Alexander M. Mood

A Method for Obtaining and Analyzing Sensitivity Data

Abstract The standard method of dealing with sensitivity of dosage-mortality data is the probit technique developed by Bliss and Fisher. This paper provides an alternative technique based on a special system for obtaining such data. It has some advantages when observations must be taken on individuals rather than groups of individuals, and it may be preferred in certain other situations. * This paper is in part an adaptation of a memorandum submitted to the Applied Mathematics Panel by the Statistical Research Group, Princeton University. The Statistical Research Group operated under a contract with the Office of Scientific Research and Development, and was directed by the Applied Mathematics Panel of the National Defense Research Committee.

The Statistical Sign Test

Abstract This paper presents and illustrates a simple statistical test for judging whether one of two materials or treatments is better than the other. The data to which the test is applied consist of paired observations on the two materials or treatments. The test is based on the signs of the differences between the pairs of observations. It is immaterial whether all the pairs of observations are comparable or not. However, when all the pairs are comparable, there are more efficient tests (the t test, for example) which take account of the magnitudes as well the signs of the differences. Even in this case, the simplicity of the sign test makes it a useful tool for a quick preliminary appraisal of the data. In this paper the results of previously published work on the sign test have been included, together with a table of significance levels and illustrative examples.

Partitioning Variance in Multiple Regression Analyses as a Tool For Developing Learning Models

Multiple regression will continue to be an extremely valuable analytical tool in educational research for many years to come even though many investigatiors (e.g., Hanushek, Levin, Michelson, Werts) recognize that such primitive single-equation models must in the long run be superseded by more sophisticated structural models. The necessity for more complicated models that make some kind of causal sense is best appreciated by econometricians who have now achieved considerable success in formulating and verifying structural models of economic activities. The most massive example is a comprehensive model of the U. S. economy (Duesenberry, et al.). We seem to be quite a long way from that happy state of affairs in education. At least my own struggles to understand educational data have not led me to any very convincing causal connections; in fact they have led me to believe that education is, at best, an order of magnitude more complex than economics and that we have much floundering searching to do before we can confidently write down identities which relate endogenous to exogenous variables as econometricians do when they state, for example, that

On the Determination of Sample Sizes in Designing Experiments

Abstract Methods are developed for determining sample sizes required to estimate means of normal populations with given precision, or to give significance when means differ by a specified amount. The methods assume that an estimate of the variance has been obtained from a previous or preliminary experiment. A simple device is suggested for using a priori information about the variance when a formal estimate is not available. * Most of this work was done under contract N7onr371 with the Office of Naval Research.

A future cities survey research design for policy analysis

Abstract Strategies for the analysis of public policy have been a major focus of interest among social scientists during the last decade. This paper introduces a survey research design and perspective which differ from most current strategies for public policy analysis. The design, which is basically an ex post facto correlational design, employs an unconventional sampling technique to derive policy-impact statements from a small sample. The policy analysis perspective of this research is focused on making prescriptive rather than descriptive statements. The specific research is the “URBIS” project, a study which is evaluating the impact of automated information systems upon the operations of local governments. After briefly discussing the general logic of public policy analysis, this paper details the methods and critical issues of this research design. The paper suggests that the URBIS research strategy might be viewed as one general model for public policy analysis.

On some basic steps in the application of systems analysis to instruction

Abstract The Systems approach to the evaluation of instruction is treated. A mathematical methodology is presented and a discussion is provided of the major aspects of the procedure i.e. definition and scope of the problem, listing of the relevant variables and their measure and construction of the model of the formulation of criteria functions. A discussion is provided of the advantages of the systems approach and the use of sensitivity analysis is treated.

Introduction to the Theory of Statistics.

1 probability 2 Random variables, distribution functions, and expectation 3 Special parametric families of univariate distributions 4 Joint and conditional distributions, stochastic independence, more expectation 5 Distributions of functions of random variables 6 Sampling and sampling distributions 7 Parametric point estimation 8 Parametric interval estimation 9 Tests of hypotheses 10 Linear models 11 Nonparametric method Appendix A Mathematical Addendum Appendix B tabular summary of parametric families of distributions Appendix C References and related reading Appendix D Tables