After conducting an experiment for two seasons one proceeds to perform analysis of variance on the data with SEASON having 1 degree of freedom. This single df is then used to compute the MS which is then used to computer the F-value. The question is: Is it mathematically correct to say that (SS) Sum of Squares divided by 1 df = MS for the season main factor? Is it correct to say you got a MEAN after dividing by 1? Should one proceed to make a conclusion on the effect of season (or any other treatment) when a single degree of freedom was used to compute the MS?
Aas as I know, this is correct as you only have two levels of your variable. Degrees of freedom becomes 1.
Yes, it's indeed correct. It seems that in your analysis, SEASON only had two levels (e.g. summer and winter), then it has 1 degree of freedom, and the mean square and sum of square coincide. There is nothing wrong with doing inference when you only have 1 degree of freedom (no problems like "the sample is too small to clearly see something"): all that matters is that you have sufficient measurements for both seasons. In some sense, a smaller df is *better*: say you have 120 measurements. If you have 2 levels - summer and winter - then for both you have about 60 measurements and you usually can have a decent impression of what's going on in those levels. If you would have 12 levels for season - each month in the year - then you only have 10 measurements per month, and the statistical uncertainty of the estimates of the means per month will be much larger.
If SEASON was the only predictor variable in your analysis, you could just as well have performed a t test. You will then see that F = t-squared, and both tests have *exactly* the same p-value.
It is perfectly in order using a 1 degree of freedom to compute since you have only two seasons in this case. In your study, you have just two levels of the variable i.e. SEASON.
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