Power Analysis

Part 1

Your colleague is upset because she/he has just done the analyses for an experiment on a worksite health promotion project and found no difference in the outcome for the people who received the intervention and the control group. When you ask your colleague what level of power the study had, he/she doesn’t know.

Your assignment is to explain to your colleague the importance of power in designing a research study and how the lack of power in the study may be why no effect was found. In about 1 page, develop this argument for your colleague.

Make sure to include:

1. A definition of statistical power.
2. The three things that influence power levels (with definitions).
3. The relationship of statistical power to which type of error (type I or type II?).
4. What an acceptable power level should be.
5. An explanation to your colleague why they may have designed an effective intervention for the worksite and still did not find a significant effect.

Part 2

Design an experimental study for which you will use a power analysis to determine your sample size (topic is your choice–anything related to public health but use an example you have not previously used in a class assignment). The experiment you design will consist of two independent groups (treatment/control). Write up a description of the research questions or hypotheses for your experiment and make sure to include and label your independent and dependent variables (3-5 sentences; 4 pts). Then calculate the necessary sample size for your study at Inference for Means: Comparing Two Independent Samples. Enter values for the mean of the two populations mu1 (μ₁) and mu2 (μ₂) and the standard difference or deviation (sigma / σ) (a measure of variability for both groups). (You can choose whatever values you would like.) Leave the analysis as a two-sided test. The goal of the power analysis is to determine the appropriate sample size you need in your study.

1. Report the values you chose and, based on these values, what should your sample size be?
2. Next, enter a different value for μ₁ or μ₂, and re-calculate the sample size (leave the other numbers as is). Report the new value you used for μ and the new sample size. Summarize what the impact of changing these values has on the sample size you need. Did it increase or decrease? Why?
3. Next try some different values for sigma (σ) and leave all other values as is. Summarize what the impact of changing the values of sigma has on the sample size you need. Did it increase or decrease? Why?
4. Finally, leave the values the same but change your power level from .80 to .90. In your answer, summarize what the impact of changing the power level has on the sample size you need. Did it increase or decrease? Why?