Chi-Square Test of Independence for 3 variables

Discuss statistics related things
Post Reply
Beth
Posts: 9
Joined: Tue Jan 17, 2023 12:27 pm

Chi-Square Test of Independence for 3 variables

Post by Beth »

Hi,

I have a question regarding Chi-square test of independence analysis with 2 vs.3 variables (adding the 3rd as the layer).
To simplify, let's say I'm researching the interaction between gender and clothing choices. There are 3 variables: color (red, white, black), clothing type (dress, pants, shirt) and gender (male, female). I also have a summary variable that has the frequencies of all combinations, which I put in the "counts" section. So I'm comparing the frequencies for all color and clothing combinations for gender to see whether there's a difference in preferences.
I'm confused between using these 3 variables and adding one of them as a layer and/or combining color and clothing type to do a regular analysis without a layer. Because color or clothing type doesn't mean anything by themselves, I decided to create a new variable with them combined e.g red dress, white shirt. Observed counts don't change, but the expected counts are different when I put 3 variables (gender, color, clothing) vs. 2 variables (gender and combined color&clothing).
The second issue is that when I put 3 variables, the chi-square tests give a chi and p-value for each level in the layer variable (let's say color). All but one are significant (red is not significant but white and black are) but I don't understand how to interpret that. Does that mean the relationship between color, clothing and gender is dependent for white and black but not for red? What exactly does the p-value for the color variable mean for the other variables?
Lastly, should I go with 3 variables, or is combining them a valid idea? If the expected counts were the same, I'd combine them without question but since they are different I want to make sure I'm not doing something wrong.

Thank you so much for your help!
Post Reply