# Frame experiment in Repeated Measures ANOVA lens

Someone is conducting the following hypothetical experiment and they've told me that a repeated measures ANOVA is required. I'm having trouble framing it like I've been taught in the texts. That is, identifying my factors, levels, indep/dep variables, etc etc.

Multiple participants are asked to look at a red square, blue square and green square as we measure their pupil opaqueness as a continuous time series for 1000ms (1 second) per trial. In each trial we show one square. We collect 100 trials looking at red, 100 at blue, and 100 at green all randomly shown. We do this for 50 participants. So our data looks like this

50 (participants) * 3 (red blue or green groups) * 100 (trials per group) * 1000 (ms samples per trial)


We then have a hypothesis that opaqueness is greater when looking at red then either blue or green (blue or green aren't really different from each other).

One way repeated measures anova

Could you help me formalize this a little more on both the group level and single subject level? Clearly identify why and how a repeated measures ANOVA is appropriate, what my independent variable is, what my dependent variable is, my factors, levels, etc?

What I think is the following: Based on the information found here:

The measurement of the dependent variable is repeated. It is not possible to use the standard ANOVA in such a case as such data violates the assumption of independence of data and as such it will not be able to model the correlation between the repeated measures.

However, it must be noted that a repeated measures design is very much different from a multivariate design.

For both, samples are measured on several occasions, or trials, but in the repeated measures design, each trial represents the measurement of the same characteristic under a different condition.

So repeated measures is appropriate because we are measuring the same participants opaqueness under different conditions, where the different conditions are either showing the red, blue or green squares? Someone also said I could compare across subjects and/or across colors? There is also the issue of performing three separate repeated measures anova, one to look at red vs blue, red vs green, and finally blue vs green. Does this make sense?

Two Way repeated measures anova

To add insult to injury, lets now say that I wanted to measure opaqueness in three different locations in someone's eye for every trial. Meaning every trail would now have 3 measurements of opaqueness. How does that fit in above? Someone told me this would be a two way repeated measures anova where factor 1: condition factor 2: measurement location.

EDIT

I updated the question to show that I am in interested in looking at a group level and at an individual level. How can I do this at an individual level? Would it involve looking at time? I'm thinking that I could 1. average across trials to generate one specific value of opaquness per time point. Then place them going down on the first column in a table similar to the one shown here. The second column would be the average value of all trials for that time point. OR I could also average across time, and place my trials there. What do you think?