Is t-test used for categorical variables?
For categorical variables, you can use a one-sample t-test for proportion to test the distribution of categories.
What statistical techniques use to test the relationship between two continuous variables?
For the first of these, the statistical method for assessing the association between two continuous variables is known as correlation, whilst the technique for the second, prediction of one continuous variable from another, is known as regression.
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 are distributions used in a statistical test?
Distributions show what percentage of the data lies within a certain range. So, given a distribution and a set of values, we can determine the probability that the data will lie within a certain range. The same data may lead to different conclusions if they are interposed on different distributions.
How to compare two p-value distributions in practice?
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. By repeating this process 1000 times, we will have 1000 KS test statistics, which gives us the KS test statistic distribution below.
How is the KS test used to compare two distributions?
As a non-parametric test, the KS test can be applied to compare any two distributions regardless of whether you assume normal or uniform. In practice, the KS test is extremely useful because it is efficient and effective at distinguishing a sample from another sample, or a theoretical distribution such as a normal or uniform distribution.