabular form. E.g.: post id voter id vote type ...
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5answers
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Correct spelling (capitalization, italicization, hyphenation) of "p-value"?

I realize this is pedantic and trite, but as a researcher in a field outside of statistics, with limited formal education in statistics, I always wonder if I'm writing "p-value" correctly. ...
52
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1answer
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Why do my p-values differ between logistic regression output, chi-squared test, and the confidence interval for the OR?

I have built a logistic regression where the outcome variable is being cured after receiving treatment (Cure vs. No Cure). All ...
51
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8answers
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Statistical tests when sample size is 1

I'm a high school math teacher who is a bit stumped. A Biology student came to me with his experiment wanting to know what kind of statistical analysis he can do with his data (yes, he should have ...
51
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2answers
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Why does frequentist hypothesis testing become biased towards rejecting the null hypothesis with sufficiently large samples?

I was just reading this article on the Bayes factor for a completely unrelated problem when I stumbled upon this passage Hypothesis testing with Bayes factors is more robust than frequentist ...
51
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4answers
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Cumming (2008) claims that distribution of p-values obtained in replications depends only on the original p-value. How can it be true?

I have been reading Geoff Cumming's 2008 paper Replication and $p$ Intervals: $p$ values predict the future only vaguely, but confidence intervals do much better [~200 citations in Google Scholar] -- ...
50
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7answers
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Why is "statistically significant" not enough?

I have completed my data analysis and got "statistically significant results" which is consistent with my hypothesis. However, a student in statistics told me this is a premature conclusion. Why? Is ...
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6answers
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Motivation for Kolmogorov distance between distributions

There are many ways to measure how similar two probability distributions are. Among methods which are popular (in different circles) are: the Kolmogorov distance: the sup-distance between the ...
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3answers
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Bootstrap vs. permutation hypothesis testing

There are several popular resampling techniques, which are often used in practice, such as bootstrapping, permutation test, jackknife, etc. There are numerous articles & books discuss these ...
47
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4answers
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Bayesian equivalent of two sample t-test?

I'm not looking for a plug and play method like BEST in R but rather a mathematical explanation of what are some Bayesian methods I can use to test the difference between the mean of two samples.
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5answers
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Why is multiple comparison a problem?

I find it hard to understand what really is the issue with multiple comparisons. With a simple analogy, it is said that a person who will make many decisions will make many mistakes. So very ...
45
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8answers
62k views

How can I test if given samples are taken from a Poisson distribution?

I know of normality tests, but how do I test for "Poisson-ness"? I have sample of ~1000 non-negative integers, which I suspect are taken from a Poisson distribution, and I would like to test that.
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2answers
55k views

Test for bimodal distribution

I wonder if there is any statistical test to "test" the significance of a bimodal distribution. I mean, How much my data meets the bimodal distribution or not? If so, is there any test in the R ...
41
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8answers
22k views

How to test hypothesis of no group differences?

Imagine you have a study with two groups (e.g., males and females) looking at a numeric dependent variable (e.g., intelligence test scores) and you have the hypothesis that there are no group ...
41
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3answers
8k views

Interpretation of p-value in hypothesis testing

I recently came across the paper "The Insignificance of Null Hypothesis Significance Testing", Jeff Gill (1999). The author raised a few common misconceptions regarding hypothesis testing and p-values,...
41
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1answer
1k views

Are there statistical lessons from the "Bible Code" episode

Although this question is somewhat subjective, I hope it qualifies as a good subjective question according to the faq guidelines. It is based on a question that Olle Häggström asked me a year ago and ...

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