The Task Difficulty of Free Throw Shooting for Males and Females

Abstract

This study demonstrated how the binomial trials model could be used to enhance performance evaluation of a psychomotor task. The study was designed to accomplish three purposes: (a) calibrate the task difficulty of shooting free throws; (b) determine if free-throw shooting is a more difficult task for females than males; and (c) demonstrate how grading scales could be developed when a difference in task difficulty exists. Adults (202 males and 196 females) ranging in age from 18 to 55 years shot 17 consecutive free throws. The performance scores were analyzed 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 continuum. The task difficulty for females was 0.793 (SE = 0.084) and 0.068 (SE = 0.081) for males, which indicated differential item functioning, χ₁ ² = 38.73, p > .0001. Shooting free throws with a men's regulation 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 mapped to observed scores for males and females separately and used to illustrate how fair grading scales could be developed.

Key Words:

• Rasch model
• free throw shooting
• item response theory