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| = How do I derive an expected total for a subset of items based on the expected overall total? = | = How do I derive an expected total for a subset of items based on the expected overall total item score? = |
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| You can derive expected totals for subsets of items by taking fractions of the expected total of all T items IF each subscale has the same expected value and each subscale is weighted equally in computing the total scale score. Expressed more formally | You can derive expected totals for subsets of T items by taking fractions of the expected total of all T items ''if'' each item has the ''same'' expected value and each item is weighted ''equally'' in computing the total scale score (e.g. by simple summation). Expressed more formally: |
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| If each of T items comprising a total expected score has the ''same weight'', W, and ''expected score'', E(S), then it follows for 1 <= t <= T: | if each of T items comprising a total expected score has the ''same weight'', W, and ''expected score'', E(S), then it follows for 1 <= t <= T: |
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| E(total of all T items) = TW E(S) and | E(total of all T items) = TW E(S) and, since TW is a constant, |
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| If ''either'' the weight or expected score is different for ''any'' of the item scores then it is not possible to derive the expected total score for each subset of items based on the expected overall item total by simple fractionation of the overall item expected total (as above). In this case it is necessary to know the individual item weights and expected scores to derive the expected total for each subset of items. | If ''either'' the weight or expected score is different for ''any'' of the item scores then it is not possible to derive the expected total score for each subset of items based on the expected overall item total by simple fractionation of the overall item expected total (as above). In this case it is necessary to know the individual item weights and expected scores to derive the expected total for each subset of items. Expected scores may be obtained by taking averages based upon frequency distributions of individual item scores taken from large samples. |
How do I derive an expected total for a subset of items based on the expected overall total item score?
You can derive expected totals for subsets of T items by taking fractions of the expected total of all T items if each item has the same expected value and each item is weighted equally in computing the total scale score (e.g. by simple summation). Expressed more formally:
if each of T items comprising a total expected score has the same weight, W, and expected score, E(S), then it follows for 1 <= t <= T:
E(total of all T items) = TW E(S) and, since TW is a constant, E(total of a subset of t items) = [TW/t] E(S) = E(total of all T items)/t
For example when t = 2 then it follows the expected total for half the items is equal to half the expected total of all T items.
If either the weight or expected score is different for any of the item scores then it is not possible to derive the expected total score for each subset of items based on the expected overall item total by simple fractionation of the overall item expected total (as above). In this case it is necessary to know the individual item weights and expected scores to derive the expected total for each subset of items.
Expected scores may be obtained by taking averages based upon frequency distributions of individual item scores taken from large samples.