6/3/2019 4:54:26 PM      1

One Way ANOVA Power Analysis

Numeric Results
						Std Dev	Standard	
	Average		Total			of Means	Deviation	Effect
Power	n	k	N	Alpha	Beta	(Sm)	(S)	Size
0.87803	15.00	3	45	0.05000	0.12197	0.13	0.25	0.5314
0.90029	16.00	3	48	0.05000	0.09971	0.13	0.25	0.5314
0.91886	17.00	3	51	0.05000	0.08114	0.13	0.25	0.5314
0.93426	18.00	3	54	0.05000	0.06574	0.13	0.25	0.5314
0.94695	19.00	3	57	0.05000	0.05305	0.13	0.25	0.5314
0.95735	20.00	3	60	0.05000	0.04265	0.13	0.25	0.5314

References
Desu, M. M. and Raghavarao, D. 1990. Sample Size Methodology. Academic Press. New York.
Fleiss, Joseph L. 1986. The Design and Analysis of Clinical Experiments. John Wiley & Sons. New York.
Kirk, Roger E. 1982. Experimental Design: Procedures for the Behavioral Sciences. Brooks/Cole. Pacific Grove,
   California.

Report Definitions
Power is the probability of rejecting a false null hypothesis. It should be close to one.
n is the average group sample size.
k is the number of groups.
Total N is the total sample size of all groups combined.
Alpha is the probability of rejecting a true null hypothesis. It should be small.
Beta is the probability of accepting a false null hypothesis. It should be small.
Sm is the standard deviation of the group means under the alternative hypothesis.
Standard deviation is the within group standard deviation.
The Effect Size is the ratio of Sm to standard deviation.

Summary Statements
In a one-way ANOVA study, sample sizes of 15, 15, and 15 are obtained from the 3 groups whose
means are to be compared. The total sample of 45 subjects achieves 88% power to detect
differences among the means versus the alternative of equal means using an F test with a
0.05000 significance level. The size of the variation in the means is represented by their
standard deviation which is 0.13. The common standard deviation within a group is assumed to be
0.25.

Details when Alpha = 0.05000, Power = 0.87803, SM = 0.13, S = 0.25
		Percent		Deviation	Ni
		Ni of		From	Times
Group	Ni	Total Ni	Mean	Mean	Deviation
1	15	33.33	-0.11	0.18	2.74
2	15	33.33	0.12	0.05	0.80
3	15	33.33	0.20	0.13	1.94
ALL	45	100.00	0.07		

	6/3/2019 4:54:26 PM      2

One Way ANOVA Power Analysis

Details when Alpha = 0.05000, Power = 0.90029, SM = 0.13, S = 0.25
		Percent		Deviation	Ni
		Ni of		From	Times
Group	Ni	Total Ni	Mean	Mean	Deviation
1	16	33.33	-0.11	0.18	2.92
2	16	33.33	0.12	0.05	0.85
3	16	33.33	0.20	0.13	2.07
ALL	48	100.00	0.07		

Details when Alpha = 0.05000, Power = 0.91886, SM = 0.13, S = 0.25
		Percent		Deviation	Ni
		Ni of		From	Times
Group	Ni	Total Ni	Mean	Mean	Deviation
1	17	33.33	-0.11	0.18	3.11
2	17	33.33	0.12	0.05	0.91
3	17	33.33	0.20	0.13	2.20
ALL	51	100.00	0.07		

Details when Alpha = 0.05000, Power = 0.93426, SM = 0.13, S = 0.25
		Percent		Deviation	Ni
		Ni of		From	Times
Group	Ni	Total Ni	Mean	Mean	Deviation
1	18	33.33	-0.11	0.18	3.29
2	18	33.33	0.12	0.05	0.96
3	18	33.33	0.20	0.13	2.33
ALL	54	100.00	0.07		

Details when Alpha = 0.05000, Power = 0.94695, SM = 0.13, S = 0.25
		Percent		Deviation	Ni
		Ni of		From	Times
Group	Ni	Total Ni	Mean	Mean	Deviation
1	19	33.33	-0.11	0.18	3.47
2	19	33.33	0.12	0.05	1.01
3	19	33.33	0.20	0.13	2.46
ALL	57	100.00	0.07		

Details when Alpha = 0.05000, Power = 0.95735, SM = 0.13, S = 0.25
		Percent		Deviation	Ni
		Ni of		From	Times
Group	Ni	Total Ni	Mean	Mean	Deviation
1	20	33.33	-0.11	0.18	3.65
2	20	33.33	0.12	0.05	1.07
3	20	33.33	0.20	0.13	2.59
ALL	60	100.00	0.07		

	6/3/2019 4:54:28 PM      3

One Way ANOVA Power Analysis

Chart Section