1 Calculate the sample size needed given these factors oneta

1. Calculate the sample size needed given these factors:

one-tailed t-test with two independent groups of equal size

small effect size (see Piasta, S.B., & Justice, L.M., 2010)

alpha =.05

beta = .2

Assume that the result is a sample size beyond what you can obtain. Use the compromise function to compute alpha and beta for a sample half the size. Indicate the resulting alpha and beta. Present an argument that your study is worth doing with the smaller sample.

2. Calculate the sample size needed given these factors:

ANOVA (fixed effects, omnibus, one-way)

small effect size

alpha =.05

beta = .2

3 groups

Assume that the result is a sample size beyond what you can obtain. Use the compromise function to compute alpha and beta for a sample approximately half the size. Give your rationale for your selected beta/alpha ratio. Indicate the resulting alpha and beta. Give an argument that your study is worth doing with the smaller sample.

3. In a few sentences, describe two designs that can address your research question. The designs must involve two different statistical analyses. For each design, specify and justify each of the four factors and calculate the estimated sample size you’ll need. Give reasons for any parameters you need to specify for G*Power.

Solution

1

By using G*Power3, we get the sample size

t tests - Means: Difference between two independent means (two groups)
Analysis:   A priori: Compute required sample size
Input:   Tail(s)   =   One
   Effect size d   =   0.2
   err prob   =   0.05
   Power (1- err prob)   =   0.8
   Allocation ratio N2/N1   =   1
Output:   Noncentrality parameter    =   2.489980
   Critical t   =   1.647323
   Df   =   618
   Sample size group 1   =   310
   Sample size group 2   =   310
   Total sample size   =   620
   Actual power   =   0.800218

2.

F tests - ANOVA: Fixed effects, omnibus, one-way
Analysis:   A priori: Compute required sample size
Input:   Effect size f   =   0.10
   err prob   =   0.05
   Power (1- err prob)   =   0.8
   Number of groups   =   3
Output:   Noncentrality parameter    =   9.690000
   Critical F   =   3.005042
   Numerator df   =   2
   Denominator df   =   966
   Total sample size   =   969
   Actual power   =   0.801101