# Solved – Is a repeated measures ANOVA appropriate for multiple within-subject measurements

I recorded 4 groups of captive birds (each group a difference species) at the same 3 times each day for 15 days. I want to determine if there is a difference in their vocalization properties such as call rate (the number of chirps per second for each call), call length, etc. during these 3 specific times of day. I repeated my recordings over several days because of the varying number of calls – sometimes the birds were silent, other times there were 10 calls in one recording session, etc.

1. My first reaction is to run a RM ANOVA (in SPSS), and if the differences between time of day are significant, do post-hoc tests for further investigation. Does this seem appropriate? I was initially going to do individual tests for each group, but now I am wondering if I can do the RM ANOVA using all of the groups and controlling for species differences.

2. I was thinking of just analyzing the actual calls that were recorded, ignoring the fact that some days there were no calls to analyze, as I am not interested in the differences between days, only between times. The problem with this is that I then have unbalanced data – for example, I may have a total of 22 calls to analyze at the beginning of the day, 17 at the middle, and 35 at the end. Would this be an issue with a RM ANOVA?

I have been confusing and second-guessing myself like crazy – so I appreciate any advice!

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The data

You have count data. Each observation is therefore something like '10 calls at time point 1 on day 4'. This has two implications:

• Unless you forgot to record at one of the 45 day/time combinations, your data are balanced. This is true even if there were no calls at some combination. In that case the observation is simply 0.

• Unless the counts are high with very similar rates, the 'sphericity' assumption (i.e. that all 45 observations have the same standard deviation) that @gung mentions is unlikely to hold.

You might therefore be better switching to a generalized linear regression framework that will allow you to model the counts as conditionally Poisson. If you really don't want to there are various transformations of your counts (e.g. square root) that might be useful to keep you in a broadly in ANOVA's linear normal framework. It may or may not be worth getting hung up about this. It's hard to tell without playing with the data. Try things a couple of ways and check your residuals.

Random effects / Repeated measures

If you consider that some days are just noisier than others and that it is scientifically irrelevant which particular days you chose to record on, but scientifically interesting to see whether and how measurements at time points 1 2 and 3 differ from each other, then it seems quite reasonable to me to treat the day of recording as a random effect and the time of recording as a fixed effect.

The interpretation would be that each day has some intercept relating to the average call rate which is a random draw from the population of all the days you could have recorded, and the time you recorded adds or subtracts something from this rate. The observation is a random draw from a distribution with this mean. You're then asking whether the time of recording stands out from the day variation.

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