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Elementary Models for Measuring Change

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Achievement Gains, Change, Mathematical Models, Measurement Techniques, Research Design, Statistical Analysis


Observed change is the difference between an individual's initial and final measures. Positive change is called gain or growth; negative change is loss. The regression effect is discussed using an example of the weight of individuals. To find variables associated with weight gain, the initial weight should be held constant, guaranteeing that the variables associated with gain were not found simply because they were associated with initial weight. Consideration of the simple difference scores may also be misleading. The obtained data should be compared with the data that would have been obtained under the appropriate null hypothesis of no treatment effect. Any significant discrepancy would be attributed to some deviations from the null hypothesis. The second major source of confusion in studies of change is measurement error, resulting in fallible variables. Averaging out these errors by replicating measurements is desirable. Estimation of change for an individual is illustrated, and reliability is discussed. The effect of change on group heterogeneity is discussed. When a correlation is computed between change and some other variable, it is not necessary to estimate the true change separately for each individual. The most likely difficulties in that case are spurious correlation, attenuation, and partial correlation. When individuals are assigned at random to two or more treatments, the problem is estimating and comparing the effects of the separate treatments, or mean change. Paper presented at the Invitational Conference on Problems in Measuring Change, Madison, Wisconsin, April 30, 1962.

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