Descriptive or Explanatory Measurement

Measurement is prescriptive in that the model required to produce the numbers from the phenomena is known in advance. Statistical theory is descriptive because the model required to explain the numbers is inferred from the numbers and any other information the researcher can bring to bear. There are well-known families of measurement models and statistical models; combining them poses a number of problems, as is illustrated through an analysis of the relationship between literacy and the last grade level completed for 17,650 respondents to the National Adult Literacy Survey. One approach is to use measurement and then description by summarizing the literacy of adults by their last grade levels. A Rasch model approach can be used. Another approach, that of explanatory measurement, is to attempt to discover how much can be explained by last grade level and how much by demography. The two analyses are based on the same data but address different questions. If the sample used for the summary analysis adequately represents the country's population, then the results summarize the population's literacy as well. The explanatory analysis enables prediction of expected reading comprehension levels. The choice of analysis depends on whether the researcher wants a picture of the situation or insight into its formation. (Contains four figures and five references.) (SLD)