Methods of item validation and abacs for item-test correlation and critical ratio of upper-lower difference

It is shown that by making the assumption that the knowledge of the test-item and the knowledge of the entire test are both distributed normally, the correlation coefficient between any item and the entire test can be expressed as a function solely of two proportions — the percentage of a high-scoring group passing the item and the percentage of a low-scoring group passing the item. This function is expressed graphically as a family of curves for each of two conditions — where the high-scoring and low-scoring groups are samples of the highest and the lowest quarters respectively, and where they are samples from the upper and lower halves. It is shown, moreover, that two other common measures of item validity, the upper-lower difference and the critical ratio of the upper-lower difference, may be drawn on the same coordinate axes.