Chi-Square Test Formula

The Chi-Square Test is implemented as follows:

Goodness-of-Fit Test

Assumptions:

The assumptions/conditions needed when testing for goodness-of-fit include:

	Measurement scale is at least nominal
	Random samples
	Weighting is not used
	Each observation is classified into exactly one cell
	Each cell has an expected frequency of at least five (the "rule of five)

Variables input:

observed	Array of the observed values
expected	Array of expected values

Compute the Chi-Square value:

Compute the result of the test:

The critical value is determined based on a table of chi-square values, which determines the critical value based on the degrees of freedom (number of categories - 1) at the selected level of confidence. If the computed chi-square value is greater than the critical value, then the result is significant.

Homogeneity or Independence Test

Assumptions:

The assumptions/conditions needed when testing for homogeneity or independence include:

	Measurement scale is at least nominal
	Random samples
	Weighting is not used
	Each observation is classified into exactly one cell
	Each cell has an expected frequency of at least five (the "rule of five)

Variables input:

observed

Array of the observed values (2-D)

Calculate expected values for each cell in the table:

Compute the Chi-Square value:

Compute the result of the test:

The critical value is determined based on a table of chi-square values, which determines the critical value based on the degrees of freedom ((number of columns - 1) *( number of rows - 1)) at the selected level of confidence. If the computed chi-square value is greater than the critical value, then the result is significant.