Is a Chi-Square test appropriate here?

Question

I was wondering if a Chi-Square test was appropriate here, or if I should/could use another test.

I’m trying to see if a type of activity is more common on some days of the week than others. How my data is broken up, I have the total amount of time spent on all activities by all people who work on a given day, then I have the amount of time spent on each specific activity. I’m interested in seeing if certain activities are more prevalent on certain days than others.

The total amount of hours spent on all activities on any given day varies, so the amount of hours spent on any given activity varies too. That is, more people work on Mondays than Sundays, and thus there are less hours for any activity on Sundays than on Mondays, but I’m interested in if the proportion of Activity A for Sundays is significantly greater or less than that for Mondays, or any other day.

My idea was to have day of week as my columns and activity type (likely 2-4 types) as my rows and run a chi-squared test. Is this valid to see if there is a significant difference in the proportion of time spent on an activity based on the day? Or is there another/better choice of test?

Sorry if my explanation isn’t clear, but I’m happy to provide more if necessary.

Thanks ahead of time

Answer 1

Chi-square is not right here. Chi-square is good when you have a crosstabulation with counts in the cells. You have amount of time.

I would look at some form of regression with "time spent" as the dependent variable, and "day of week", "type of activity" and their interaction as independent variables. The interaction answers your question of whether some are more common on certain days of the week.

What type of regression? That depends. If you have multiple measurements on the same people then you will need to account for that - one way is a multilevel model. Otherwise, OLS regression is probably the place to start.