6/3/2019 5:13:00 PM      1

Two-Sample T-Tests Allowing Unequal Variance

Numeric Results for Two-Sample T-Test Allowing Unequal Variance
Alternative Hypothesis: δ ≠ 0

Target	Actual						
Power	Power	N1	N2	N	δ	σ1	σ2	Alpha
0.80	0.80187	155	155	310	0.1	0.3	0.3	0.050
0.80	0.80924	20	20	40	0.2	0.3	0.3	0.050
0.80	0.82704	12	12	24	0.3	0.3	0.3	0.050

References
Julious, S. A. 2010. Sample Sizes for Clinical Trials. Chapman & Hall/CRC. Boca Raton, FL.
Chow, S.-C., Shao, J., and Wang, H. 2008. Sample Size Calculations in Clinical Research (Second Edition).
   Chapman & Hall/CRC. Boca Raton, FL.
Machin, D., Campbell, M., Fayers, P., and Pinol, A. 1997. Sample Size Tables for Clinical Studies, 2nd
   Edition. Blackwell Science. Malden, MA.
Zar, Jerrold H. 1984. Biostatistical Analysis (Second Edition). Prentice-Hall. Englewood Cliffs, New Jersey.

Report Definitions
Target Power is the desired power value (or values) entered in the procedure. Power is the probability of
   rejecting a false null hypothesis.
Actual Power is the power obtained in this scenario. Because N1 and N2 are discrete, this value is often
   (slightly) larger than the target power.
N1 and N2 are the number of items sampled from each population.
N is the total sample size, N1 + N2.
δ is the difference between population means at which power and sample size calculations are made.
σ1 and σ2 are the assumed population standard deviations for groups 1 and 2, respectively.
Alpha is the probability of rejecting a true null hypothesis.

Summary Statements
Group sample sizes of 155 and 155 achieve 80.187% power to reject the null hypothesis of equal
means when the population mean difference is 0.1 with standard deviations of 0.3 for group 1
and 0.3 for group 2, and with a significance level (alpha) of 0.050 using a two-sided
two-sample unequal-variance t-test.

	6/3/2019 5:13:01 PM      2

Two-Sample T-Tests Allowing Unequal Variance

Chart Section