# Questions tagged [hypothesis-testing]

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

6,341 questions
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### Is Chi-Square Correct

I took bacteria samples at 30 grocery stores. Each grocery store was tested for 3 different bacteria types. I then taught a foodborne illness class to the managers of the grocery stores. After ...
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### The equivalence of hypothesis testing and confidence intervals in the test of proportions

Why, in this case, is the test using a confidence interval not equivalent to the test using hypothesis testing, and is it? Hypothesis testing for $H_0: \pi = \pi_0$ $H_1: \pi\neq\pi_0$ A single ...
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### Hypothesis testing of sum of uniform distribution

I want to have some clarifications related to below question from Casella Berger Regarding $\phi_1(X_1),$ I understand that $\alpha$-value is 0.05 and hence we are looking for a value of $C$ for ...
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### How do I interpret the results of this t-test?

I have two datasets, dataset A going from 1980 to 1990, and dataset B going from 1990 to 2000. I wanted to check if there is a significant difference between the two datasets so I ran a t-test. The ...
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### How can you test two datasets to determine if they originate from the same generating process?

I have two feature matrices X_i and X_j, with identical features but their own n - is there a statistical test to determine if the latent data generating process behind X_i is indistinguishable from ...
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### Chi Squared Test to see if a treatment group spent more than a control group

I have two groups of people. One group were shown an ad and the other were not. I know in aggregate that the treatment group spent \$799 and the control group spent \$412, so overall it seems people ...
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### Evaluate methods across datasets based on distance metrics

I want to evaluate $n$ methods, says $M_1,\cdots,M_n$ on $m$ datasets $D_1, \ldots, D_m$. For each method $M$, I have a score function $f(M,D) \in [0, \infty)$ for dataset $D$. A perfect method will ...
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### Tests to use to claim the new classifier is not as bad as the old classifier for a multi-level categorical variable

Here's a example table I have. ...
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### Two-sample unpaired hypothesis test of ROC AUC?

I wish to calculate the p-value to reject the null hypothesis that the AUC, i.e. area under a receiver operating characteristic (ROC) curve, is equal between two independent samples. That is, given ...
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### Is it correct to do a one tailed test based on observed direction? [duplicate]

Suppose I am testing whether there is a difference between the mean of two normally distributed variables X and Y, where ...
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### Prove the relevance of the Pearson correlation distribution for hypothesis testing?

The statistic used in testing $H_0: \rho=0$ versus $H_A: \rho \ne 0$ is: $t_r=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}} \sim t_{n-2}$ in which $r$ is the sample Pearson correlation of two variables, say $X$ ...
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### How to conduct multivariate hypothesis testing?

I have 60 samples which form 1 population. Each contain 9 variables, saying, $X_1, X_2, X_3, X_4, ..., X_9$, continuously ranging from 0 to 10. Now I would like to test if there is anomaly in each ...
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### Difference in results of permutation tests through coin::oneway.test and resample::permutationTest2

I'm trying to run a same permutation test for the null hypothesis of no difference between means with the coin and resample R ...
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### Detecting changing mean and variance using Sequential Probability Ratio Test (SPRT)

I have a process that outputs values that should conform to a normal distribution with a known mean and variance. I would like to perform sequential testing in order to detect changes in the mean and/...
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### Testing equality of difference in coefficients from four regressions

This question is a follow-up/extension to this post. Suppose I have four regressions. $y_i=x_i\beta_i+\epsilon_i,\quad i=1,2,3,4$ I want to test whether $(\beta_1-\beta_2)-(\beta_3-\beta_4)>0$....
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### Hypothesis test for composite null hypothesis of exponential parameter

I'm having trouble defining the reject region based on the generalized likelihood ratio test. This is from a question of past exam I'm self-studying and still have the doubt, given that I got it wrong....
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### How do power calculations for binomial distribution work?

I'll use R for the example calculations. I want do design a controlled study. A usual one-tailed A/B test on the web. So, let's say we have a base conversion rate of 10% and we want to determine our ...
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### Do I want a p-value of 1?

I am doing a biology experiment for the first time, and even though the teacher did not require me to do this, I calculated the p-values for the data on my experiment. They all are above 0.25. From ...
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### What is the equation to calculate the sample size for A/B testing? [closed]

I have been searching for information on how to calculate sample size for A/B testing. My research was fruitless. I found many online calculators, but not any blog/paper that explains how the ...
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### Chi Square Homogeneity Test : proportions & total

In an experiment I observe counts for 2 species of fish on 10 random days in 2017 and 2018 (the number of fish sampled in each year can vary). I'd like to run the chi square test of homogeneity ...
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### Multiple correction for 3 different models

The paper I am reading gives a table of results for 3 different models: The paper doesn't explain how the correction is performed, and it clearly isn't Bonferroni. Does someone have an idea how this ...
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### Diagnostic test to test for change in regressor

In the previous part of this question, I worked out there is a structural change in the Chow test as 5.04> 2.1 (Fc) hence H0 is rejected and the restriction does not hold. In the next part of the ...
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### Calculate power for my test [closed]

I need some help with the following problem: Let's consider a density function $f_\theta(x):=\theta x^{\theta -1}$, with $x \in [0, 1]$, the null hypothesis $H_0: \theta=2$ and the alternative ...
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### Is pseudorandom number generator testing atypical?

