Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	1    05/07/2011 16:51:07

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
0,2451	30	-1,11	1,11	0,00	2,15	0,0500	0,7549
0,4632	40	-1,11	1,11	0,00	2,15	0,0500	0,5368
0,6288	50	-1,11	1,11	0,00	2,15	0,0500	0,3712
0,7472	60	-1,11	1,11	0,00	2,15	0,0500	0,2528
0,8300	70	-1,11	1,11	0,00	2,15	0,0500	0,1700
0,1686	30	-1,11	1,11	0,50	2,15	0,0500	0,8314
0,2932	40	-1,11	1,11	0,50	2,15	0,0500	0,7068
0,3808	50	-1,11	1,11	0,50	2,15	0,0500	0,6192
0,4471	60	-1,11	1,11	0,50	2,15	0,0500	0,5529
0,5021	70	-1,11	1,11	0,50	2,15	0,0500	0,4979
0,0549	30	-1,11	1,11	1,00	2,15	0,0500	0,9451
0,0738	40	-1,11	1,11	1,00	2,15	0,0500	0,9262
0,0810	50	-1,11	1,11	1,00	2,15	0,0500	0,9190
0,0855	60	-1,11	1,11	1,00	2,15	0,0500	0,9145
0,0892	70	-1,11	1,11	1,00	2,15	0,0500	0,9108

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.

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 30 achieves 25% 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 2,15,
and the equivalence limits are -1,11 and 1,11.

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 40 achieves 46% 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 2,15,
and the equivalence limits are -1,11 and 1,11.

	Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	2    05/07/2011 16:51:08

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 50 achieves 63% 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 2,15,
and the equivalence limits are -1,11 and 1,11.

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 60 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 2,15,
and the equivalence limits are -1,11 and 1,11.

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 70 achieves 83% 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 2,15,
and the equivalence limits are -1,11 and 1,11.

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 30 achieves 17% power at a 5% significance level when the true
difference between the means is 0,50, the square root of the within mean square error is 2,15,
and the equivalence limits are -1,11 and 1,11.

Chart Section