# 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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### Determining the power of the test in this question

The following problem is from Devore's Probability and Statistics for Engineering and the Sciences, 8th edition, exercise 8.1 question 33:
Reconsider the accompanying sample data on expense ratio(%...

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### Hypothesis test for arbitrary distribution

Given a sample of $N$ observed values I'd like to test the null hypothesis that they arose from an arbitrary PDF (for which I have the analytical form). There are tests in place that can handle some ...

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### dhsic.test returning different p-values?

I am using dhsic.test in R, and I have this doubt:
For this example of clearly uncorrelated data I get different p-values:
...

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### Why do we also consider the probability of more extreme events in hypothesis testing? [duplicate]

Why do we also consider the probability of more extreme events in hypothesis testing?
I'm a beginner in statistics and I am trying to understand why do we take into consideration the probability of ...

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### Chow test or simple t-test for the interaction term in regression?

If I want to check whether a specific regression coefficient differs between two samples, let us say men and women, I believe the right approach is to combine the samples, add a men/women dummy, and ...

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### Expected Counts in Chi-Squared Goodness-of-Fit Tests of Normality

I have a variable with of 200 values that I would like to test for normality using the Chi-square Goodness of Fit test. To do this, I have to calculate, for each value, the expected value in a normal ...

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### How to test the significance of order of fixed features among various samples

A practical statistic question was proposed here during my current research work.
There are various sites across the country with identical features, which denote the content of 6 metal species (i.e....

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### Hypothesis test for comparing 6 means to find the greatest result?

I have six groups of continuous data, each representing the performance of a computer program, with which I want to compare the means to find if the one with the greatest performance is such by a ...

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### A/B test sample size calculation

I want to conduct an A/B test where main metric is ālogged in visitors/total visitorsā to my website
I assume, and want to verify with you that Iām correct:
- my null hypothesis is that thereās no ...

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### How to decide between goodness of fit tests

I have a question on BIC and AIC.
I have a data set and I need to test this data set if it fits various distributions (for example, Gamma or Poisson, etc.) I need to use AIC and BIC statistics for ...

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### Proof that p-value equals probability of observing equal or more extreme value of test statistic?

I'm trying to prove Theorem 10.12 in All of Statistics, which states the following:
Suppose that the size $ \alpha $ test is of the form
$$
\text{reject } H_0 \text{ if and only if } T(X^n) \geq ...

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### Bootstrap hypothesis test for median of differences

I have not found any examples of bootstrap hypothesis tests for the median of differences. Hence, I'd like to suggest my approach. Question: Do you a agree that the reproducible example below would be ...

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### AB/Hypothesis testing in multiple groups

Let's say I have two variants of my website and I would like to know which variant generates more revenue. This website operates in multiple countries and I will choose a variant for all countries at ...

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### Test to prove Poker deals are not random

I played on a mobile app of Texas holdem poker called pokerrrr 2. I suspect the game deals non-random hands.
How can I prove the deals are not random?
I prefer a test that can get an answer using ...

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### Correlation between two variables as time series with multiple samples

Main objective
I have two variables ($A$ and $B$) as two time series for $n$ samples, and I would like to test if $A$ and $B$ are correlated. Let's first assume that these $n$ samples are independent ...

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### Hypothesis Test on the Difference between two random vectors

Each of my vectors consists of beta estimates for two separate models of the same data and the same number of explanatory variables. The question is asking whether the difference between these two ...

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### Hypothesis testing for difference in medians vs. median difference

I found this post saying that one should test for the median difference instead of the difference in medians, in particular if the data is skewed: http://onbiostatistics.blogspot.com/2015/12/median-of-...

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### Model selection based on Jarque-Bera, Shapiro-Wilk and Ljung-Box tests

I am kinda new to econometrics
I have six models with Jarque-Bera, Shapiro-Wilk and Ljung-Box results. How can I choose the best model using the tests mentioned above?
Thank you

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### Multivariate One-Tailed Tests

I know when performing hypothesis tests like the z-test or the t-test for one variable, the one-tailed test (when fitting, usually in the case of verifying claims of superiority) provide stricter ...

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### Understanding Hypothesis tests for a Pareto distribution

I'm writing an essay that's looking at the presence of the Pareto Principle in data. Unfortunately, as a consequence of interest, I've picked a topic that involves statistical analysis well above what ...

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### Reason behind the test statistic when testing differences in the means of two normal samples

A well known method of testing the differences between the means of two normal populations (with unknown, equal variances $\sigma^2$), involves computing the test statistic $t=\frac{\overline{X_1}-\...

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### Relationship between two nominal variables with many categories

I have two nominal variables, one with 10 categories and one with 12 categories (n = ~800).
I hypothesise that these variables aren't related, but have been searching for tests that would show a ...

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### How can I show that $\prod^n_{i=1}X_i$ has a monotone likelihood ratio?

We have a random sample $X_1,\cdots,X_n \sim Beta(\theta,1), \theta > 0$ is unknown. My ultimate goal is to find a UMP size $\alpha$ test for $H_0: \theta \le \theta_0$ v. $H_1: \theta > \...

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### Compare two Kolomogorov tests with exponential distribution

I try understanding implementation of Kolomogorov test for one Sample.
...

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### Sample size calculation with multiple conditions

I am interested in computing the required sample size for bioreactor yields. The mean yield should be 60% or more with no yield being less than 25% and at-least 60% of runs should have more that 60% ...

