Dangers Inherent in Correlating Averages
Joseph W. Halliwell · The Journal of Educational Research · 1962
OVER A PERIOD of years many studies in edu cation and psychology have been conducted in which statistical techniques involving the correlation of averages have been employed. Few basic statistical texts have devoted sufficient coverage to the dangers inherent in the use of this technique. A survey of ten basic statistics texts indicated that seven of the ten texts included no cautions concerning the correlating of averages. One of the texts pointed out the possi bility of obtaining coefficients that were spuriously high (2), and two texts emphasized the fact that the correlation among means might actually be reversed in sign from the correlations within the samples (3, 4). Garrett (2), in his treatment of the correlation of averages, cites correlational studies containing state or occupational averages as illustrations of spurious ly high correlations resulting from the canceling out of factors which ordinarily reduce correl ations. There is ample justification for the assumption that, in general, correlations among samples tend to re sult in higher coefficients than correlations with in dividual scores. It is important to note, however, that with certain variables in education the reverse tendency might prevail. This would be particularly true in correlational studies involving teachers' marks. Teachers seem to have a tendency to utilize the class as aframe of reference, so that in a school system in which traditional grading practices are employed, a boy of average intelligence in a bright class will not fare nearly so well as does his counter part in a dull class. Under ordinary circumstances such relativism in grading practices would lead to a situation in which the correlations within classes would be of greater magnitude than the correlation among the classes. This would be particularly true in school systems which feature homogeneous group ing. There is also a distinct possibility that although correlations within classes are positive and high that the correlation among the classes might be negative. Lindquist (4) in his discussion concerning the possi ble reasons for the correlation among the means being negative while correlations within the samples are positive and high, states that such an occurance would be very rare. If the possibility of sucha phen omenon occuring is as rare as Lindquist assumes, there would be little need for extended coverage of