ANOVA: [3 points] Why is s­ P 2 not simply the average of the I sample variances

Question

ANOVA:

[3 points] Why is s­P2 not simply the average of the I sample variances?

[3 points] What does it mean if the F-statistic from ANOVA is so small that the chance of getting an F-statistic that small or smaller is only 0.001?

[3 points] The following data are sample means of (wing length – tail length) in mm, for 24 flycatchers in each of 10 different species of flycatcher (a kind of bird):

Average wing-tail (n = 24)

Explain why a conclusion that this measurement tends to differ in the 10 species cannot be made from these averages alone. What additional piece of information is needed to test for group differences and to evaluate the extent to which individuals from different species can be distinguished?

Average wing-tail (n = 24)

Explanation / Answer

a) s­P2 is not simply the average of the I sample variances

We need to combine estimate or variance row effect and effect of treatments too.

Generally , it gives sum of over all squares - sum of either row effect or coulmn effect os sum of squares divided by n.

Its not simply average of variance

What does it mean if the F-statistic from ANOVA is so small that the chance of getting an F-statistic that small or smaller is only 0.001?

F calculated statistic is 0.001 it indicates there is no difference between treatments or groups or both which are taken for study to compare them.

Take a F table, always F table value > 0.001, which doesnot reject null hypothsis

Averages alone are not sufficient to carry ANOVA.

Its better to produce all individual results or provide sum of sqaures of row effect, treatment effect and also sum of sqaures of all the elements.

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