Bert F. Green

A method of scalogram analysis using summary statistics

A method of Guttman scalogram analysis is presented that does not involve sorting and rearranging the entries in the item response matrix. The method requires dichotomous items. Formulas are presented for estimating the reproducibility of the scale and estimating the expected value of the chance reproducibility. An index of consistency is suggested for evaluating the reproducibility. An illustrative example is presented in detail. The logical basis of the method is discussed. Finally, several methods are suggested for dealing with non-dichotomous items.

Complex analyses of variance: General problems

Problems in applying the analysis of variance are discussed. Emphasis is placed on using the technique to understand the data. The scale of the dependent variable is important for the analysis. Crossed and nested categories must be recognized. The error terms in the analysis depend on whether the classes of each independent variable are (1) all out of a few or (2) a few out of many. To simplify the analysis, mean squares should be aggregated with their error term when they are less than twice its size. An illustrative example is discussed in detail.

Empirical Tests of an Additive Random Number Generator

Several empirical tests were made of the apparent randomness of numbers generated by the additive process <italic>X<subscrpt>j</subscrpt></italic> = (<italic>X</italic><subscrpt><italic>j</italic>-1</subscrpt> + <italic>X</italic><subscrpt><italic>j</italic>-n</subscrpt>) mod 1, where the Xs are positive fractions. The results show that the numbers are uniformly distributed on the unit interval and that there is no significant serial correlation in the sequence. However, for <italic>n</italic> < 16, a test of run lengths indicates nonrandomness. This difficulty can be overcome by discarding alternate numbers.

Latent Structure Analysis and Its Relation to Factor Analysis

Abstract * Paper presented at the Annual Meeting of the American Statistical Association on December 29, 1950.

Computer models of cognitive processes

ConclusionFrom the small sample of achievements that I have had time to mention, we can only conclude that automation is here to stay. Nor is there any doubt that more powerful automata will be built. A great many of the “higher” human abilities will be given to machines. The great rush to automation is sure to stimulate psychologists to learn more about the human symbolic processes being mimicked by the machines. And the computers, which are the ultimate cause of the feverish scramble toward automation, are providing both the framework for describing complex models of behavior and also the means for testing these models. With both the means and the motivation at hand, psychologists are sure to make rapid progress in understanding complex human behavior.From the small sample of achievements that I have had time to mention, we can only conclude that automation is here to stay. Nor is there any doubt that more powerful automata will be built. A great many of the “higher” human abilities will be given to machines. The great rush to automation is sure to stimulate psychologists to learn more about the human symbolic processes being mimicked by the machines. And the computers, which are the ultimate cause of the feverish scramble toward automation, are providing both the framework for describing complex models of behavior and also the means for testing these models. With both the means and the motivation at hand, psychologists are sure to make rapid progress in understanding complex human behavior.

A Note on Item Selection for Maximum Validity

HORST 0) and Gulliksen (2) have both suggested procedures for selecting a set of nz items from a test so that the new test composed of the selected set of items will have maximum validity for some external criterion. A concise review of other methods of obtaining such a set of items has recently been given by Gleser and DuBois ( I ) . They propose a method, similar to those of Horst and Gulliksen, for dealing with the problem when no restriction is placed on the number of items to be used. When any of these selection procedures is used, i t is helpful to have a quick, simple method for estimating the validity of any selected subset of items. It would be extremely time-consuming to actually compute the validity for all possible subsets of items. Gulliksen has proposed such an estimate, and i t is possible to alter Horst’s formulation slightly to obtain a similar estimate. Some of the properties of these estimates are discussed in this note. The validity considered here is the validity for the group on which the item statistics and item selection are based. Other procedures are needed for estimating what the validity of the selected items would be in a new sample. The argument for considering the validity for the group on which the item selection is based is that if one subset of items shows a higher validity in this group than another subset, then it is hoped that i t will also show a higher validity in the new sample although both validities will shrink. Let the subscript c refer to the criterion, t to the total test, s to the selected subtest, ZI to the subtest composed of the un-

Using Computers to Study Human Perception

AT the Lincoln Laboratory, there is great interest in computers not only among the engineers but also in the psychology group. We have been interested in using a computer in a variety of different ways. As you know by now, if you have been following these lectures, computers are not giant brains at all; they are giant clerks. Giant clerks can help you prepare stimuli for experimental psychology just as well as they can calculate the results of experiments. For example, studies in rote memory often involve large numbers of lists of words that must be randomized. Since it is easy to teach a computer to make random numbers, the computer can easily generate random permutations of stimuli. If a different list is needed for each