How to compare two p-value distributions in practice?

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 to compare two distributions in real life?

The red line is the actual test statistic and the green line is the test statistic for 1000 random normal variables. By inserting the KS test statistic for the actual sample (i.e. the red line), we can see that the actual KS test statistic is contained inside the distribution.

When is the difference between the actual value and predicted value?

Each actual value has a predicted value and hence each data point has one residual. If the difference between the actual value and the predicted value is positive, then the data points are above the regression line. If the difference between the actual value and the predicted value is negative, then the data points are below the regression line.

How to compare a sample to a theoretical distribution?

1. Sample distribution vs. theoretical distribution When we compare a sample with a theoretical distribution, we can use a Monte Carlo simulation to create a test statistics distribution.

How to calculate the density of two groups?

Use PROC KDE to compute kernel density estimates of the two groups. Use the GRIDL= and GRIDU= options so that the two kernel densities are evaluated on the same grid of points. Use the OUT= option on the UNIVAR statement to write the density estimates to a SAS data set.

What does the difference in densities plots look like?

When I compute the difference in densities, the difference plot will look like the following plot. The difference plot shows that the N (0, 1) distribution is to the left of the other distribution, but the plot doesn’t warn the reader that the two distributions are essentially identical.

How to form difference between two density estimates?

In SAS, you can form the difference between two density estimates by doing the following: Use PROC KDE to compute kernel density estimates of the two groups. Use the GRIDL= and GRIDU= options so that the two kernel densities are evaluated on the same grid of points.

How are probability metrics related to class distribution?

Probability metrics will summarize how well the predicted distribution of class membership matches the known class probability distribution. This focus on predicted probabilities may mean that the crisp class labels predicted by a model are ignored.

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 to compare two distributions using discrete KS?

The following is a procedure to conduct the discrete KS test for two samples: Find the min and max of the combined sample to define our range. e.g. for a sample size of 500, we can expect 25 samples per bin by choosing 20 buckets.

Which is the best test for paired data?

I turned to the paired t-test, which requires normality of difference between the two variables. But is it even possible to use this when the data is discrete? The histogram (with normal distribution plotted on top) and a qqplot can be seen in attached figure.

Why does the t-test work on discrete data?

Just to expand on why the t-test is working: this is a result of the Central Limit Theorem, which tells us that the sample mean has a Normal distribution as n grows. Your data is clearly non-normal, taking discrete values only, but the sample mean will be fairly Normally distributed on account of your large sample size.

How are T-values, probabilities, and t-distributions work?

How t-Tests Work: t-Values, t-Distributions, and Probabilities. T-tests are statistical hypothesis tests that you use to analyze one or two sample means. Depending on the t-test that you use, you can compare a sample mean to a hypothesized value, the means of two independent samples, or the difference between paired samples.