Thomas R. Knapp

The Unit-of-Analysis Problem in Applications of Simple Correlation Analysis to Educational Research

This paper summarizes the interrelationships among within-aggregate, between-aggregate, and total-group correlation coefficients, with artificial and “real-data” examples. It also discusses the relevance of correlation analyses at various levels of aggregation and some of the difficulties encountered in cross-level inference.

An Application of Balanced Incomplete Block Designs to the Estimation of Test Norms

A perennial problem in standardized testing is the inability of test authors and publishers to obtain a representative sample of individuals (students, employees, etc.) to whom they can administer their tests for norming purposes. No matter how carefully the sample is drawn there is the inevitable unwillingness on the part of many school principals and job supervisors to release the requisite number of individuals for the often substantial blocks of time involved in completing the tests. As a result there are count-

A Benefit-Cost Analysis of New York State's "Bundy Aid" Program.

Abstract This paper attempts to summarize the economic costs and benefits of “Bundy Aid” from the point of view of New York States taxpayers. The results indicate that the program has not been cost-beneficial, relative to the alternative approach of absorption of affected students into the state system, even under “best-case” assumptions.

The Unit and the Context of the Analysis for Research in Educational Administration

A fairly common error in research in educational administration is the inappropriate choice of the unit or the context of the analysis for a given research question. The statistical treatment of data for a particular unit and a particular context is often accompanied by an interpretation of the results for a different unit or context. This paper discusses those problems, using examples from recent Educational Administration Quarterly articles, and offers some suggestions for reducing such errors in future research.

A case against the single‐sample repeated‐measures experiment

This article attempts to defend the thesis that the disadvantages of single‐sample repeated‐measures experiments outweigh the advantages and that they should be avoided unless explicit substantive considerations require them.

A Demographic Approach to Teacher Supply and Demand

Data for the period 1934 to 1978 are presented in order to illustrate a demographic model of the demand for and supply of public elementary and secondary school teachers in the United States and to describe the supply of teachers related to fertility changes. The analysis reveals that there has been remarkable adaptability of the educational system, considering the strikingly rapid changes in the number of students, but that the current situation evidences a supply of teachers that is greater than present demand.

Using Incidence Sampling to Estimate Covariances

This paper is an attempt to illustrate the generality of incidence sampling for estimating a parameter whose estimator preserves the unbiasedness of generalized symmetric means, a property which the sample covariance possesses but which the sample correlation coefficient does not. The problem of missing data is also addressed.

Notes and Comments: N vs. N-l

If there is any one topic in statistics that all students have trouble with, it is the problem of whether to use N or N-1 in the denominators of the formulas for the variance and standard deviation. The purpose of this paper is to reiterate the statistical dogma concerning when N should be used and when N-1 should be used, and to show how textbook authors have managed to confuse so many of us. N should be used in the denominator whenever the investigator 1. is dealing with a population rather than a sample, 2. is interested solely in the description of sample data and not in the inference from sample to population, or 3. wants to determine the maximum likelihood estimate of the population variance or standard deviation. (See, for example, Freund, 1962). N-1 should be used in the denominator only when the investigator wants to determine the unbiased estimate of the population variance. As Hays (1963) and some other authors point out, the square root of the unbiased estimate of the population variance is not an unbiased estimate of the population standard deviation. Why all the confusion? 1. Just about half of the authors of applied statistics textbooks introduce the concepts of variance and standard deviation using N in the denominator and the other half use N-1. Those and many instructors