Question

18. Suppose you ran a between-subjects ANOVA in a study that had 3 levels of the independent variable, with 5 subjects assigned to each level. As part of your analysis, you calculated the following results: SStotal=1216. 738, SSbetween=787.930, and SSwithin=428.808. Calculate the F ratio. Was there a statistical difference between the three groups at the α=.05 significance level?

19. What is the effect size for the study described in Question 18? Is this a small, medium, or large effect size according to Cohen?

20. Suppose that the mean scores on the dependent variable for the three groups in the study described in Question 18 were 19, 26, and 23. Use Tukey’s HSD statistic (also called the q statistic) to determine whether any pair of these three means differed statistically from one another at the .05 significance level.

Please answer all the questions. 19 and 20 is an attachment to 18. Please also show how you got the answers so I can better understand these types of questions later in the future. Thank you

Answer 1

18)

	SS	df	MS	F
Between:	787.93	2	393.97	11.02
Within:	428.81	12	35.73
Total:	1216.74	14

			p-value
			0.0019
			α =	0.05
	conclusion :	p-value<α , reject null hypothesis

yes, there a statistical difference between the three groups

19)

Effect size = SS Between / SS TOTAL

0.6476

medium

20)

Level of significance   0.05
no. of treatments,k   3
DF error =N-k=   12
MSE   35.734
q-statistic value(α,k,N-k)   3.7700

population mean difference	critical value	lower limit	upper limit	result
µ1-µ2	-7.00	10.08	-17.08	3.08	means are not different
µ1-µ3	-4.00	10.08	-14.08	6.08	means are not different
µ2-µ3	3.00	10.08	-7.08	13.08	means are not different

NO three means differed statistically from one another

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