Question
Download Solution PDFWith reference to analysis of variance, which of the following statements is/are correct?
(I) Change of origin will affect the value of F.
(II) Change of scale will affect the value of F.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation
With reference to analysis of variance change of origin or scale will not affect the value of F.
The analysis of variance is a method of splitting the total variation of data into the constituent part which measures different sources of variation. The total variation split up into 2 components
1 - Variation within the subgroups of samples
2 - Variation between the subgroups of the samples
The total variance is the sum of variation within the subgroups of samples and Variation between the subgroups of the samples.
F – Test = Variance ratio test
F = S21/S22
S12 = [1/(N1 – 1)]∑(X – X̅)2
S22 = {1/(N2 – 1)}∑(Y – Y̅)2
N1 = Size of first sample
N2 = Size of the second sample
X̅ and Y̅ are sample means of the random variable(X and Y)
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