My dataset comprises of 400 respondents. They are shoppers from different sociodemographic backgrounds.
I asked each of them (among other things) how likely or unlikely they are to purchased ice-cream. Similarly, I asked them how likely or unlikely they are to purchase yogurt. They responded on a five point Likert scale.
I am doing a correlation between ice cream purchase and yogurt purchase by gender. So I have r=.8296 for females and r=.7784 for males. Both are significant at p<0.05.
I have then compared the two corrleation coefficients to determine if there is a difference between purchase by male vs. female. I have used one of the online calculators that can compare the coefficients (The calculator is from a reliable source.). The result is not significant.
Is this the right way to test the three relationships? (i.e. male, female, and male-female)
I have asked this question because someone pointed out that using correlation coefficients to assess relationships in this way is at best a weak approach and at worst it is wrong and misleading. I was told to consider more conventional analyses.
I am not statistically trained (I know that is no excuse) and I have to present my findings to an audience who is not very statistically orientated, so I used Pearsons corrleation (which appears quite straight forward to me).
Best Answer
At the very least, you would have wanted to consider polychoric correlations, which are specifically formulated to provide estimates between correlations of the underlying traits rather than their crude categorizations (as is done by Pearson correlation). Depending on the purposes of your analysis, you may or may not be OK with the simple correlation. If you are thinking whether to place yogurt and ice cream on the same shelf in the supermarket, without knowing who will be buying it, then this information may suffice. If you are doing a more in-depth analysis of who are the buyers of the two products, you would have to consider other demographic characteristics, like age, marital status, number of children, whether the person is the one who does the regular grocery shopping, and probably a ton of other things. Then you could put an ordinal logistic regression for each Likert scale to explain the purchasing behavior. It may or may not make sense to try to combine them, as the products are rather different.