Question

A friend has been collecting data on the impacts of the COVID-19 pandemic on daily physical activity. Specifically, he has surveyed 18 individuals, collecting information on two variables: gender identity (female, male, other) and how the individual’s level of physical exercise has changed since the start of the pandemic (increased, decreased, stayed about the same). Your friend has been told that a chi-square test would be useful for investigating the association between gender identity and change in exercise patterns? Do you agree? What concerns would you have in applying chi-square in this situation?

Answer 1

Solution :

For chi_square test of independence, we have three assumptions :

1) Sampling method must be Simple random sampling.

2) Data variables must be categorical.

3) Expected frequency for each cell in contingency table must be atleast 5.

Here in given example, friend has surveyed 18 individuals, collecting information on two variables: gender identity (female, male, other) and change in the individual’s level of physical exercise (increased, decreased, stayed about the same)

Here data obtained by surveying individuals and variables: gender identity and change in the individual’s level of physical exercise, are categorical. Hence first two assumptions are satisfied.

We have, sample size = n = 18. As there are 3 categories of each variable. Hence there are total 3*3=9 cells in contingency table. Hence expected frequency for each cell in contingency table cannot be greater than or equal to 5. Hence third assumption is not satisfied.

Answer :Some cells will have frequency less than 5. This is the important concern in applying chi-square test in this situation.