ISDS WEEK 16 - CHI-SQUARE TEST FOR INDEPENDENCE

What is a chi-square test of a contingency table (test for independence)?

A goodness of fit test analyzing the relationship between 2 categorical variables.

Example of chi-square test of a contingency table

What is a contingency table?

A table that shows the frequencies for 2 categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values

What happens when you reject the null hypothesis in a chi-square test?

Rejecting the null hypothesis means the two categorical variables are dependent. If the null hypothesis is not rejected then the two categorical variables are independent

Example of contingency table for two categorical variables

What does the “ij” subscript in an observed frequency refer to?

i = the row

j = the column

How do you find the row and column total?

Just add across a row or down a column to get the total

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The totals of each row and column should add up to the sample size

How do you calculate marginal row and column probabilities?

We can calculate a marginal row/column probability by dividing the row/column sum by the total sample size

How is the expected frequency for each cell in a contingency table calculated?

(Row i total)(Column j total)/ Sample size

What does the chi-square test statistic X^2df measure?

It measures how much the observed frequencies deviate from the expected frequencies

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The smallest frequency the test statistic can assume is zero. This occurs when each observed frequency equals its expected frequency. Thus, a test for independence is also implemented as a right-tailed test

How is the chi-square test statistic X^2df calculated?

df = (r-1)(c-1)

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oij and eij are the observed (o) and expected frequency (e), respectively, in each cell in a contingency table

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Test is valid when the expected frequency for each cell are five or more

What is the excel function to find the p-value for chi-square test?

CHISQ.DIST.RT (Test statistic, df)

Full example of chi-square test for contingency table