It seems to (if I understand your design correctly) thet you could use a 3-way repeated measures ANOVA on the %% correct answers of the participants as dependent variable. You have 3 within (repeated measures) factors:

- Sessions: 3 levels

-VOT: 2 levels

-Ear: 2 levels

Inspect the histograms of the %%. If they look fairly normal, go ahead. (Remember that the Shapiro test is biased by size. You (only) have 32 participants , so this test should not be significant. On the other hand, the ANOVA is known to be quite robust against (a.o.) non-normality of ditributions. Also check the sphericity test. If significant, use the corrected p-values.)

Thanks so much Jos Feys

Sadly, I may have fewer than 32 participants, as the study is yet to begin. I was merely attempting to structure the way in which I would capture the data and run analyses.

Would the VOT not be 4 levels however? (SS, SL, LS, LL).

I also realised last night that I can calculate a laterality index for LE-RE (positive number showing right or negative showing left ear advantage) and similar values for all combinations of variables, reducing (SSxLE, SSxRE, LExLE, etc etc) down to +/-0 values for each state (so a -66.67 value for LS demonstrates a strong left-ear advantage).

With this could I assess LE/RE index (1 DV Mean per phase) over Menstrual Phase (IV, 3) to measure the degree to which it changes over time? Similarly, I would have four measures of VOT-laterality (+50.00 for LL, showing a dominance of the right ear, or -25.00 for LS etc). Would this cause any problems?

I should admit I am quite confused about what you would like to do. As I understand, you would like to find out whether sex hormones affect consonant-vowel syllable accuracy. To measure this accuracy, you would simultaneously present pairs of monosyllables to your subjects, one in the Left and the other in the Right ear. Each pair is a combination of Short or Long VOT (voice-onset-time), with 4 possible combinations: SS, SL, LS, and LL. Your dependent variable is the number (or proportion) of Left Ear (LE) correct answers, e.g. presented in the left ear from a short-long combination (LE-SL, meaning the short VOT syllable was presented to the left ear, and long to the right). In this example the subject correctly identified the monosyllable with a Short VOT. Am I wright? In this example, you particularly want to compare these number of correct responses to a short VOT monosyllable, when it is presented in the Right Ear (RE-LS combination). You are interested in this instance in the Left – Right Ear distinction. This corresponds to the first repeated measures factor: Ear, with 2 levels.

Secondly, you are also interested in the VOT combinations: SS, SL, LS, and LL. In my opinion this corresponds to the second repeated measures factor: VOT combination, with (indeed) 4 levels.

Thirdly, you also are interested in the menstrual cycle, which 3 Sessions (repeated measures).

I understand that you are interested in differences in accuracy between Left and Right Ear, but I would not calculate difference scores. You can assess these differences with testing the effect of Ear.

So, the 3-way repeated measures ANOVA on the %% correct responses – in my opinion – still holds.

Thanks Jos Feys you are a star :)

I've refined my question somewhat and no longer need to directly compare all of these facets now.

I realised I can use the laterality-indices to compare the mean difference between VOT neutral pairings (mean of SS and LL combined laterality of accurate responses) with SL or LS means, to create a mean baseline-laterality (as this excludes any VOT length). So SS+LL only shows REA without VOT effect, and remaining figure shows VOT effect strength without REA.

Then I can compare the mean difference between neutral and non neutral pairings over phase. This will give me either a significant difference (showing that VOT effect remains roughly equal, and so the processes are independent of one another) or no difference (showing that VOT effect varies over cycle in tandem with REA).