Question

"sleep latency time in minutes"

CBT	melatonin	control
7	12	27
9	11	31
5	14	32
9	12	22
8	11	37
7	13	24
9	14	39
10	13	42
9	14	25
6	14	39

Use the data to compute the following:

1. One-way ANOVA

2. Tukey’s HSD

3. Eta squared post hoc test

4. Effect size

5. T obs

6. F obs

Answer 1

for soltution i used Excel.

part1)

SUMMARY
Groups	Count	Sum	Average	Variance
CBT	10	79	7.9	2.544444
melatonin	10	128	12.8	1.511111
control	10	318	31.8	51.28889

	ANOVA
	Source of Variation	SS	df	MS	F	P-value	F crit
	Between Groups	3187.4	2	1593.7	86.38807	1.85E-12	3.354131
	Within Groups	498.1	27	18.44815
	Total	3685.5	29

we reject H0 based on pvale and critical statistics. there is significant difference

part2) Tukey HSD

SE=sqrt(0.5*MS_w*(1/n_i+1/n_j))

q = abs(differece)/SE

		Difference	n(group1)	n(group2)	SE	q
CBT	melatonin	-4.9	10	10	1.35824	3.607611
control	CBT	23.9	10	10	1.35824	17.59631
melatonin	control	-19	10	10	1.35824	13.9887

tukey statistics n=30 and group=3 is 3.49

so that we can infere that all the pairs are significantly differe.

3) Eta squared post hoc test

neta = ss.between/ss.total

= 3187.4/3685.5 =0.864849

4) Effect size = 0.864849 which means the independent variable explained the variation of dependent varible by 86.48 percent. which is large effect size.

5) T statistics = sqrt(F) =sqrt(86.38807) =9.294519

6) F statistics =86.38807 = MSST/MSE