INVESTIGATION IS CONTINUED INTO VARIOUS EFFECTS OF NON-INDEPENDENT ERROR INTRODUCED INTO MULTIPLE-CHOICE TEST SCORES AS A RESULT OF CHANCE GUESSING SUCCESS. A MODEL IS DEVELOPED IN WHICH THE CONCEPT OF THEORETICAL COMPONENTS OF SCORES IS NOT INTRODUCED AND IN WHICH, THEREFORE, NO ASSUMPTIONS REGARDING ANY RELATIONSHIP BETWEEN SUCH COMPONENTS NEED BE MADE. UTILIZING THIS MODEL, AN EXAMINATION OF THE DEPENDENCE OF RELIABILITY ON GROUP HETEROGENEITY REVEALS THAT THE NECESSARY AND SUFFICIENT CONDITIONS UNDER WHICH THE CLASSICAL EQUATION DESCRIBING THIS RELATIONSHIP HOLDS. MODELS IN WHICH ASSUMPTIONS OF THESE CONDITIONS ARE NOT APPLICABLE ARE EXAMINED. COEFFICIENT ALPHA AND OTHER RELIABILITY ESTIMATES ARE EXAMINED. IT IS FOUND THAT THE NECESSARY AND SUFFICIENT CONDITIONS FOR THE RELIABILITY OF A COMPOSITE TEST OF N PARTS TO EQUAL COEFFICIENT ALPHA ARE IDENTICAL TO THOSE UNDER WHICH RELIABILITY OF A TEST LENGTHENED N TIMES IS GIVEN BY THE SPEARMAN-BROWN FORMULA. FURTHER, THESE CONDITIONS ARE ANALOGOUS TO THOSE UNDER WHICH THE RELIABILITY OF A TEST OF N ITEMS IS EQUAL TO KUDER-RICHARDSON FORMULA 20. THE INCREASE IN TEST RELIABILITY WITH INCREASE IN NUMBER OF ALTERNATIVES PER ITEM IS CONSIDERED. THE DERIVED EQUATION DESCRIBING THIS RELATIONSHIP IS EXPRESSED IN A FORM SIMILAR TO THE SPEARMAN-BROWN FORMULA FOR INCREASE IN RELIABILITY WITH INCREASE IN TEST LENGTH. (AUTHOR)