British Journal of Mathematical and Statistical Psychology

Lovie, A. D.

doi: 10.1111/j.2044-8317.1981.tb00614.xpmid: N/A

Newcomers to experimental psychology might be forgiven for thinking that the flurry of interest in repeated measure designs and their problems is of recent vintage only and that, prior to 1900, most psychologists experienced little or no difficulty with their use or analysis. This is not the case, however, and an interest in their problems and analyses can be detected even in the earliest applications of analysis of variance to psychology. The purpose of this paper, therefore, is to survey critically work on repeated measure designs and their analysis over the period 1940 to 1950. During this decade it is possible to discover the beginnings of all of the approaches and attitudes that colour contemporary thinking, from the outright radicalism of those who would reject the use of repeated measure designs almost completely, to those who view the problem as one of adapting existing techniques in design and analysis to take account of the specific features of such designs. The keys to understanding the work are the degree of insight into the structure of the designs exhibited by the people involved and their attitudes to subjects as a factor.

Bezembinder, Thorn G. G.

doi: 10.1111/j.2044-8317.1981.tb00615.xpmid: N/A

Let R be a linear order on a set Z = {x, y,…} of n objects. Let Dm and D(t) be systems of paired comparisons on Z such that in every one of the pairs with xRy the system Dm contains an observed proportion p = 0, 1/m,…, 1 of choices for x over y while D(t) contains a probability of choosing x over y as given by a choice theory (t) which also specifies R. For systems D1 a circularity index is proposed as an alternative to Kendall's and Slater's consistency indices. Some properties of these three indices are investigated in the sets of all possible D1 for some small n. If m > 1, Dm may be more or less compatible with D(t) and also give rise to a D1, estimating R. It is argued that the compatibility of Dm with D(t) may be regarded as an index of the external consistency of D1, with respect to R which is to be distinguished from its circularity or internal consistency. This distinction is corroborated by computer simulations of paired comparisons under Thurstone's case V model. The correlations between the three circularity indices and four indices of external consistency are essentially zero. Finally, the bearing of assessing circularity to the assessing and testing of the (in)transitivity of data systems is indicated.

French, Simon

doi: 10.1111/j.2044-8317.1981.tb00616.xpmid: N/A

It is standard practice in examinations to sum a candidate's marks over individual papers and award a final grade according to the overall total. This paper questions the adequacy of such an approach and, drawing on results from the theory of measurement, tentatively suggests an alternative.

Strauss, David

doi: 10.1111/j.2044-8317.1981.tb00617.xpmid: N/A

The standard counter‐examples to Luce's choice axioms involve similarities between some of the choice alternatives. If one regards choice as a random utility process then the similarities can be interpreted as correlation between the utility variables; the counter‐examples are then simply explained. A class of multivariate double exponential distributions is discussed which modifies Luce's probability formula to allow for similarities. The choice by features model proposed here defines one way in which several features, or similarity groupings, may be combined. An important special case of the model is an extension of Luce's to account for similarities; this model can be parameterized in a natural way, and it is then possible to estimate and test hypotheses about the parameters of interest.

Sahlin, Nils‐Eric

doi: 10.1111/j.2044-8317.1981.tb00618.xpmid: N/A

A method is presented for collecting data which yield a scale on which the entities are ranked in preference and all combinations of value distances are ranked (higher‐ordered metric scale). The method is based on the concept of secondary preference, i.e. preference among preferences. This method is compared with a classical method based on 50–50 game comparison. Two empirical studies are presented. The first examines whether both methods yield the same ordering of value distances. The second involves empirical derivation of a higher‐ordered metric scale.

Heath, Richard A.

doi: 10.1111/j.2044-8317.1981.tb00619.xpmid: 7284278

A random walk model for decision making in psychological discrimination tasks is described which provides a satisfactory account of the observed non‐stationarity of the representation of stimulus information. The model successfully predicts the relationship between RT and response proportion in a temporal order judgement task performed under instructions emphasizing both speed and accuracy. The implications of the model for memory‐dependent tasks are discussed.

Bartholomew, D. J.

doi: 10.1111/j.2044-8317.1981.tb00620.xpmid: N/A

The term posterior analysis is used in this paper to refer to methods of drawing inferences about the latent variables in factor analysis after the model has been fitted. In particular with the problem of locating each individual in the latent space on the basis of the values of the observed variables. This problem has been traditionally treated by determining factor scores. It is argued here that, if all variables in the model are random, then Bayes' theorem provides the logical link between the data and the unobserved latent variables. Viewed in this perspective the indeterminacy of factor scores is simply an expression of the fact that the latent variables are still random variables after the manifest variables have been observed. The name, factor scores, can then reasonably be given to the location parameters of the posterior distributions. The paper is primarily expository and it contains no new mathematics. Its concern is with the logical framework within which the analysis should be carried out and interpreted.

McDonald, Roderick P.

doi: 10.1111/j.2044-8317.1981.tb00621.xpmid: N/A

An explication is offered for the notion of dimensionality both for tests and items. A set of n tests or of n binary items is unidimensional if and only if the tests or the items fit a common factor model, generally non‐linear, with one common factor, that is, one latent trait. Both test scores and item responses in general contain stable specific factors as well as errors of retest measurement. The two‐parameter normal ogive model can be obtained from a joint space which in general is of n + 1 dimensions. One of these is the latent trait continuum while the remaining n are dimensions of unique (specific and error) variation. If and only if the items fit the perfect scale the n + 1 dimensions collapse into one dimension. Proposals to regard coefficient alpha as a coefficient measuring homogeneity, internal consistency, or generalizability, do not appear to be well founded.

Plewis, Ian

doi: 10.1111/j.2044-8317.1981.tb00622.xpmid: N/A

Marascuilo & Serlin (1979) discuss the problem of measuring relative change for a dichotomous variable and suggest ways of testing for the statistical significance of such changes. This article considers alternatives to the non‐parametric approach adopted by Marascuilo & Serlin, alternatives which emphasize statistical models and which can be extended to all types of longitudinal categoric data. The models are fitted to the data presented by Marascuilo & Serlin, the results are compared and the advantages and disadvantages of the various approaches are discussed.

Blair, R. Clifford; Higgins, J. J.

doi: 10.1111/j.2044-8317.1981.tb00623.xpmid: N/A

Bradley (1977) has shown that the mixed normal family of distributions is an important population model in many behavioural science research contexts. Researchers engaged in studies of the type discussed by Bradley (1977) might well wonder about the relative appropriateness of various statistical techniques that might be employed in data analyses. For example, in the case of a two‐sample test for shift, should one use the parametric t test or some non‐parametric counterpart such as Wilcoxon's rank‐sum test? The primary purpose of this paper is to examine some of the characteristics of the asymptotic relative efficiency (ARE) of the Wilcoxon rank‐sum test relative to the independent means t test under various mixtures of two normal distributions. Pursuant to this goal, the equation for finding the ARE of the two tests under various mixtures of two distributions is developed, the equation is applied to various example situations, and certain limiting values of the equation are noted. As a result, it is concluded that the Wilcoxon statistic tends to have large ARE advantages over the t test in research contexts similar to those considered by Bradley (1977). It is concluded, therefore, that the Wilcoxon test is the more appropriate statistic for the research situations considered.