Question

Which one of the following is a non-parametric test?

• A. $X^2$ - test
• B. t - test
• C. F - test
• D. z - test

Answer 1

The Correct Option is A

The Chi-square (\(\chi^2\)) test is a non-parametric test. Non-parametric tests do not rely on assumptions about the underlying distribution of the data. The \(\chi^2\)-test is primarily used for categorical data to assess whether the observed frequencies differ significantly from the expected frequencies, making it a distribution-free test. Mathematically, the test statistic for the \(\chi^2\)-test is given by: \[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \] where:  \(O_i\) represents the observed frequency in category \(i\),  \(E_i\) represents the expected frequency in category \(i\),

 The summation is over all categories.  If the calculated value of \(\chi^2\) is greater than the critical value from the Chi-square distribution table for a given significance level, we reject the null hypothesis.