# ANOVA (Tukey HSD)

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The following is hypothetical data similar to the actual research results about birds. The numbers represent relative brain size for the individual birds in each sample.

NON-MIGRATING SHORT DISTANCE MIGRANTS LONG DISTANCE MIGRANTS

18 6 4 N=18

13 11 9 G=180

19 7 5 EX2=2150

12 9 6

16 8 5

12 13 7

M=15 M=9 M=6

T=90 T=54 T=36

SS=48 SS=34 SS=16

USE AN ANOVA WITH o=.05 to determine whether there are any significant mean differences among the three groups of birds. (use two decimal places)

SOURCE SS df MS F F-critical

BETWEEN ______ _____ _____ _____ _______

WITHIN ______ _____ _____

TOTAL ______ ______

F distribution

numerator degrees of freedom=6

denominator degrees of freedom=16

conclusion

* fail to reject the null hypothesis; there are significant differences among the three groups of birds

* reject the null hypothesis; there are significant differences among the three groups of birds

* reject the null hypothesis; there are no significant differences among the three groups of birds

* fail to reject the null hypothesis; there are no significant differences among the three groups of birds.

n2=

the results show significant differences in the 3 groups of birds______________.

use the Tukey HSD posttest to determine which groups are significantly different (use 2 decimal places)

q=________

non-migrating vs. short distance migrants:

* not enough information

*no significant mean difference

* significant mean difference

non-migrating vs. long distance migrants

* no significant mean difference

* not enough information

* significant mean difference

short distance migrants vs. long distance migrants

* no significant mean difference

* not enough information

* significant mean difference.

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##### Solution Summary

This solution explains the one-way ANOVA test procedure and the pair-wise comparison using Tukey HSD.

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Solution

The entries in the ANOVA table are computed as follows:

SS(Total) = ∑X2 - G2/N = 2150 - (180^2)/18

= 2150 - 1800 = 350

SS(Between) = ∑(T2/n) - G2/N = [(90^2)/6 + (54^2)/6 + (36^2)/6] - [(180^2)/18]

= 2052 - 1800 = 252

SS(Within) = SS Total - SS Between = 350 - 252 = 98

df(Total) = N - 1 = 18 - 1 = 17

df(Between) = k - 1 = 3 - 1 = 2

df(Within) = N - k = 18 - 3 = 15

MS (Between) = SS(Between)/ df(Between) = 252/2 = 126

MS(Within) = ...

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