Question

how do i know when to use a t or chi distribution or any other?

Answer 1

The selection of the t or chi distribution or any other distribution is depends on the testing scenario. If all the conditions are met then you can select proper test. The selection of the test is depends on what is your claim. We can conduct multiple types of tests on the same data. For example, suppose you want to check the claim for the average of a single population, then you should use one sample t or z test. Some of the common scenarios are given below for identifying when to use t or other tests.

Use one/two sample t test for population mean when you don’t know the value for population standard deviation/s and sample sizes are small (n<30).

Use one/two sample z test for the population mean when you know the value for the population standard deviation/s and sample sizes are larger (n>30).

Use Chi square distribution when you are given two categorical variables for independence.

Use Chi square distribution when you want to check whether data follows a specific distribution or not.

Use Chi square distribution when you want to check for population standard deviation or variance.

Use t test for testing population correlation coefficient.

There are hundreds of tests and you need to select the proper test based on your claim, fulfilment of assumptions for test, and some other conditions.