Question

We want to examine the effects of three different diet plans on later weight loss. Three different conditions were created:

Diet A - 5,6,7,4,2

Diet B, 10,6,9,8,5

and No Diet, 2,4,5,3,6

and each condition has 5 subjects.

After two weeks on the diet plan, participants’ weight loss was measured.

Is there a difference in the effectiveness of these diet plans?

8. What is your ?????ℎ???  - ?????ℎ?? = ?????ℎ?? ?????ℎ?? =

9. What is your Fobs?

Fobs = ????????? ?????ℎ?? =

10. Do you reject or fail to reject your null hypothesis? Explain your decision.

11. What is your effect size?

η 2 = ??? ??? =

12. On average, what value is expected for the F-ratio if the null hypothesis is true?

13. An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment. For this study, what is df total? –

a. 0

b. 1.00

c. Between 0 and 1.00

d. Much greater than 1.00 a. 2 c. 33 b. 11 d. 35

Answer 1

	Diet A	Diet B	No Diet	Total
Sum	24	38	20	82
Count	5	5	5	15
Mean, Sum/n	4.8	7.6	4
Sum of square, Ʃ(xᵢ-x̅)²	14.8	17.2	10

Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3

H1: At least one mean is different.

Number of treatment, k = 3

Total sample Size, N = 15

df(between) = k-1 = 2

df(within) = N-k = 12

df(total) = N-1 = 14

SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N = 35.7333

SS(within) = SS1 + SS2 + SS3 = 42

SS(total) = SS(between) + SS(within) = 77.7333

MS(between) = SS(between)/df(between) = 17.8667

MS(within) = SS(within)/df(within) = 3.5

F = MS(between)/MS(within) = 5.1048

p-value = F.DIST.RT(5.1048, 2, 12) = 0.0249

Decision:

P-value < α, Reject the null hypothesis.

ɳ² = SS(between)/SS(total) = 35.7333/77.7333 = 0.4597

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12. Expected value for the F-ratio if the null hypothesis is true: Between 0 and 1.00

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13. k = 3

n = 12

df(Total) = nk - 1 = 12*3 - 1 = 35