# Questions tagged [two-sample]

The two-sample problem is: given samples X and Y from two distributions, test whether the two underlying distributions are the same. One of the most common classical nonparametric approach is the Kolmogorov-Smirnov test.

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### How to perform a 2 sample Kolmogorov-Smirnov test controlling for a type II error instead of type 1

I have four completely different sets of two samples and want to check for each set if both samples come from the same distribution, so four Kolmogorov-Smirnov tests total. If it's going to be ...
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### How to Run a Standard Two-Sample t-test when given delta and not the two means

I am trying to find the p-value to test a null hypothesis using a Standard Two-Sample t-Test. Usually I would use ...
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### Validity of Bootstrap Inference for Bounds

I am facing the following problem: I have access to iid $X_1,\dots ,X_{N_X}$ and $Y_1, \dots, Y_{N_Y}$ from $F_X$ and $F_Y$, respectively, where $X$ stochastically dominates $Y$. My goal is to conduct ...
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### Two-sample statistical significance test taking into account group membership (proportions) and numeric comparison

Say I have two samples of observations, S1 and S2, which can be of unequal sizes. For each observation, I have two variables: G (a categorical group assignment, say it is binary with values A/B), and ...
1 vote
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### Two sample proportions: How to test the hypothesis that the difference in proportions is less than a specified threshold?

Say I have treatment and control, perfectly randomized. I have 70000 conversions for treatment in 80000 users. I have 70100 converions for control in 800100 users. My null hypothesis is that there is ...
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### Is two-sample Kolmogorov test working correctly?

I have two one-dimensional samples that I'm trying to quantifiably distinguish (or deny such distinction). I.e. the null-hypothesis is that they come from the same population (distribution?). The ...
1 vote
56 views

### Comparing means in Box-Cox transformed data

Deeply sorry as this wasn't really covered in my statistics classes. I am current comparing datasets for people divorcing vs. dissolving their marriages. I have two variables, length of marriage, and ...
1 vote
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### Kolmogorov Smirnov Test Consistency

I was reading that the Kolmogorov Smirnov 2 sample test is consistent, that is Probability of rejection under $H_1$ is 1 for sample size going to infinity. Say we have 2 random variables X and Y. K-S ...
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### Which statistical test is more suitable?

In an exam question I was asked to consider the following data related to education loan taken or not for pursuing higher education and formulate a suitable hypothesis and validate it by using an ...
1 vote
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### When transforming a dataset using the square root (or any other procedure), does the standard deviation of the dataset get transformed too?

Taking an introductory statistics course, and I am confused about the impact of a transformation on the df for a two-sample t-test. The df is dependent on n of each sample and SD of each sample, but I'...
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### Compare two samples when each observation is a pair of dependent values

At an airport there is a company that offers a specific service for travellers (there are no competitors offering the same service at the location). They performed an experiment - they temporarily ...
1 vote
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### Two-sample test + paired/independent samples

This might be an easy question but I got lost in my thinking so thank you for clarifying that for me. So I have some troubles with understanding the ideas of two-sample tests in addition to paired and ...
149 views

### The mean of natural log of some data

I have the following data in natural log: N = [0.929, -1.745, 1.677, 0.701, 0.128] O = [2.233, -2.513, 1.204, 1.938, 2.533] I want to calculate the mean ratio of ...
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### Two-sample test when samples are not completely independent?

Let's say I measure the height of 100 individuals every week in both Illinois and Texas while allowing for the same individual to be measured multiple times in the following weeks. This way, my ...
1 vote
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### Performing a two sample t-test for equal means on subset of a dataset

If I have a dataset that, of among other variables, contains the gender and wealth for a sample of a population with a year variable that represents the year the data about the individual was ...
108 views

### test whether two samples are from the same high dimensional multinomial distribution

I have two high dimensional vectors (~150 dims), assumed to be sampled from multinomial distributions. How can I test whether the two are from the same multinomial distribution or different ones? (...
304 views

### Kolmogorov-Smirnov two-sample test p-value evaluation

I'm using python's scpipy implementation of the Kolmogorov-Smirnov two-sample test (ks_2samp). Q1: Why are my p-values in the examples below so low, specifically on the first example? Q2: Can I ...
183 views

### two-sample Kolmogorov-Smirnov test suggest that sample with the same data generating process from different populations

I have two different samples I need to test if they are drawn from the same population distribution. The two samples are of the volatility of an asset that I simulated. Since the data is simulated I ...
Suppose I have two samples $S_1,S_2$ of categorical data, and I'd like to design a hypothesis test to check the null hypothesis that they are both iid samples from the same underlying distribution. ...