# 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?

## 1 Answer

You are on the right track. A repeated measures ANOVA will begin to address your hypothesis. Between subjects ANOVA assumes independence of observations. This is violated in your study because many observations are taken of single participant. In terms of sorting out your variables recall that in an experiment your dependent variable is the one that you measure. It's value depends on the variables you manipulate, your independent variables. Thus, pupil opaqueness is your dependent and colour and location are your independent variables or factors. A handy way to summarize all of this information is as follows: You are doing a 3 (colour, red/green/blue) x 3 (location on eye) within subjects ANOVA. Two factors each with 3 levels. The 'x' indicates you are also interesting in testing interactions between location and colour. Will some locations be more opaque with certain colours? Incidentally, you would not be able to test for such possible interactions if you performed 3 one-way ANOVAs. In addition, you would inflate your familywise error rate. Stay away from that option. Finally, note that ANOVA tests for equality of all conditions. Thus, follow up t-tests or a linear contrast would be required to answer your original hypothesis following a significant ANOVA.

• Could I conduct a one way repeated measures anova (not considering location of measurement) on a per subject level? I measure opaqueness as a continuous time series for 300 seconds per trial Aug 16 '12 at 22:35
• Can you please expand on what you mean by 'per subject level'. Are you interested in individual differences? Aug 17 '12 at 14:14
• I'm interested in looking at whether there was a difference between red blue and green squares on an individual rather than just a group. For example, say if the person had red have a large difference (blue and green didn;t) then I would give that person a special filter for their glasses. I want to be able to make statements per individual as well, not just as an entire group Aug 17 '12 at 17:29
• What is the difference between a categorical predictor and a factor? Aug 17 '12 at 21:20
• Categorical predictor and factor have the same meaning. You would tend to hear the first in the context of regression and the second in the ANOVA framework but they are identical. Aug 20 '12 at 15:39