Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	1    05/07/2011 17:17:44

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
0,8961	10	-75,29	75,29	0,00	54,73	0,1000	0,1039
0,9478	12	-75,29	75,29	0,00	54,73	0,1000	0,0522
0,9740	14	-75,29	75,29	0,00	54,73	0,1000	0,0260
0,9872	16	-75,29	75,29	0,00	54,73	0,1000	0,0128
0,9938	18	-75,29	75,29	0,00	54,73	0,1000	0,0062
0,8707	10	-75,29	75,29	10,00	54,73	0,1000	0,1293
0,9261	12	-75,29	75,29	10,00	54,73	0,1000	0,0739
0,9574	14	-75,29	75,29	10,00	54,73	0,1000	0,0426
0,9753	16	-75,29	75,29	10,00	54,73	0,1000	0,0247
0,9856	18	-75,29	75,29	10,00	54,73	0,1000	0,0144
0,7958	10	-75,29	75,29	20,00	54,73	0,1000	0,2042
0,8590	12	-75,29	75,29	20,00	54,73	0,1000	0,1410
0,9018	14	-75,29	75,29	20,00	54,73	0,1000	0,0982
0,9315	16	-75,29	75,29	20,00	54,73	0,1000	0,0685
0,9524	18	-75,29	75,29	20,00	54,73	0,1000	0,0476
0,6784	10	-75,29	75,29	30,00	54,73	0,1000	0,3216
0,7447	12	-75,29	75,29	30,00	54,73	0,1000	0,2553
0,7968	14	-75,29	75,29	30,00	54,73	0,1000	0,2032
0,8385	16	-75,29	75,29	30,00	54,73	0,1000	0,1615
0,8720	18	-75,29	75,29	30,00	54,73	0,1000	0,1280

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 17:17:44

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 90% 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 54,73,
and the equivalence limits are -75,29 and 75,29.

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 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 54,73,
and the equivalence limits are -75,29 and 75,29.

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 97% 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 54,73,
and the equivalence limits are -75,29 and 75,29.

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 99% 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 54,73,
and the equivalence limits are -75,29 and 75,29.

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 99% 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 54,73,
and the equivalence limits are -75,29 and 75,29.

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 87% power at a 10% significance level when the true
difference between the means is 10,00, the square root of the within mean square error is
54,73, and the equivalence limits are -75,29 and 75,29.

	Power Analysis of 2x2 Cross-Over Design for Testing Equivalence Using Differences
Page/Date/Time	3    05/07/2011 17:17:44

Chart Section