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### Statistical test for non uniform counts

I have data on counts for about 1000 categories in a sample. I want to get an estimate if the counts are somewhat uniformly distributed across 1000 categories, or most of the counts are cominf from ...

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### One tailed test

I was reading about an article on One tailed test and Two tailed test. I know that using one tailed test we focus only in one direction and are not concerned about direction.
I came across the below ...

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### Which statistical test should I use for 1 ordinal and two categorical variables?

It would be great if someone could help me out
I would like to know if there is an association between 3 variables, mental health, having a health plan and income level. Below is a contingency table.
...

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### After derivng a test statistc using p-value combination method, what is the associat null hypothesis

First I generate two one-sided p-values from independent samples using null hypothesis $H_0: \Delta\leq0$, so that $p_1$ and $p_2$ are generated. Next, I apply the inverse normal combination function $...

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### Testing joint hypothesis where one of the parameters is assumed to equal a non-zero value

So I ran a regression and would like to test the the joint hypothesis
$\gamma_0 = \gamma_2 = 0 \text{ , } \gamma_1=\overline{r_m - r_f}$
I'd know how to run an F-test if all were equal to 0 because ...

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### Which specific statistical tests should I use?

I am an amateur researcher. I would like to know for the following data set, which statistical test should I use?
one compression garment and a control garment was tested among ten participants for ...

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### Power of a test in the case of Bernoulli sample

I'm solving the following exercise:
We consider a sample $X_{1}, \cdots, X_{n}$ of size $n$ of the Bernoulli distribution with parameter $\theta,$ where $0<\theta<1$
Prove that this family of ...

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### Can I use inferential statistics from a “non-random” sample of 34000? [duplicate]

I have 10 years of data on football players individual games which works out to 34000 samples. Can I use this to draw inference about football players in general?
Drawing on 3 requirements of CLT ...

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### Comparing experimental and control group consisting of two measures for each participant

I'm conducting an experimental study. For each group (treatment/control) I have measured the biometrics of both eyeballs (left/right) of each participant.
Can I make a comparison between values of ...

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### Random Sample vs. As Large a Sample as Possible?

I'm struggling to differentiate scenarios where you would use random sampling vs. getting as large a sample as possible. For instance, one thing I am trying to test is the notion that being in a "home"...

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### Hypothesis testing variable monotonicity

In my job, I often use variables to build models that traditional business sense would suggest are monotonic in their relationship with the target variable of interest. For example, in business ...

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### In null hypothesis can mu be a non average value? [closed]

In null hypothesis can mu be a non average value? I have come upon some experiments where mu in null hypothesis is not an average of something but only a total number.

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### Wilcoxon Rank Sum Test vs $t$-test Power Simulation

It is well known that the Wilcoxon rank sum test is more powerful for detecting shifts in location when the data is non-normal. However, I am conducting a brief simulation study and my results ...

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### Is a sample collected over 10 years sufficient for testing if not random?

I have aggregated football player box score statistics from the years 2008 - 2018. As a result I have almost 40 thousand observations and I would like to start doing hypothesis testing on this data ...

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### Null Hypothesis P-value Interpretation [duplicate]

I do a two sample comparison with alpha = 0.05. The p-value I get is 0.33. I know that we do not reject the null hypothesis because it greater than 0.05. My question is can I interpret that the 0.33 ...

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### Statistical test to compare success rate in different groups

We had different samples of blood with bacterias. With a new method we tried to quickly identify the bacterias in these samples and then we calculated success rate of our method (we know the correct ...

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### t test for stationarity of time series

How is the t test used for testing the stationarity of time series.
I have tried to search literature which says that if the mean , standard deviation and higher moments of the partitioned time series ...

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### Multiple comparisons problem in survival analysis

I would like to determine which variables have impact on the survival of patients suffering from a disease. It requires performing e.g. log-rank tests. The question is what about the multiple ...

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### Hypothesis Test for how quickly a variable drops off (Neural Network Training)

I have a series of Neural Networks being tested against each other, from which I can calculate the cost on each training example or averaged over some number of examples. Graphing this cost per batch ...

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### Hypothesis Testing Using Tail Probability ā Negative Binomial Distribution

I am comparing count data in treatment versus control.
The question suggests that the count data follows a negative binomial distribution with mean and variance estimated from the controls.
To ...

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### Which statistical test is applicable if the variance within groups is large?

I have multiple groups, each group with 3 replicates so I performed a Kruskal-Wallis One Way Analysis of Variance on Ranks since normality was not achieved; however, post-hoc Tukey tests show no ...

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### P-value from data [duplicate]

Suppose I have a dataset that contains all possible combinations of samples of size 3 from c(11,12,13,14,15). Total of 125 combos. First 6 of 125 combinations are shown below:
I then proceeded to ...

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### Sample Proportion $\hat p$ versus $p$ as the probability of success in a Binomial Distribution

I'm new to hypothesis testing and I have a homework problem which says:
" For a certain coin test,
$H_0: P = 1/2$ against $H_1: P = 1/3$ can be retained where $P$ represents the probability of ...

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### Determine the NULL and Alternate Hypothesis

The following is a question related to Hypothesis testing from an introductory level stats book:
Every year on Groundhog Day (February 2), the
famous groundhog Punxsutawney Phil tries to predict
...

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### Clarification on Bayesian hypothesis testing

I understand the mathematics behind Bayesian hypothesis testing, however I'm struggling to find many examples, specifically ones that apply to the problem I'm working on and was hoping to get some ...