Question

Chi-squares tests of independence Critical thinking: If two variables are absolutely independent of each other, what's the difference between the expected and observed frequencies? What will be the value of the test statistic (x2)? Given the value of the test statistic, what's the expected p-value? Explain.

Answer 1

Solution:

Given: two variables are absolutely independent of each other.

The difference between the expected and observed frequencies:

If : two variables are absolutely independent of each other, then there must be All observed frequencies = All Expected frequencies and hence the difference between the expected and observed frequencies would be 0 for all.

The value of the test statistic:

If the difference between the expected and observed frequencies are 0 for all, then Chi-square test statistic would be 0.

Since it is given by:

So numerator is difference between the expected and observed frequencies which is 0 for all.

The expected p-value:

The expected p-value would be 1.0000, since = 0 and area right of 0 for is 100% or 1.0000