Particular pseudo-random number generators are tested for their their ability to produce sequences of numbers that behave like values of independent variables that are each uniformly distributed on [0,...
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### Hypothesis Testing w/ Year Indicator Variables

This is a fairly basic question, but I was hoping that you all could help me nail down the language of this test. I have six years of data in the sample and the following general model: y = b_0 +...
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### Finding a test using asymptotic theory. for Poisson $(\lambda)$

If we have a sample of Poisson $(\lambda)$ (a) Find a test for $H_0: \lambda =2$ vs $H_a: \lambda =\lambda_1> 2$ (b) Find a test using asymptotic theory. (c) Compare the results in en (a) y (...
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### Why is the p-value defined as $P = F(T)$ or $P = 1 - F(T)$ when the null hypothesis is true?

I'm having trouble with the theoretical definition of the p-value. Let $T$ be a test statistic with CDF $F(T)$ and supose the null hypothesis is true. If we were to reject the null hypothesis for ...
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### generalized linear mixed model - model specificating + testing

I would like to examine, if the wording of a person described in a short story (1.”person”, 2. “homosexual person”, 3. “lesbian or gay person”, 4. „gay or lesbian person“) has an effect on the gender (...
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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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### Analysis for ordinal categorical outcome

I am not sure how to evaluate my data correctly, since the outcome (dependent variable) is on an ordinal categorical scale and there are two independent variables. To simplify my experiment: Each ...
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### Test whether two means are significantly different?

I have an anonymized database of a fictional bank with approximately 30,000 entries. These database contains for each customer whether he uses online banking (0 = he doesn't, 1 = he does) and the ...
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### How does bootstrapping (wild) calculate a t-statistic?

I am using the wildbootstrap. Intuitively how do I calculate a t-critical values? Do I use original ones or do I somehow generate them?
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### AB Test - Why are percentages used e.g. click rate, conversion rate?

For running AB test can i use absolute numbers as the performance metric instead of ratios? Is this statistically sound? I want to use number of conversions, instead of conversion rate.
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### Which statistical tool would be useful to check whether a variable has changed significantly over years

I have precipitation data of around 40 years of 10 stations but some missing data in the middle. I want to check whether the precipitation has changed significantly over the decades in the region so ...
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### Statistics: what kind of test to use to test this hypothesis?

I am unsure what kind of a hypothesis test to use in my case: So we are filling 500 ml bottles with water; It's a known fact that before a max of 3% of all the bottles could be under-filled; Now I ...
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### Comparing hazard function of subset and whole data

Is there a way to compare the hazard function that comes from a stochastic process with the hazard function which comes from a subset of that process? Simulations of a stochastic process generate ...
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### If I wanted to see if their was a difference between two groups and paired each person with someone of similar age what test would I do?

I was thinking of doing a paired samples t-test, since we are pairing specific individuals from each group with each other. Is this correct?
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### How to determine the sample size for variance calculation in AB testing?

I am studying AB testing. I can understand that the sample size for AB testing would require the variance information. And many online calculators can provide sample size for each group in AB testing. ...
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### How to check if a distribution is different from uniform distribution using the values only?

I have a discrete empirical distribution, where the values D1 = {1,2,3,7,9,15,16,17,18,19,20} occurs with some different frequencies. The frequencies are not of interest to me. I am interested in how ...
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### Determine which performance intervention is best?

Suppose I have numerical data describing the total process time for a given software simulation. This data is broken up into 5 groups (Base, AD1, AD2, AD3, AD4) each detailing a different performance ...
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### How can I do t.test when I don't have a null value?

I have a dataset containing 20,000 records of home sales. I'm asked Choose a numerical variable from your dataset. 1. Calculate a 98% confidence interval for the mean of this variable. I chose the ...
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### Bootstrapping an 1 and 2 sided tests

Correct me if I am wrong, but I understand that if I have the p-value for a one-sided hypothesis test then I can double it to get the p-value of a two-sided test. Can I do the same thing if I am ...
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### Power of a Poisson hypothesis test

A textbook of mine has online worked solutions, and the answer in the back of the book does not match the answer in the online solutions - they're not even close. My book says that the power of a ...
If we just use the normal distribution, we can find that $\alpha = 0.025$ covers more area at the tails than $\alpha = 0.01$. So it's clear that you may or may not reject at $\alpha = 0.01$. But ...