Question

in a study of 140 women, the relationship between working status (full time, part time, not working).and obesity (BMI <30 or not) would be examined using which of the following statistical test
chi square
independent t test
McNemar test
paired t test

Answer 1

Here we are comparing 2 categorical variables (i) Working status and (ii) obesity level. When we need to see if there is a relationship/Association between 2 or more categorical variables we use the Chi Square Test () of independence.

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Independent t tests and paired t tests are tests for quantitative variables. They are not tests for nominal variables. The independent t test compares the difference between 2 means, while the paired t test compares the difference in means for a single population who have been tested before and after a treatment.

McNemar's test is a nominal test to test consistency of responses, not for testing a relation. Also this test can be used only for a 2 x 2 category. Here we have 3 categories of 1 variable and 2 of another.

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About Chi Square:

The Hypothesis in this case would be

H0: Working status and obesity are independent or there is no relation between working status and Obesity.

Ha: Working status and obesity are not independent or there is a relation between working status and Obesity.

Based on the observed values, we calculate expected values = Row Total * Column Total / N

And then calculate the test statistic = SUM[(O-E)²/E]

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