# 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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### Using Chi-Square-Test for single item likert type hypothesis testing?

I conducted a Survey to find reasons why firms invest in a specific asset. I asked them in a Likert-question if different aspects are a reason to invest in [asset]. The Response for each aspect can be:...
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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 ...
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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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### Which statistical significance test should I use to solve this?

Which statistical significance test can i use. all are binary outcomes. Here is my table. I would like to know if there is a significant difference in mortality between the two groups (kidney injury ...
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### Mean Estimation from 1 Sample that gives Mean and Standard Deviation

The title didn't feel right to me either, but here is my problem: I am attempting to estimate the mean of lead concentration using a handheld x-ray gun, which takes a measurement at a point on the ...
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### What is the proper test for sparse binomial data?

I'd like to preface this by saying I am a statistics newbie. I have a single sample from a binomial distribution of some experiment. The exact numbers are: Yes: 1 No: 45 I'd like to determine (1) ...
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### A/B testing for control and test stores

I have historical data for 1000 stores across US. Now I want to introduce an offer in few of the stores (eg 20 Stores) and see its effect on overall sales of those stores after two months. The way I ...
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### t-test on the difference of two independent observations

I want to check if there is any significant difference in my two sets of observations (which are not dependent). Now my first observations have two stages stag1_before and stage2_after same is with ...
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### WALD test for risk ratio/odds ratio

Can I perform a WALD test for the log transformed risk ratio? I have calculated the null log risk ratio and the risk ratio from data. Can I use these two values along with variance of log risk ratio ...
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### Hypothesis test of distributions from two biased samples using NPMLEs

Suppose $X_1, ..., X_n$ is a biased sample (bias mechanism known) from distribution function $F_1$ and suppose $Y_1, ..., Y_m$ is another set of observations sampled in a differently known biased ...
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### Weird thing: The larger my lags, the smaller my Ljung Box test p-values

I am doing analysis to a dataset about U.S. Imports of Goods by Customs Basis from China. I deleted the data of the first 5 years, logged the data, and then decomposed it (or ...
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### How to write the log likelihood for a full model of a negative binomial distribution

I would like to know how to write the log likelihood for a full model of a negative binomial distribution to test a null hypothesis that population mean group1 = population mean group2 vs not equal (i....
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### Significance test for Patient Years

Previously, I had a question about CI for Patient-Years (py) and there was a great answer from @TamasFerenci. Now I need to find out the $p$ value for the py of two different groups. I have a table ...
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### Hypothesis Testing: “Confidence Interval” Nomenclature

I am fairly happy with the concept of confidence interval. In a very basic guise we have a certain level of confidence that a statistic, say the population mean of a random variable, lies in an ...
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### What is the relation between the effect size and correlation?

Correlation refers to the degree to which a pair of variables is linearly related. The effect size quantifies some difference between two groups (e.g. the difference between the means of two datasets)....
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### Testing exam results

Given five exams per student (three oral presentations, two essay based) and between 14 and 24 students per course. Over eight courses the average scores are calculated. The last three courses, ...
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### Is there a way of evaluating the quality of the result of a statistical test? [closed]

Is there a way of evaluating the quality of the result of a statistical test, depending on the representativeness of a sample (or dataset) with respect to the whole population? For example, suppose ...
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### How to calculate a confidence interval for a series of Bernoulli Trials?

I have to test if a event have a p probability of happening. I can run this event as much times I like (given it can be run by a computer). So I was searching a way ...
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### Advantage of the Gail-Simon Test (qualitative/ crossover interaction test)

It is common to use a product of two variables to test whether an interaction is present. In regression analysis, for example, we can include both main effects and the interaction and see whether the ...
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### Why is the concept of the Null hypothesis associated with the student's t distribution?

There are dozens of continuous probability distributions like Gaussian (normal), Variance-gamma, Holtsmark, etc. Yet, the concept of the Null hypothesis is basically associated with Student's t-...
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### What to bootstrap for hypothesis testing

I have a small question about the concept behind hypothesis testing using bootstrap. Assume that I need to evaluate two independent population mean differences: population a and population b. My doubt ...
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### How to model negative, neutral and positive sentiment

I am wondering how best to model sentiment with three categories: negative, neutral and positive. Negative sentiment is represented with a value of -1 Neutral sentiment is represented with a value ...
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### Switching $H_0$ and $H_1$ by replacing $p$ with $1 - p$

I was reading the source code of tseries::adf.test, and it writes ...
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### Leave-One-Out Property (LOOP)

I was reading this paper, and I was looking at the leave-one-out property that they mention in Appendix B. The property is as follows: For $x\in \mathbb{R}^n$, define $x_i$ to be the $i$th element ...
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### Test for equal mean

I have a control experiment and an experiment. In these two experiments, I can detect different peptides. The presence of the peptides in the experiment is measured by determining the concentration of ...
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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 ...