Power Analysis - Lab Exercises

Exercise 1: Power Analysis

1. Examine the data contained in BodyMeasures.txt. The file lists a series of measures for individual brain structures in range of African Great Lake Cichlids. A description of the data set is found here
   • What is the effect size for differences in standard length (STDL) between individuals from the lakes Victoria and Malawi
2. You have just finished collecting data from an awesome, nifty, schnazzy, wickedly cool experiment you designed. You know that it is true, and you will gladly demonstrate, that "acupuncture gives pain relief right after finishing a 30 minute treatment". The effect size, measures as the average magnitude of the improvement in pain scores for someone who undergoes acupuncture, is a standardized mean difference (SMD, Cohen's d) of -0.61. You measure pain before and after the treatment on a point scale for physical pain. The pain scale asks "How much pain do you feel, on a scale of 1-10?" 
1. You know you want to conduct the analysis with a criterion for rejecting your null hypothesis set at p = 0.01 and you want to ensured that you had at least a 70% chance of detecting this as a treatment effect, if it really existed. How many individuals would you have to include to match these conditions.
2. Your associate beat you already to it and she already measured changes in pain levels in 5 individuals between before and after. What are her chances of detecting the effect at a p level of 0.05?
3. What would he effect size have to be minimally to detect the effect in 5 individuals and p=0.05 and a power of 0.9?
3. Why might one argue that "low" power is incompatible with doing science?