Chi-square test

• To determine if two categorical variables have a significant correlation between them.
• Is used to determine if a difference between observed data and expected data is due to chance, or if it is due to relationship between the variables.
• In chi-square test, the data are frequencies rather than numerical scores.

Formula

i) For goodness of fit test, expected frequency ( f_0­) = p x n

where, P = proportion from the null hypothesis

           n = size of the sample

ii) For test for independence, expected frequency ( f_e) = (row total x column total) / n total

X² = Σ ( f₀ – f_e)²/ f_e

Or, X² =  Σ (O-E)²/ E

Z-test

• A statistical test used to determine whether two population means are different when the variance are known and the sample size is large.

Difference between t-test and z-test.