Peter Dunn-Rankin

The similarity of lower-case letters of the English alphabet

A study was made of the similarity between lower-case letters of the English alphabet by means of a relative discrimination task. Scales of letter similarity were produced which indicate the relative position of such letters to the target letters. Analysis of the scales reveals clearly definable clusters of letters. Implications for discrimination training, for diagnosis of reading readiness, and for studies of the critical features of letters are discussed.

Multiple Comparisons in a Simplified Rank Method of Scaling

RANK totals that accrue to each object from the paired-comparison frequency matrix can be linearly transformed to yield scale scores for the objects. Tests of significance may be applied to the rank sum differences depending upon the objectives of the scaling process. Where the Bradley-Terry (1952) and Thurstone (1927) procedures yield scales based on a normalizing transformation, the rank scale is a variance-stable scale, as is, e.g., the arcsine transformation of percentages. This is immediately apparent from the fact that any given rank-sum difference has the same significance no matter where the rank totals may be located on the scale. Thus the variances for all scale values are equal, a feature that other methods assume but do not guarantee. Moreover, with a given number of judges and items, scale variances are independent of the nature of the items being scaled. Therefore the technique lends itself to scaling a wide variety of stimuli. Use of multiple-comparison tests of a significance would appear to be an important adjunct to the scaling process for the following

The true distributions of the range of rank totals in the two-way classification

This paper presents the results from an investigation of the true probability distributions of the range of rank totals. A procedure for generating an approximation to the true distributions is also given. A comparison of the results of this approximation with an extensive criterion of generated true and sample distributions, and with other approximations is indicated. Accurate estimates of the critical ranges necessary to reach significance at three commonly used alpha levels, where the number of judges and items is less than or equal to sixteen, are presented in tabular form.

Accuracy of Kendall's Chi-Square Approximation to Circular Triad Distributions.

This paper contains an assessment of the accuracy of Kendalls chi-square approximation to circular triad distributions. Estimated indices are compared to enumerated values across the upper and lower tails of cumulative proportions of circular triad distributions for 5–15 objects. In general, the approximation is found to be quite good. The median difference between the exact distribution and Kendalls approximation is .000692. Critical value approximations are never in error by more than one circular triad and are almost always in the conservative direction. A researcher can be confident that little meaningful error will be present when using Kendalls approximation for experiments outside the range of tabled values. It appears that the chi-square approximation will be accurate to at least two decimal places for distributions beyond 15 objects.

HIERARCHICAL GROUPING PROCEDURES FOR COMPARING INDICES OF LETTER SIMILARITY

Congruency and similarity indices of lower-case English letters were previously obtained in theoretical and empirical studies of letter similarity. The data obtained in the studies were analyzed by hierarchical grouping procedures. Comparison of the letter groups obtained through these procedures supports the validity of the congruency index as a measure of letter similarity.