Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	1    05/07/2011 16:47:21

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
0,4752	10	-2,18	2,18	0,00	1,97	0,0500	0,5248
0,6216	12	-2,18	2,18	0,00	1,97	0,0500	0,3784
0,7349	14	-2,18	2,18	0,00	1,97	0,0500	0,2651
0,8168	16	-2,18	2,18	0,00	1,97	0,0500	0,1832
0,8745	18	-2,18	2,18	0,00	1,97	0,0500	0,1255
0,4220	10	-2,18	2,18	0,50	1,97	0,0500	0,5780
0,5467	12	-2,18	2,18	0,50	1,97	0,0500	0,4533
0,6450	14	-2,18	2,18	0,50	1,97	0,0500	0,3550
0,7200	16	-2,18	2,18	0,50	1,97	0,0500	0,2800
0,7776	18	-2,18	2,18	0,50	1,97	0,0500	0,2224
0,2953	10	-2,18	2,18	1,00	1,97	0,0500	0,7047
0,3706	12	-2,18	2,18	1,00	1,97	0,0500	0,6294
0,4321	14	-2,18	2,18	1,00	1,97	0,0500	0,5679
0,4837	16	-2,18	2,18	1,00	1,97	0,0500	0,5163
0,5292	18	-2,18	2,18	1,00	1,97	0,0500	0,4708

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 10 achieves 48% 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 1,97,
and the equivalence limits are -2,18 and 2,18.

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 62% 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 1,97,
and the equivalence limits are -2,18 and 2,18.

	Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	2    05/07/2011 16:47:21

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 14 achieves 73% 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 1,97,
and the equivalence limits are -2,18 and 2,18.

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 82% 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 1,97,
and the equivalence limits are -2,18 and 2,18.

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 87% 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 1,97,
and the equivalence limits are -2,18 and 2,18.

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 42% 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 1,97,
and the equivalence limits are -2,18 and 2,18.

Chart Section