Ipsative Measure

Data are ipsative if a given set of responses always sums to the same total. In practice, the term ipsative is used roughly as a synonym for “interdependent” and refers to some type of dependency among the variables measured on a survey, scale, test, or other measure. An example of data that are ipsative can be seen by asking respondents to choose between two items[Page 489] that measure different psychological constructs. For example, a choice between “I am the life of the party” (extraversion) and “I am always prepared” (conscientiousness) will result in ipsative data because a choice of the extraversion item necessitates that the conscientiousness item is not chosen.

Many different properties of data collection and analysis exist that can create ipsative relationships between scale scores. For example, Likert scale data can be made to be ipsative by simply subtracting the grand mean of each individual's scale scores (averaged across all scales) from each of his or her individual scale scores (i.e., ipsatized data). With this type of data, scores for each respondent will always sum to the same total across scales. However, there is no constraint on the variability of responses because respondents are free to choose any point on the scale without constraint. Data can also be ipsative via the properties of the item response format, such as rank-ordered scales, or through forced-choice responses from a set of items. With forced-choice and rank-order data, respondents are more constrained in their response options, and thus more interdependence exists in these types of ipsative data.

There are two primary types of interdependence that arise from ipsative data. The first type, covariance-level interdependence, relates to constraints that are placed on covariance matrices via the properties found in all types of ipsative data. Mathematically, (a) the sums of the columns, or rows, of an ipsative covariance matrix must equal zero; (b) the sums of the columns, or rows, of an ipsative intercorrelation matrix will equal zero if the ipsative variances are equal; (c) the average intercorrelations of ipsative variables have –1/(m – 1) as a limiting value where m is the number of variables; (d) the sum of the covariances obtained between a criterion and a set of ipsative scores equals zero; and (e) the sum of ipsative validity coefficients will equal zero if the ipsative variances are equal. A second type of interdependence, item-level interdependence, occurs in rank-order and forced-choice scales because choosing any one item from a set is contingent upon the content of the other items.

Generally speaking, increasing the number of scales appearing on a survey will serve to lessen the amount of covariance-level interdependence among constructs. Similarly, decreasing the percentage of measured scales that are used in analyses will also lessen the covariance-level interdependence. However, not using some scales in subsequent analyses will have no effect on the item-level interdependence of forced-choice and rank-order data. Although the issue remains controversial, these interdependencies can affect reliability estimates and factor analyses.