Question

A chi-square homogeneity test is to be conducted to decide whether a difference exists among the distributions of a variable of six populations. The variable has five possible values. What are the degrees of freedom for the x²-statistic?

Short answer

Degrees of freedom for the x²-statistic is given by$=20$

Step-by-step solution

Step 1. Given information

A chi-square homogeneity test is to be conducted to decide whether a difference exists among the distributions of a variable of six populations. The variable has five possible values.

That is,

Number of populations,$r=6$

Number of possible values for the variable,$c=5$

Step 2. Finding the degrees of freedom for the x2-statistic

Degrees of freedom for the x²-statistic is given by

$$\begin{gathered} df=(r-1)(c-1) \\ =(6-1)(5-1) \\ =5\times 4 \\ =20 \end{gathered}$$