ANOVA: [These are based on some of the Conceptual Exercises from Chapter 5. You

Question

ANOVA: [These are based on some of the Conceptual Exercises from Chapter 5. You therefore have access to the answers at the end of the chapter, and are welcome to look at it to improve your understanding. However, when you write up your answers to the homework, you should do it without looking at the answer! A word-for-word copy will not be acceptable.] Why is sp^2 not simply the average of sample variances? 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? 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): 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?

Explanation / Answer

a) what is p and what is I? more info required.

b) F-statistic is the ratio of mean squares between groups and means squares within groups

I.e. F = MSB/ MSW

Usually the calculated F-statistic is compared with the F-critical value

If F-value (F-stat) is high then we can reject H0 (the Null) which says the means among the groups are same. Meaning – reject that hypotheses, means between groups are same. We have evidence that means between groups are different. In other words mu1 not equals mu2 not equals mu3 and so on.

The statement means F-statistic is so small (smaller than F-crit) that the MSD between groups is so close to 0 (almost like the two groups are one and the same). That you can get such low value of MSD bet is very very rare to the point of 1 in 1000.

c) We have 10 groups and 24 samples in each group. We are comparing the means of all these 10 groups G1, G2, G3..G10. Their means are mu1, mu2..mu10. To conclude if these means are same or difference, we can do an ANOVA test.

For doing that, we will need the exact samples within each group. Why we need exact 24 points in every of the 10 groups? So that we can calculate the groups means, group variance and compute the mean square deviation between groups and mean square deviation within groups.

Otherwise, we will need the variances of each of the 10 groups if not for the exact data points because mean square deviation (MSD for between and group) is nothing but variance

MSD between groups = (mean of all groups var - var1)^2 + (mean of all groups var – var2)^2+…+(mean of all groups var - var10)^2

MSD within groups = var1+var2 +…+var10

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