Is it right to use REPEATED MEASURES ANOVA to analyse a dataset with a variable "y" (eg. growth rate) measured during three seasons from two stations (with random replicates from each station)?.
It's fine if y is a continuous variable. But with only 2 stations you probably won't have enough data to make a meaningful conclusion. A better option would be to used a mixed effects model.
@Stephen Politzer-Ahles
Sir, actually I have 3 stations. For the sake of simplicity, only 2 stations are mentioned.
But the problem is that since replicates are randomised within each station, I have little chance to take the measurement from exactly the same spot in successive seasons (for example, repl-1 of station A of post-monsoon may not be the same as that of monsoon). It is unlike the clinical trials (with within-subject design) where you measure the same subject repeatedly over seasons. Would this cause any problem with Repeated Measures ANOVA?. Or can it be analysed by both independent and repeated measures ANOVA?.
I think the difference between 3 stations and 2 stations is negligible. If 2 stations is not enough for an ANOVA, 3 is also probably not enough.
Even if replicates come from slightly different places, if they come from the same station it's still important to represent that. It's never expected that every observation from the same repeated measure is exactly the same; there will always be some noise. But presumably two replicates from the same station (even if they're from slightly different spots) are expected to be correlated more than two replicates from different stations. That's the idea of a repeated measures analysis (and the same logic you have with people, for example; we can't fully control whether or not the same subject will be the same across measurements, but we can still expect that two measurements from the same subject will be more similar than two measurements from different subjects).
As per your suggestion, I have decided to use mixed effects model (I hope mixed ANOVA belongs to this category) with station as within subject factor and season as between subject factor. I would also like to know if I could include a third factor - duration (2 duration within each season for each station as the between factor). I want to compare the effects of station , season, and duration (and the 2-way interactions). Is mixed ANOVA sufficient to deal with the number of sampling stations I have?. If not, any other alternative exists?
Mixed ANOVA is not quite the same as a mixed effects model. And Season is definitely a within-subject factor (if "Stations" are subjects).
It sounds like this can be a lot simpler. If you're predicting a difference between stations and this is one of the effects of interest, then this can be treated as a fixed factor rather than a random factor. Your unit of observation can be the individual samples, rather than the averages for stations. And then you can use a simple ANOVA, with no repeated measures. Each sample is a data point, and it is associated with three independent variables (station, season, and duration) and one dependent variable (growth rate). All those independent variables are between samples, so there is no need for a repeated measures analysis.
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