In a study involving 4 treatment groups, and numerous trials done in each, the variances gave the totals of : SST=25.8 and SSE=145.7 for dfT=3 and dfE=31.Consider the mean squares and calculate the F-statistic for this data?
Question
In a study involving 4 treatment groups, and numerous trials done in each, the variances gave the totals of : SST=25.8 and SSE=145.7 for dfT=3 and dfE=31.Consider the mean squares and calculate the F-statistic for this data?
Solution
To calculate the F-statistic, we first need to calculate the mean squares for both the treatment (MST) and the error (MSE).
Mean squares are calculated by dividing the sum of squares by the degrees of freedom.
So, for the treatment (MST), we have:
MST = SST/dfT = 25.8/3 = 8.6
And for the error (MSE), we have:
MSE = SSE/dfE = 145.7/31 = 4.7
The F-statistic is then calculated by dividing the mean square of the treatment by the mean square of the error.
So, F = MST/MSE = 8.6/4.7 = 1.83
Therefore, the F-statistic for this data is 1.83.
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