A Simulation Approach for the Calculation of Statistical Power in Longitudinal Experimental Designs that Include Missing Values
Simcha Pollack and Robert Fireworker, Department of Computer Information Systems/Decision Sciences, The Peter J. Tobin College of Business
Leonard Presby, William Patterson University
Abstract: Designing an experiment in almost any area of research necessitates a power analysis for sample size determination. Results from the power analysis enable researchers to plan for the proper sample size so that, if the alternative hypothesis is true, they would have a high probability of reporting statistically significant findings. Many computer programs and formulas exist for calculating power when the research design and statistical analysis is relatively simple. These include independent and paired t-tests, one way analysis of variance and multiple regression. When the designs become more complex it is difficult or impossible to do a proper power analysis with the available tools. One example of this complex design is the longitudinal study with missing data points. For example, one sample of workers, being motivated by Method A, is observed for 5 months. The relevant measure of productivity has a correlation between time points of .4 and mean productivity increases of 1% from one month to the next. Another sample of workers being motivated by Method B, the experimental approach, is similar in every way except that the mean is hypothesized to increase by 2% each month. In both groups the residual variance is 3 at all time points. The correlation structure (e.g. compound symmetry) between time points greatly affects the findings. The existence of missing data, often occurring in experiments on humans, complicates the statistical analysis and the power analysis. No analytical formula exists to project the proper sample size under these conditions. This poster reports on work toward modeling this situation. Using SAS (Statistical Analysis System) code, we will demonstrate how to calculate power for this situation and how to easily modify the program to handle an even wider range of models. A real-time computer demonstration will be made as well.