Which statistical test to use, 20 subjects, 6 categorical variable, 4 parameter

Hi I have an experiment and are not sure which statistical test I should use. I hope some of you can help me, as this is not my strong side..

I have 20 subjects looking at 6 different categories of images, 40 trials per categori. I have 4 numerical variables I measure for each trial:

20 subjects x 6 categories x 40 trials = 4800 trials
Each trial gives 4 numerical values

I want to know if categories differ significantly from each other, when you look at the 4 variables, if yes which.

Right now I have for each subject made a one way anova for each variable, followed by a Turkey post hoc. But it dosen't look that nice when you have 20 sets of results and try to sum it up..

(I was told that you could not use the one way anova on a mean across the subjets, that is why I have done it for each subject)

I really hope someone can tell me a better way to do it.. THANKS!
/Karsten

Re: Which statistical test to use, 20 subjects, 6 categorical variable, 4 parameter

For each variable, you could aggregate a subject's responses to the
40 images within each category. You did not describe what you actually
did measure and on which scale; if they are continuous variables, then
you could use the mean or the median across the 40 images as the
aggegated mesaure which you can further analyse. In effect, you would
have 6 measurements (one for each category) for each variable and
could then perform a repeated-measures ANOVA or a Friedman test
for each variable. If they turn out to be "significant", then you could
do pairwise comparisons (e.g. Wilcoxon rank sum tests).

Re: Which statistical test to use, 20 subjects, 6 categorical variable, 4 parameter

Thanks for your answer Karabiner, describe it a bit better, I just feared it would be a too long post.

20 subjects
Each subject looks at 240 images of faces, showing 6 different emotions, 40 images for each emotion. Each image is shown for 5 seconds while an eye tracker records their fixations.
The four variables is:
Number of fixations during the 5 sec
The duration of the fixations
The distance between fixations
The total distance between all the fixations during the 5 sec

What I have done right now for each subject
Taken the mean of each of the variables for each emotions set (40 images) and run an one way anova on this.
Ex.

Re: Which statistical test to use, 20 subjects, 6 categorical variable, 4 parameter

What a terrible mistake KarstenDK has done!
Here:

by a Turkey post hoc

And here again:

TurkeyPostHoc(stads)

Calling the great John Tukey for a “turkey”! What an insult!

I assume he means Tukeys honestly significant difference (HSD) post hoc test. (Which seems appropriate here.) But Tukey did many great other great things.

Anyway, since the four response variables sees to be ratio variables anova seems possible. I would think of a three way anova with subjects, category and image as factors. I guess that each subject is looking at the same image. And that many subjects might think of e.g. image 3 as more aggressive than image 7. So image should be a factor. But image is hierarchical under category, so that factor can only come in as an interaction effect with category.

The number of fixations could maybe be modelled as a Poisson distribution (and the rest as normally distributed).

Re: Which statistical test to use, 20 subjects, 6 categorical variable, 4 parameter

I send a sincere apology to Mr. Tukey up in the sky. When that have been given, then I would say that it isn't that big an insult, I have been on holiday many times in Turkey, and it is a nice place (I did know it was the name of a person and not the country that had laid name to the test, but spelling it.. and yes, it were the HSD)

Yes, they are ratio variables, and each subject looks at the same 240 images (40*6) in the same order.

Hmm.. I would like to keep the single images out as factor, as they are posed by different models (each model doing an image for each emotion), the subjects would properly have different values for each model, where I am interested in finding some general patterns related to looking at specific emotions.
Let's say one of the models have a big pimple, the subjects notice this and focus on it for a long time. The gives longer fixation duration and shorter total path and lower number of fixations. But it will happen for all images of that model, one image for each of the 6 emotions. In this way it should not give a difference between the means of each emotion.

Also.. I just think I also just think the data is already getting hard to keep track of.. so would like to keep the single images out..

Re: Which statistical test to use, 20 subjects, 6 categorical variable, 4 parameter

Well it is your study. If there is a relevant explanatory factor and you chooses not to include it then it is your problem.

In this case, which seems to be a balanced design, i.e. the same number of observations in each cell, exclusion of one variable would not influence the values of the parameter estimates. But exclusion of the variable will influence the variance estimate, i.e. how “uncertain” the parameters are. The omitted variable will create some extra variation and thereby cause something that seems to be random error, and will be included in the estimates of the random error.

It will take one minute or two to include that effect in the model and test if it has an effect.

(Maybe other things should be taken into account but I stop here.)

Re: Which statistical test to use, 20 subjects, 6 categorical variable, 4 parameter

Yeah, it is my study, but also kind of my first real study of this kind.. So sorry if I sounded a bit stubborn, now that it is me who ask for help..
I think I understand now.. It should not affect the values, but yes of course it will affect the variation, and can help explain some of the variation if I include the model/poser or image number..