Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	1    05/07/2011 17:19:21

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
0,6090	10	-71,71	71,71	0,00	58,60	0,0500	0,3910
0,7464	12	-71,71	71,71	0,00	58,60	0,0500	0,2536
0,8392	14	-71,71	71,71	0,00	58,60	0,0500	0,1608
0,8994	16	-71,71	71,71	0,00	58,60	0,0500	0,1006
0,9378	18	-71,71	71,71	0,00	58,60	0,0500	0,0622
0,5810	10	-71,71	71,71	10,00	58,60	0,0500	0,4190
0,7116	12	-71,71	71,71	10,00	58,60	0,0500	0,2884
0,8023	14	-71,71	71,71	10,00	58,60	0,0500	0,1977
0,8641	16	-71,71	71,71	10,00	58,60	0,0500	0,1359
0,9063	18	-71,71	71,71	10,00	58,60	0,0500	0,0937
0,5042	10	-71,71	71,71	20,00	58,60	0,0500	0,4958
0,6155	12	-71,71	71,71	20,00	58,60	0,0500	0,3845
0,6983	14	-71,71	71,71	20,00	58,60	0,0500	0,3017
0,7613	16	-71,71	71,71	20,00	58,60	0,0500	0,2387
0,8104	18	-71,71	71,71	20,00	58,60	0,0500	0,1896
0,3975	10	-71,71	71,71	30,00	58,60	0,0500	0,6025
0,4811	12	-71,71	71,71	30,00	58,60	0,0500	0,5189
0,5482	14	-71,71	71,71	30,00	58,60	0,0500	0,4518
0,6050	16	-71,71	71,71	30,00	58,60	0,0500	0,3950
0,6545	18	-71,71	71,71	30,00	58,60	0,0500	0,3455

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 17:19:21

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 61% power at a 5% 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 75% power at a 5% 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 84% power at a 5% 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 90% power at a 5% 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 94% power at a 5% 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 58% power at a 5% 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 17:19:21

Chart Section