| The purpose of this study was to examine the power of the Hanson method for determining differences in score distributions across multiple forms of an examination when sample sizes are small. The study used simulated data generated in SAS. The Hanson method was applied to three pairs of score distributions that varied by standard mean differences (SMD) for sample sizes of 3500, 3000, 2500, 2000, 1500, 1000, 500, 250, 200, 150, 100, 50, and 25, 1000 times each. The results indicated that the Hanson method was not sensitive to distributional differences as sample size decreased and the sensitivity of the method depended on the size of the SMD. For score distributions with very small SMDs (.008), the power of the Hanson method decreased beginning with n=2000. Score distributions with larger SMDs (.33 and .79) required smaller sample sizes (around n=100) to detect these larger differences. |
