Hello Paul,

What an interesting problem! I suspect that, no matter what scheme is chosen, if your total N is 21, the statistical power of any comparisons is going to be very low, unless the differences are large. Did you mean to say "sense" instead of "age" in your explanation of the 5 x 2 table in your description? If you're genuinely disaggregating cases even further by age, then the sample size is even more of an issue.

One option, though likely not very satisfying to you, would be to create for each object, a sum of the senses applied to inspection of the given object. Then, use that score as if metric data, and treat the statistical design as a simple repeated measures anova design with 5 observations per case (one "sense" score--something between 1 and 5--for each of 5 objects). Of course, I doubt that many of the people shut their eyes, so seeing is likely always involved, as is touch (if handling is encouraged). So the scores won't likely vary all that much.

Barring that, a descriptive table of the percent or proportion of time participants used "taste" with objects A, B, C, D, E (and likewise additional rows for touch/feel, listen/hear, etc.) would be very simple and still may spur some useful discussion.

Good luck with your work!

If your dependent variable is use/non-use, I think you can analyze this with a mixed effects logistic regression. This isn't as scary as it sounds.

Something like:

Use_NonUse ~ Sense + Object + Sense:Object + (1|Subject).

I don't understand the set-up enough to be more specific in exactly how you would want to set up the model.

You would then use post-hoc analysis (emmeans) to compare among, say, the senses, or the Sense:Object interactions.

It's usually better to put all the data into one model rather than split it up into smaller tables or hypothesis tests. I'm not entirely sure this makes sense for your situation, though.

Thank you for the responses both. I ran a Chi Squared on the individual objects, (n = 21) and naturally it came up with a non-significant result by quite a margin as you'd expect. Unfortunately, I think I just needed a bigger sample. Doh well.

In response to your idea David, that's a nice suggestion. I've had a look into the mean sensory usage values and ran a quick ANOVA but as you stated, it does seem to be rather invariant as expected. Sample size again is a limitation I feel and I'm not sure I'd get much useful information out of it.

In terms of Salvatore's response, I think sample size is still going to be pain with regard to this. I'll have a look into Logistic Regression though.

Thank you both again for your input but I think as David said, it's going to have to be qualitative only here!

Cheers

Paul

I agree that mixed effect (also known as multilevel) regression logistic regression or one using counts (Poisson, quasipoisson or negative binomial) would be worth trying. It will have greater power for some inferences than separate chi-squares tests.