Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	1    05/07/2011 17:19:48

Numeric Results for Testing Equivalence Using a Cross-Over Design

	Total					
	Sample	Lower	Upper		Standard	
	Size	Equiv.	Equiv.	True	Deviation		
Power	(N)	Limit	Limit	Difference	Sw	Alpha	Beta
0,8085	10	-71,71	71,71	0,00	58,60	0,1000	0,1915
0,8873	12	-71,71	71,71	0,00	58,60	0,1000	0,1127
0,9342	14	-71,71	71,71	0,00	58,60	0,1000	0,0658
0,9619	16	-71,71	71,71	0,00	58,60	0,1000	0,0381
0,9781	18	-71,71	71,71	0,00	58,60	0,1000	0,0219
0,7802	10	-71,71	71,71	10,00	58,60	0,1000	0,2198
0,8589	12	-71,71	71,71	10,00	58,60	0,1000	0,1411
0,9086	14	-71,71	71,71	10,00	58,60	0,1000	0,0914
0,9404	16	-71,71	71,71	10,00	58,60	0,1000	0,0596
0,9609	18	-71,71	71,71	10,00	58,60	0,1000	0,0391
0,6998	10	-71,71	71,71	20,00	58,60	0,1000	0,3002
0,7761	12	-71,71	71,71	20,00	58,60	0,1000	0,2239
0,8307	14	-71,71	71,71	20,00	58,60	0,1000	0,1693
0,8713	16	-71,71	71,71	20,00	58,60	0,1000	0,1287
0,9020	18	-71,71	71,71	20,00	58,60	0,1000	0,0980
0,5809	10	-71,71	71,71	30,00	58,60	0,1000	0,4191
0,6485	12	-71,71	71,71	30,00	58,60	0,1000	0,3515
0,7030	14	-71,71	71,71	30,00	58,60	0,1000	0,2970
0,7487	16	-71,71	71,71	30,00	58,60	0,1000	0,2513
0,7874	18	-71,71	71,71	30,00	58,60	0,1000	0,2126

References
Blackwelder, W.C. 1998. 'Equivalence Trials.' In Encyclopedia of Biostatistics, John Wiley and Sons. New York.
     Volume 2, 1367-1372.
Chow, S.C. and Liu, J.P. 1999. Design and Analysis of Bioavailability and Bioequivalence Studies. Marcel
     Dekker. New York
Chow, S.C.; Shao, J.; Wang, H. 2003. Sample Size Calculations in Clinical Research. Marcel Dekker. New York.
Julious, Steven A. 2004. 'Tutorial in Biostatistics. Sample sizes for clinical trials with Normal data.'
     Statistics in Medicine, 23:1921-1986.
Senn, Stephen. 2002. Cross-over Trials in Clinical Research. Second Edition. John Wiley & Sons. New York.

Report Definitions
Power is the probability of rejecting non-equivalence when the means are equivalent.
N is the total number of subjects split between both sequences.
EU & EL are the maximum allowable differences that still result in equivalence.
D is the difference between the means at which the power is computed.
Sw is the square root of the within mean square error from the ANOVA table.
Alpha is the probability of rejecting non-equivalence when the means are non-equivalent.
Beta is the probability of accepting non-equivalence when the means are equivalent.

	Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	2    05/07/2011 17:19:48

Summary Statements
In an equivalence test of means using two one-sided tests on data from a two-period cross-over
design, a total sample size of 10 achieves 81% power at a 10% significance level when the true
difference between the means is 0,00, the square root of the within mean square error is 58,60,
and the equivalence limits are -71,71 and 71,71.

In an equivalence test of means using two one-sided tests on data from a two-period cross-over
design, a total sample size of 12 achieves 89% power at a 10% significance level when the true
difference between the means is 0,00, the square root of the within mean square error is 58,60,
and the equivalence limits are -71,71 and 71,71.

In an equivalence test of means using two one-sided tests on data from a two-period cross-over
design, a total sample size of 14 achieves 93% power at a 10% significance level when the true
difference between the means is 0,00, the square root of the within mean square error is 58,60,
and the equivalence limits are -71,71 and 71,71.

In an equivalence test of means using two one-sided tests on data from a two-period cross-over
design, a total sample size of 16 achieves 96% power at a 10% significance level when the true
difference between the means is 0,00, the square root of the within mean square error is 58,60,
and the equivalence limits are -71,71 and 71,71.

In an equivalence test of means using two one-sided tests on data from a two-period cross-over
design, a total sample size of 18 achieves 98% power at a 10% significance level when the true
difference between the means is 0,00, the square root of the within mean square error is 58,60,
and the equivalence limits are -71,71 and 71,71.

In an equivalence test of means using two one-sided tests on data from a two-period cross-over
design, a total sample size of 10 achieves 78% power at a 10% significance level when the true
difference between the means is 10,00, the square root of the within mean square error is
58,60, and the equivalence limits are -71,71 and 71,71.

	Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	3    05/07/2011 17:19:48

Chart Section