Calculations and Discussions Based on Power Analysis - Coursework Example

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).

The 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).