Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	1    05/07/2011 16:46:52

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
0,7116	10	-2,18	2,18	0,00	1,97	0,1000	0,2884
0,8114	12	-2,18	2,18	0,00	1,97	0,1000	0,1886
0,8774	14	-2,18	2,18	0,00	1,97	0,1000	0,1226
0,9208	16	-2,18	2,18	0,00	1,97	0,1000	0,0792
0,9491	18	-2,18	2,18	0,00	1,97	0,1000	0,0509
0,6453	10	-2,18	2,18	0,50	1,97	0,1000	0,3547
0,7362	12	-2,18	2,18	0,50	1,97	0,1000	0,2638
0,8009	14	-2,18	2,18	0,50	1,97	0,1000	0,1991
0,8482	16	-2,18	2,18	0,50	1,97	0,1000	0,1518
0,8836	18	-2,18	2,18	0,50	1,97	0,1000	0,1164
0,4790	10	-2,18	2,18	1,00	1,97	0,1000	0,5210
0,5437	12	-2,18	2,18	1,00	1,97	0,1000	0,4563
0,5961	14	-2,18	2,18	1,00	1,97	0,1000	0,4039
0,6410	16	-2,18	2,18	1,00	1,97	0,1000	0,3590
0,6805	18	-2,18	2,18	1,00	1,97	0,1000	0,3195

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 71% 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 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 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 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 16:46:52

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 88% 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 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 92% 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 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 95% 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 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 65% 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 1,97,
and the equivalence limits are -2,18 and 2,18.

Chart Section