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discussed previously, involves elimination of alternative interpretations of test scores through examining correlations with indicators of other constructs Campbell and Fiske pioneered the use of the multitrait-multimethod matrix as a powerful tool for examining these correlation patterns within a single study With this approach, the investigator assesses two or more constructs (the traits) using two or more measurement techniques (the methods) and then evaluates the intercorrelations among the various measures Campbell and Fiske proposed four classic criteria for interpreting the matrix as supportive of construct validity: 1 The correlations among multiple measures of the same construct (monotrait-heteromethod correlations) should be suf ciently large and signi cantly different from zero; 2 The correlations described in Criterion 1 should be larger than correlations between differing constructs, measured across different methods (heterotrait-heteromethod); 3.

taking the examination at the same time. Others choose to borrow materials from a colleague who recently took the examination. While the biannual national examination is renewed and updated each time it is given, certain areas of psychology such as statistics do not change radically between administrations. Some choose not to use any of these testing materials at all. With adequate preparation, many successfully pass the written examination. States do vary in designating what constitutes a passing score. Some states consider a fixed number of correct items such as 150 out of 200 as the criterion for passing, while others use the national median, which changes with each testing administration. Approximately 2,200 people take the examination across the United States each time it is given. An applicant may take the exam again if not passed on the first (or subsequent) attempt(s).

such as people, can be used (see Gorsuch, 1983; Thompson, 2000) Understanding is aided when several variables are found to correlate suf ciently so that they are measuring the same construct (ie, factor) In the area of intelligence, for example, scales with labels of vocabulary and similarities correlate highly together and can be considered manifestations of verbal ability Because vocabulary and similarities have been found to relate to the same factor, theoretical development may account for vocabulary and similarities simultaneously by accounting for the factor Scale construction is aided when the correlations among items show the items to fall into a certain number of clusters or groups In psychology of religion, motivation items, for example, fall into groups of items representing an intrinsic motivation (eg, the main reason I go to church is to worship God) and extrinsic motivations (eg.

, the only reason to go to church is to meet friends) The items fall into several groups so that within a group the items correlate with one factor and not with the other factors Items can then be picked by their correlations with the factors to form scales Note that there is little generalization across factors (because the variables of one factor do not correlate with the variables of another factor) and so factor analysis identi es qualitatively different dimensions Within a factor there is generalization identi ed with quantitative differences (ie, how each variable correlates with the factor) In addition to the classical factor analysis of scales, there are other uses of factor analysis It can be used to reduce several problems encountered in data analysis One problem in data analysis is the multiple collinearity problem.

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This occurs when several scales that are designed to measure the same construct are used in the same study Such scales correlate so well that it affects the statistics, such as multiple correlation First, with multiple collinearity, multiple regression beta weights are unstable, and therefore are dif cult to replicate Second, another degree of freedom is used for each additional scale that measures what one of the other scales also measures Yet having the additional measures is desirable because they increase the overall accuracy of the study Multiple collinearity can be among either the independent or dependent variables A solution to the multiple collinearity problem is to factor the variables; then the factors are used instead of the variables The same domains are covered with the factor analysis as the ones covered by the variables, and the factor analysis also shows the overlap among the scales.

The multiple collinearity among the factors will be low Another problem with statistics such as multiple correlation is that the regression weights have all the covariation.

= Pr A(n) (n(H + ) + 2) + Pr A(n) n(H + ) + n(log |X|) + 2 = n(H + ),

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