Simulation of Classroom Variables by Computer

Abstract

The digital computer can be programmed to produce fictitious data which are largely indistinguishable from real data. The data produced by such a program could serve as a good instructional product for disseminating information on class characteristics and the results of research. Careful study of the same data might suggest hypotheses for field testing against student and teacher data.This paper describes an illustrative computer program which serves as a model for generation of data with specified characteristics. The data generated by computer resemble data observed in a sample of fourthgrade classes. The general approach is opposite in direction to usual research procedures in which data are used to generate descriptive statistics. The approach described in this paper is to use descriptive statistics (and the computer) to generate data.The development of the program, written in MAD (Michigan Algorithm Decoder), was facilitated by subroutines for generating random numbers. Galler (1962) discusses several methods by which random numbers may be produced by computer. As an example, the power-residue method starts with an initial number r and repeatedly multiplies it by a carefully selected number P, each time retaining only the rightmost n digits. If m is the number system and n is the number of digits in a computer word, it theoretically is possible to generate m n different numbers. These are referred to as pseudorandom numbers since the method of production yields sequences of numbers which if carried far enough produce a repeating sequence. A transformation sited by Galler (1962) can be used to generate normally distributed numbers from the uniformly distributed values.The program employs the random numbers to generate sets of random variables with arbitrary intercorrelations. (For instance, it may be desired that a distribution of Y values have a correlation of .60 with a distribution of X values.) Hoffman (1959) describes a procedure in which a linear transformation of scores on an existing variable can be used to produce the desired distribution. The Y values also can be made to exhibit any arbitrary mean and standard deviation. The author notes that 289 at UNIV OF MASSACHUSETTS on April 13, 2015 http://aerj.aera.net Downloaded from