## How do you test if two samples come from the same distribution?

The Mann-Whitney U test is similar to the Wilcoxon test, but can be used to compare multiple samples that aren’t necessarily paired. The null hypothesis for this test is that the two groups have the same distribution, while the alternative hypothesis is that one group has larger (or smaller) values than the other3.

**Do two samples come from the same distribution?**

While its technically a test of whether they are from different populations rather than the same, if the distributions don’t differ on any of the deciles then you can be reasonably sure they are from the same population, especially if the group sizes are large.

### Which distribution is used to compare two variances?

F distribution

We begin with the F distribution and the test of hypothesis of differences in variances. It is often desirable to compare two variances rather than two averages. For instance, college administrators would like two college professors grading exams to have the same variation in their grading.

**How do you compare two frequency distributions?**

If you simply want to know whether the distributions are significantly different, a Kolmogorov-Smirnov test is the simplest way. A Wilcoxon rank test to compare medians can also be useful.

## How can you use random samples to compare two populations?

How to Compare Two Population Proportions

- Calculate the sample proportions. for each sample.
- Find the difference between the two sample proportions,
- Calculate the overall sample proportion.
- Calculate the standard error:
- Divide your result from Step 2 by your result from Step 4.

**Why is F test used?**

The F-test is used by a researcher in order to carry out the test for the equality of the two population variances. If a researcher wants to test whether or not two independent samples have been drawn from a normal population with the same variability, then he generally employs the F-test.

### What is the difference between F test and t-test?

T-test is a univariate hypothesis test, that is applied when standard deviation is not known and the sample size is small. F-test is statistical test, that determines the equality of the variances of the two normal populations. T-statistic follows Student t-distribution, under null hypothesis.

**How to compare a sample with a distribution?**

When we compare a sample with a theoretical distribution, we can use a Monte Carlo simulation to create a test statistics distribution. For instance, if we want to test whether a p-value distribution is uniformly distributed (i.e. p-value uniformity test) or not, we can simulate uniform random variables and compute the KS test statistic.

## How is the KS test used to compare two distributions?

The idea behind the KS test is simple: if two samples belong to each other, their empirical cumulative distribution functions (ECDFs) must be quite similar. This suggests that we can evaluate their similarity by measuring the differences between the ECDFs. To achieve this, the KS test finds the maximum distance between the ECDFs.

**How to compare two income distributions in practice?**

The red vertical line is the KS test statistic value of the two original samples. As expected, the KS test statistic for the actual income samples is far away from the distribution. This suggests we can reject the null hypothesis that states the income samples are identical (i.e. p-value is zero).

### Can you compare two samples from the same population?

The tests that compare distributions are rule-out tests. They start with the null hypothesis that the 2 populations are identical, then try to reject that hypothesis. We can never prove the null to be true, just reject it, so these tests cannot really be used to show that 2 samples come from the same population (or identical populations).