Question

A researcher wanted to see whether there was a difference between dogs, cats and ferrets in the mean number of trials required to train them to touch a target with their nose. The researcher samples 6 dogs, 6 cats and 6 ferrets and trained them to touch a target with their nose. The amount of trials required for each animal is listed in the table below. The overall mean was M_Total = 23.5. Assume that the amount of trials distributes normally in each population and that the assumption of homogeneity of variances is not violated.

Dogs	Cats	Ferrets
12	40	21
25	31	25
20	10	26
22	20	22
18	24	30
26	28	23
M1 = 20.5 SS1 = 131.5	M2 = 25.5 SS2 = 519.5	M3 = 24.5 SS3 = 53.5

a. Conduct the appropriate hypothesis test. Use α=0.05. You must submit your calculations (if you do not submit your calculations, you will lose points). (12 points).

b. Calculate the appropriate effect size measure. You must submit your calculations (if you do not submit your calculations, you will lose points). (4 points).

c. If the researcher had decided not to use the ferrets’ data and only compare dogs and cats, could she still have used the same test? Could she have used another test as well/instead? If so, which test? If she could have used more than one type of test, would she get the same results on both tests? Explain your answer. (4 points).

Answer 1

Solution :

a)

Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3

H1: At least one mean is different.

Number of treatment, k = 3

Total sample Size, N = 18

df(between) = k-1 = 2

df(within) = N-k = 15

df(total) = N-1 = 17

SS(between) = (x̅1)²*n1 + (x̅2)²*n2 + (x̅3)²*n3 - (Grand Mean)²*N =84

SS(within) = SS1 + SS2 + SS3 = 704.5

SS(total) = SS(between) + SS(within) = 788.5

MS(between) = SS(between)/df(between) = 42

MS(within) = SS(within)/df(within) = 46.9667

F = MS(between)/MS(within) = 0.8943

p-value = F.DIST.RT(0.8943, 2, 15) = 0.4296

Decision:

P-value > α, Do not reject the null hypothesis.

ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	84	2	42	0.8943	0.4296
Within Groups	704.5	15	46.9667
Total	788.5	17

b)

Effect size: ɳ² = SS(between)/SS(total) = 84/788.5 = 0.1065

c)

Yes, we can perform the same test.

Yes, we could have another test.

Two independent sample t-test is the other test that can be used.

Yes she would get the same result from both test.

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