Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	1    05/07/2011 17:36:48

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
0,4511	14	-2,43	2,43	0,00	3,30	0,1000	0,5489
0,6148	18	-2,43	2,43	0,00	3,30	0,1000	0,3852
0,7322	22	-2,43	2,43	0,00	3,30	0,1000	0,2678
0,8150	26	-2,43	2,43	0,00	3,30	0,1000	0,1850
0,8730	30	-2,43	2,43	0,00	3,30	0,1000	0,1270
0,4221	14	-2,43	2,43	0,50	3,30	0,1000	0,5779
0,5700	18	-2,43	2,43	0,50	3,30	0,1000	0,4300
0,6764	22	-2,43	2,43	0,50	3,30	0,1000	0,3236
0,7537	26	-2,43	2,43	0,50	3,30	0,1000	0,2463
0,8109	30	-2,43	2,43	0,50	3,30	0,1000	0,1891
0,3459	14	-2,43	2,43	1,00	3,30	0,1000	0,6541
0,4537	18	-2,43	2,43	1,00	3,30	0,1000	0,5463
0,5315	22	-2,43	2,43	1,00	3,30	0,1000	0,4685
0,5916	26	-2,43	2,43	1,00	3,30	0,1000	0,4084
0,6410	30	-2,43	2,43	1,00	3,30	0,1000	0,3590

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 14 achieves 45% 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 3,30,
and the equivalence limits are -2,43 and 2,43.

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 61% 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 3,30,
and the equivalence limits are -2,43 and 2,43.

	Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	2    05/07/2011 17:36:48

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 22 achieves 73% 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 3,30,
and the equivalence limits are -2,43 and 2,43.

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 26 achieves 82% 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 3,30,
and the equivalence limits are -2,43 and 2,43.

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 87% 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 3,30,
and the equivalence limits are -2,43 and 2,43.

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 42% power at a 10% significance level when the true
difference between the means is 0,50, the square root of the within mean square error is 3,30,
and the equivalence limits are -2,43 and 2,43.

Chart Section