THE TASK-DIFFICULTY OF FREE THROW SHOOTING FOR MALES AND FEMALES

This study demonstrated how the binomial trials model could be used to enhance performance evaluation of a psychomotor task. The study was d esigned to accomplish three purposes: (a) calibrate the task difficult y of shooting free throws; (b) determine if free-throw shooting is a m ore difficult task for females than males; and (c) demonstrate how gra ding scales could be developed when a difference in task difficulty ex ists. Adults (202 males and 196 females) ranging in age from 18 to 55 years shot 17 consecutive free throws. The performance scores were ana lyzed using the binomial trials model. The model fit the data for the total group and the females. Because no males scored 0 or more than 13 , the model did not fit the data at the extremes of the score continuu m. The task difficulty for females was 0.793 (SE = 0.084) and 0.068 (S E = 0.081)for males, which indicated differential item functioning, ch i(1)(2) = 38.73, p < .0001. Shooting free throws with a men's regulati on basketball was a more difficult task for females than males, which indicates the task does not measure the same latent trait ability for both groups. On average the males' probability of making a free throw was .146 units higher than for the females. Ability estimates were map ped to observed scores for males and females separately and used to il lustrate how fair grading scales could be developed.