chi-square and non-parametric tests

chi² test

evaluate whether the observed frequency distribution for categorical variables significantly differs from what we would expect under the null hypothesis

chi² goodness-of-fit test

single nominal variable, and the goal is to determine whether its frequency distribution deviates from randomness or a specific expected distribution

chi² test of association

examines whether there is a significant association between two nominal variables

H₀ - the distribution of one variable is the same across the different categories of the other variable

H₁ - the distribution of one variable depends on the category of the other variable

non-parametric tests

used when data does not meet the assumptions for the t-test

• normality 

• ordinal scale 

use median instead of mean (data is ranked)

wilcoxon rank test

• one sample

• paired samples 

the mann-whitney u test

• independent samples

effect size in non-parametric tests

rank biseral correlationX