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Thus the average of each column of the hypothetical matrix would be the same and this would be the same as the average correlation of the whole matrix. This, then, is the basic assumption of the model: that the average correlation of each item with all the others is the same. Correlation of an item with the true score With this basic assumption it can be proved that the correlation of an item with the true score equals the square root of its average correlation with all other items. where rit =the correlation of an item with the true score, and r( average)ij = the average correlation of an item with all other items.
6) is used in the calculation of the split-half reliability of a test where the correlation between the two halves is corrected for length, the original correlation being an underestimate because the test is twice as long. 6 applies because each half of the test may be regarded as a sample from the universe of items. This enables the formula to be simplified for the special case (k = 2). 6 applies regardless of the size of units, items or tests. 6) r kk = 2r]2/1 +r]2 where r 12 = the correlation between the two halves of the test.
However, even when a test has clear content validity it is advisable to demonstrate that it is valid by some other means. With tests of attainment and ability this is not usually difficult: predictive validity against the criterion of public exams or teachers' ratings is usually possible. One further point needs brief discussion. If with these tests predictive validity is a viable procedure it is pertinent to ask why content validity needs to be established. The answer to this is that predictive validity is only required because it could be that a content-valid test was rendered invalid by poor instructions or poor modes of responding.