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Volume :4 Issue : 14 1987      Add To Cart                                                                    Download

The Relationship betweem the Amount of inflation in item Total Score Correlation and the Standard Deviation of the Item

Auther : Al-Adel M. Abou-Alam

A theoretical analysis of the relationship between the amount of inflation in item-test correlation coefficient and the standard deviation of the item is presented. An approximation to this relationship is derived and presented in the form:

Li = si (1 - r1)

         st

In this expression, li is the size of inflation in the correlation coefficient between item i and the totl score of the test containing the item itself, si is the standard deviation of item i, st is the standard deviation of the total test score, and ri is the average of the correlation coefficienst between item i and all other items in the test.

The above expression was tested empirically using 80 item -- each of which was a part of three tests containing 20, 40 and 80 items. The ratio between the actual and the estimated inflation values found to lie between. 98 and 1.02 for 85% of the items, and between .96 and 1.02 for 95% of the items. The correlation coefficient between the actual and the estimated values was .999. Both sets of values were exactly in their means, and were close in their moment coefficients of skewness. The standard deviation of the estimated values was slightly less than that of the actual values. These results were true of all the seven sets of items which were analyzed separately.

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