Sample size determination using g * power

If you do a quantitative study for your dissertation, you must estimate the sample size you will need in order to have a reasonable chance of finding a relationship among the variables stated in your research hypotheses (should one exist), given your statistical analysis(es) and assumptions/calculations of factors 2-4 above. You must do this, even if you plan to use a convenience sample (see below). There are a number of sample size calculators available. Northcentral uses G*Power, which is required in this Activity. You will use G*Power’s “a priori power analysis” function to calculate a sample size. If it yields an unrealistically large size sample, you will rethink your design and assumptions and, perhaps, use G*Power’s “compromise power analysis” to estimate a workable sample size that makes sense. If you plan on using a convenience sample, you would use both analyses as part of your argument that your convenience sample is large enough.
Warm-up:
Download G*Power and play around with it. See how changes in assumptions and parameters affect sample size estimates. 
Submit:

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
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.

1. Calculate the sample size needed given these factors:
   • ANOVA (fixed effects, omnibus, one-way)
   • small effect size
   • alpha =.05
   • beta = .2
   • 3 groups
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 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.

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.

Length: 5-7 pages not including title page and reference page.

References: include at least 3-5 resources