Correlational Study of Distribution of Totals on the "Toad" Stimulus
of the Grade 4 English Language Arts

Gerald E. DeMauro

The skills assessed by the Toad question (#2) were most closely related to those assessed by question #3. If the distribution of performance on the Toad question were affected by some contaminating variable, we would expect to see a disruption of the correlations and of the variances. We hypothesize that if there were no disruption, performance on the Toad question should have a higher correlation with question #3, indicating convergent validity, and lower correlations with other questions, indicating discriminant validity. The data uphold these hypotheses, supporting the construct validity of the question.

 

Correlations

Question 1  Question 2  Question 3  Question 4

Question 1 - .446 .485 .498

Question 2  .446 - .629 .451

Question 3  .485 .629 - .503

Question 4  .498 .451 .503 -

Finally, we would expect that the distribution of the best related questions would be most similar if there were no distributional anomalies. The ratio of variances on questions scored similarly and measuring similar traits should converge, and therefore approach 1. The data show that this is true of the ratio between the Toad question (question #2) and question #3.

Variance of Ratios (larger=denominator)

Question 1   Question 2   Question 3   Question 4

Question 1 - .811 .749 .768

Question 2 .811 - .924 .623

Question 3 .749 .924 - .575

Question 4 .768 .623 .575