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# 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.

https://brainmass.com/statistics/hypothesis-testing/anova-tukey-hsd-585992

#### Solution Preview

Please see the attachment for detailed explanation of the solution.

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) = ...

#### Solution Summary

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

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