Calculations and Discussions Based on Power Analysis In order to respond to each of the questions adequately, the following data wasmade up for calculation comparison and demonstration. Assumptions: α = 0.05, β = 0.2, one-tailed t-test with two independent groups of equal size, small effect size. The calculation was carried out in the G-Power application (Erdfelder, Faul & Buchner, 1996) yielding the following results. Based on the output, we realize that the adequate sample size is 102 (51 items for Lot 1 and 51 for Lot 2) (critical t = 1.6602, df = 100, actual power = 0.8059).
The procedure was repeated with minor amendments to undertake a compromise analysis with half the sample sizes. Figure 2 below illustrates the results obtained. The sample sizes for each independent group were set at 26 (approximately half of the initial samples per lot). Further output shows that the values of α (0.085) and β (0.34) changed from their initial values of 0.05 and 0.80 respectively (power = 0.66, δ = 1.803, critical t = 1.39, df = 50). We find that the value of α becomes 0.1526 (β = 0.61, power = 0.39, numerator df = 2, denominator df = 27, λ = 1.875, critical F = 2.017). The second case involves a calculation with the following assumptions: ANOVA (fixed effects, omnibus, one-way), small effect size, α = 0.05, β = 0.2, with three groups.
The resultant output is shown in figure 3 below. The analysis shows that the sample has 33 items (numerator df = 2, denominator df = 30, λ = 2.06, critical F = 3.316, actual power = 0.213). Further analysis was undertaken with the compromise function, assuming that only half the sample could be used.
This yielded the following. The new values of α and β are 0.176 and 0.704 respectively (λ = 0.9375, critical F = 2.015, numerator df = 2, denominator df = 12, power = 0.296). References Erdfelder, E., Faul, F. & Buchner, A. (1996). GPower: A general power analysis program. Behavior Research Methods, Instruments, & Computers. 28(1): 1-11). Mayr, S., Erdfelder, E., Buchner, A. & Faul, F. (2007). A short tutorial of GPower. Tutorials in Quantitative Methods for Psychology. 3(2): 51-59.