# Questions tagged [hypothesis-testing]

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

6,351 questions
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### Constant value in Neyman Pearson lemma

To know the k value in Neyman Pearson lemma, do we need to know the alternate hypothesis. To what I understood (from articles like PenStateNotes), we could get value of k using null hypothesis and the ...
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### Relationship between Matthews correlation coefficient (MCC) and the Pearson's Chi-square

I would like to find a reference showing that the MCC follows a Chi-square distribution. This is suggested in this Wikipedia article: https://en.wikipedia.org/wiki/Matthews_correlation_coefficient, as ...
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### Statistical test for significance on difference in scoring values on ordinal scale between two groups

Statistical test for significance of the difference in scoring values on an ordinal scale between two groups. Respondents were asked how worried they are about something on a scale between 1 (least ...
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### Is my lottery machine fair?

I have a lottery machine with 100 balls inside. Each trial, I draw 7 of the balls and record their numbers. How do I determine if the results are biased or not?
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### How to compare two samples with not independent observations within each one?

To best of my understanding, both parametric two-sample t-test and non-parametric Mann–Whitney U test assume that observations are independent. I believe that making a permutation test (randomly ...
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### Advantage of the Gail-Simon Test (qualitative/ crossover interaction test)

It is common to use products of original variables as the basis of testing whether interaction is present. In regression analysis, for example, we can include both main effects and the interaction and ...
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### Comparing survival times in overlapping groups

I have a following statistical setup I don't know how to attack: I have two therapies: say A and B. For some patients A works better, for other B works better. I want to direct patients to their ...
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### Comparing heteroscedastic groups with sample sizes from 1 to 24… No valid tests?

I'm comparing 1 continuous variable across 36 groups (nurses grouped into 36 hospital units). Several groups have only 1 observation, but most have more, ranging from 1-24 observations per group. ...
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### Statistical significance of binomial variable when sample sizes are different?

Suppose we have two groups of students given the same difficult test. However, one group of students was given an extra training session before the test. normal students = 123 students with extra ...
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### What test do I use to check if two samples came from different population?

I'm aware that t-test checks if two sample data sets have the same difference in means with confidence. But testing difference in means is not equivalent to testing if the two distributions came from ...
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### Is learning how to do deep learning and machine learning actually harder than learning how to do regression (lm, nlme), t-tests, classical statistics? [closed]

It seems like because most people are still using regression like logits or covariance pattern models and the work of Ronald Fisher to solve problems and machine learning is less popularly used, is ...
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### Hypothesis test for pixel matrix equivalence

I'm going through this tutorial and I'm reworking it in R and I was able to do so. I tried to extend this tutorial by thinking of ways to objectively detect differences in images; e.g., can I run a ...
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### Asymptotic relationship between tests of compact composite nulls and one sided tests

A motivating example Let $x_t\sim N(\mu,1)$ for $t=1,\dots,T$. Consider testing the null $H_0: \mu\in[-1,1]$ against the alternative $H_1:\mu\in\mathbb{R}\setminus [-1,1]$. The natural (UMPU?) test ...
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### What is the correct statistical test?

I'm despaired about planning the evaluation of my experiment for my bachelor thesis and urgently need help with the selection of statistical tests. Brief outline: I want to transfer the mood ...
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### Statistical test to measure whether certain candidates progress further in a job application process

If I have an interview process where people are phone screened, then if they pass then are moved unto another stage, and then another stage etc until they get an offer. I want to identify the ...
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### Reporting difference in distributions for text

I am working on a problem that can be translated to determining which of two corpora generated a given sample text. I have a hypothesis for before some processing and other for after processing, and ...
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### Is chi squared test of independence correct with control group?

I'm analyzing some data from an experiment in which passage of time between conflicting tasks is my independent variable and one of my dependent variables is a dichotomous one ("A","B"). I also have a ...
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### Implementation of Hypothesis test on R² for regressions in cross-sectional setup

I am confused by the paper of Kan et al. (2013 - "Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology") which proposes the execution of hypothesis tests on R² of ...
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### Hypothesis Testing : To Test the presence of Seasonality Given the Seasonal Indices

I was just looking at this tool by Professor Hossein Arsham to check for the presence of seasonality in the data using seasonal indices. https://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/...
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### Using the $Z$-test instead of the binomial test for small $n$ - effect on power and Type I error

Setup Let $M \sim \text{Bin}(p,n)$. Let us then state the following two hypotheses: \begin{align} H_0: p = 0.5 \text{ vs } H_1: p > 0.5 \end{align} To test these hypotheses, I could use the ...
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### Is this a sign of a bad IRT implementation? [on hold]

This data is from the Indonesian UTBK SBMPTN (a university entrance exam). It is said to use Item Response Theory for scoring. I found something interesting about it. The image below shows the ...
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### Test to identify outliers with R

I would like to identify outliers in a sample of 6,000 observations. My variable doesn't follow a normal distribution and my series is spread out on the right. So an extreme value is not necessary an ...
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### Apply normal or not-normal test to heterogeneously normal data sub-sets

I have a dataset made by measuring something on standard dilutions ranging from let's say 10, 100, 1000 and 10000. I checked how the results are distributed with the Shapiro-Wilk test, and it turns ...
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### games-howell test with multiple independent variables

my data doesn't meet the homogeneity of variances criterium. After a welch one way test I wanted to perform a post hoc games-howell test since it doesn't require the homogeneity of variances criterium....
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### Clarification on equal variance vs unequal variance t-test

In unequal variance t-test (Welch t-test): $$H_0 = \text{No difference in means, but variance can differ}$$ $$H_1 = \text{Two sample means are significantly different}$$ I don't see the point of ...
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### Why is the population standard deviation approximated as the sample standard deviation?

This question addresses calculating a p value from the mean and standard deviation statistics of a sample. I understand that the -general- philosophy is to divide the sample standard deviation by the ...