Statistical Power
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Researchers, as a whole, tend to underestimate the need for power. I'm just now starting to get it. I recently gave a brief, easy-to-follow presentation on statistical power, it's importance, and how to go about getting it. Hope you find it useful.
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Statistical Power
- 2. TOPICS What is Statistical Power? Why is it important? Estimating Statistical Power Useful Software An example: Mobile Health study 2
- 3. WHAT IS POWER? Power = the probability of correctly rejecting a false null hypothesis (when the alternative hypothesis is true) Power = 1 - β More powerful experiment = better chance of rejecting a false null hypothesis Thus, reducing the likelihood of Type II error 3
- 4. WHAT IS POWER? Statistical power can help answer questions like these: How large must my sample size be? How should I design my experiment? Which measures/test should I use? I can get about X amount of people in my study, will I have enough power? 4
- 5. ESTIMATING STATISTICAL POWER One should estimate statistical power during the design phase of the study Especially after: Selecting measures Choosing a valid statistical test Power can be estimated for many types of tests (t-Tests, ANOVA, regression, etc.) Very common in treatment effectiveness research 5
- 6. ESTIMATING STATISTICAL POWER It’s OK to try out different designs and statistical tests in the search for the most powerful or practical study. However, these trials must be done before conducting the study. 6
- 7. ONE WAY TO ESTIMATE POWER Use population means and standard deviations (or best guesses) Example: Say you want to assign 20 individuals to two groups, control (C) and treatment (T)*. Table 1: Population Parameters Mean Standard Deviation Control 9.64 3.17 Treatment 6.58 3.03 Step 1. Draw 20 random observations from a population with scores like the C group Step 2. Draw 20 random observations from a population with scores like the T group Step 3. Calculate the t statistic Step 4. Repeat above steps 9,999 more times To estimate how much power this study will have, you can follow these steps *Example from Howell (2013) 7
- 8. ONE WAY TO ESTIMATE POWER 86% of the results greater than 2.024 Power (given the parameter estimates) is .86 *Howell (2013), pg 221 Out of the 10,000 t values, how many are greater than tcrit(38) = 2.024? 8
- 9. THE TRADITIONAL WAY We know that power depends on the degree of overlap between sampling distributions *Howell (2013), pg 222 9
- 10. THE TRADITIONAL WAY Overlap/power depends on: Statistical test Alpha level Sample size Effect size (ES) μT – μC σ Means for treatment and control populations Pooled standard deviation ES = 10
- 11. USEFUL SOFTWARE Commercial: SAS sample and power size PASS sample size software Free: R package pwr G*Power And many more! I will be using G*Power to illustrate an example Download G*Power here: http://www.gpower.hhu.de/ 11
- 12. MOBILE HEALTH STUDY Research Question: Will regular (text) messages and targeted messages increase drug adherence for adult patients with diabetes when compared to diabetic patients who do not receive messages? Control Group (G1): No messages Treatment Group 1 (G2): regular messages Treatment Group 2 (G3): targeted messages 12
- 13. MOBILE HEALTH STUDY What we know Dependent variable: drug adherence (range=5-25) Independent variables: G1, G2, G3 Minimally importance difference: 3 (a difference of 3 points is needed to show clinical significance) Want power = .80 13
- 14. MOBILE HEALTH STUDY 1. Choose test Here, we will be using an omnibus F test of a one- way ANOVA with 3 levels (or groups) 14
- 15. MOBILE HEALTH STUDY G*Power offers plenty of tests 15
- 16. MOBILE HEALTH STUDY 2. Determine the effect size Means and standard deviations are guided by our hypotheses and previous research SD = 3 Means:G1= 12, G2 = 13, & G3 = 15 *change power and group size 16
- 17. MOBILE HEALTH STUDY 3. Calculate estimates Our results: To achieve a power of .80 and given the parameter estimates, We will need at least 60 patients (20 per group) in the study *note effect size 17
- 18. MOBILE HEALTH STUDY Alternatively, you can manually enter the effect size. Again, guided by hypotheses and previous research 18
- 19. A NOTE ON PRACTICALITY That last test (with ES = .20) calls for a total sample size of 246 patients. What if that’s not feasible? You can: Revisit your study design Revise hypotheses, attempt other tests, change measures, etc. Or, work backwards. Estimate power from a sample size that is practical 19
- 20. REFERENCES Howell, D., C. (2013). Power. In J. D. Hage (Ed.). Statistical methods for psychology (8th ed., pp. 229- 249). Belmont, CA: Wadsworth, Cengage Learning. Kraemer, H. C., Thiemann, S. (1987). How many subjects? Newbury Park, CA: Sage Publications, Inc. Lipsey, M. W. (1990). Design sensitivity: Statistcal power or experimental research. Newbury Park, CA: Sage Publications, Inc. 20
- 21. BIG THANKS To Dr. Philippe Gaillard for his wonderful guidance (and books!) Also to the STAT 7970 class - wonderful audience. To contact me email - cdatubo@gmail.com visit - http://cdatubo.weebly.com/ connect - http://www.linkedin.com/in/cdatubo 21
Editor's Notes
- We’re trained to think about significance level or reducing Type I error (finding a difference that is not there) Rarely trained to consider an equally important topic which is NOT finding a difference that IS there (Type II error) Knowing the degree of statistical power can lead to a more efficient use of the researchers resources (e.g., not wasting money on small samples that give unreliable results or large samples that are unnecessary)
- Knowing the degree of statistical power can lead to a more efficient use of the researchers resources (e.g., not wasting money on small samples that give unreliable results or large samples that are unnecessary)
- Knowing the degree of statistical power can lead to a more efficient use of the researchers resources (e.g., not wasting money on small samples that give unreliable results or large samples that are unnecessary)
- control = 9.64, 3.17 (sd); treatment 6.58, 3.03(sd); 20 participants in each group draw 20 observations from pop with similar scores to the control group and 20 from pop like treatment group. Calculate the t stat. do this 9, 999 more times (10,000 t values). Note critical value =t(38)=2.024
- Note critical value is for 38 df =2.024
- Recall what it looks like when we compare two sampling distributions H0= when mu=mu0 = when null hypothesis is true H1= when mu=mu1 = when null hypothesis is false dark blue= alpha or probability of Type I (one-tailed) rejecting a true null hypothesis Light blue = to the left of critical t value, Type II error, failing to reject false null hypothesis Power = the probability that we will correctly reject a false null hypothesis Power is affected by alpha (or significance level), the true alternative hypothesis, the sample size, and statistical test
- Rules of thumb: Smaller significance level, the larger the necessary sample size Two-tailed tests need larger sample sizes than one-tailed The smaller the effect size, the larger the necessary sample size