# Which statistical analysis should I use for this experiment?

I conducted an experiment but I have difficulties in finding a proper statistical analysis.

The experiment consiste of a listening test in which participants had to rate the audio stimuli along 5 scales representing an emotion (sad, tender, neutral, happy and aggressive). Each audio stimulus was created in order to represent a particular emotion (I do not give the details...). Participants had to move 5 sliders each of which corresponded to one of the 5 emotions.

The sliders range was [0,10] but participants were only informed about the extremities of the sliders (not at all - very much).

There was not a force choice, therefore potentially each audio stimulus could be rated with all the scales (e.g. sad = 0.1, tender = 2.5, neutral = 2., happy = 8.3, aggressive = 1.7).

There were 20 participants, each stimulus was repeated twice.

Which analysis should be performed?

I want to demonstrate that the created stimuli were actually correctly classified in the corresponding emotion.

On the other hand I need to verify that the differences between the ratings of the stimuli are actually significant.

The problem is that for each stimulus I have 5 evaluations...should I take the maximum? But in that case I would ignore the other 4 evaluations...

Any suggestion?

• I admit that this may not be extremely helpful at this point in time, but I would suggest that the next time, you ask yourself this question before performing the study. If only to allow you to do a proper sample size requirement analysis. That said, I just voted +1 on the answer by @Marcus Morrisey below. – S. Kolassa - Reinstate Monica Jul 27 '12 at 20:57

One option would be to consider your audio stimuli as the independent variable in a multivariate analysis of variance or MANOVA. That is, the audio stimulus is your independent variable with a number of levels equal to the number of different audio simuli you used (I'm not clear what that number is from your description). Your 5 responses are each dependent variables. This approach treats your response variables as continuous, which is probably reasonable in this case. Given that you have measured each individual twice, you would want to include a within-subjects factor for trial number.

A similar, but potentially more powerful approach, would be to use a mixed models approach, treating participants as a random variable.

On Multivariate Mixed Model Analysis Yasuo Amemiya Lecture Notes-Monograph Series , Vol. 24, Multivariate Analysis and Its Applications (1994), pp. 83-95

In answer to your comment regarding PCA...

I cannot claim to be an expert in principle components analysis either. However, I don't believe that it directly addresses your research questions. PCA is generally interpreted as revealing the latent structure, or underlying variables in your data. If i am interpreting correctly, your expected finding would be that happy sounds (for example) result in happy ratings by participants and that these happy ratings are greater than the other 4 responses. If so, rejecting the null hypothesis with a MANOVA (or a mixed-models extension) would indicate that changes in the audio stimulus affect their ratings. That is, not all ratings are equal between your stimuli. It would be reasonable to follow up a significant MANOVA with planned linear comparisons testing, for each stimulus type, whether the predicted emotion was higher than all other ratings. Chapter 4 of Maxwell and Delaney's Designing Experiments and Analyzing Data discusses procedures for such comparisons.

• Thanks a lot, I will study your suggestions and I will get back to you as soon as possible. Any other suggestion? What about PCA? Does it sounds a good idea? I am not an expert in PCA... ;-) – L_T Jul 25 '12 at 12:59
• Thanks a lot. Now I try to do everything with R. Any useful link for inspiring R code? – L_T Jul 25 '12 at 14:07
• This thread might point you in some useful directions. – Marcus Morrisey Jul 25 '12 at 14:34