Question

can someone explain when/ how you know when to use a t-test, sign test and the wilcoxon signed rank test.

Answer 1

t test can be used to test the mean of a population or testing the means of two populations provided the population standard deviation(s) of the population(s) is unknown .

Sign test is used to test the null hypothesis that the median of a distribution is equal to some value. It can be used a) in place of a one-sample t-test b) in place of a paired t-test or c) for ordered categorial data where a numerical scale is inappropriate but where it is possible to rank the observations.It is a non-parametric or “distribution free” test, which means the test doesn’t assume the data comes from a particular distribution, like the normal distribution.

The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test that is used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student's t-test ( when the population cannot be assumed to be normally distributed. A Wilcoxon signed-rank test is a non-parametric test that can be used to determine whether two dependent samples were selected from populations having the same distribution.