A table for estimating the significance of the difference between correlated percentages

A table to aid in testing the statistical significance of the difference between correlated percentages is presented. Percentage points which range from .10 to .001 are included.     

Note on the correction for continuity in testing the significance of the difference between correlated proportions

Methods of correcting for continuity in tests of significance of the difference between correlated proportions are presented. These corrections should increase the range of usefulness of the formulas developed by McNemar (1).     

Note on the sampling error of the difference between correlated proportions or percentages

Two formulas are presented for judging the significance of the difference between correlated proportions. The chi square equivalent of one of the developed formulas is pointed out.     

The significance of difference between means without reference to the frequency distribution function

Most existing tests for significance of difference between means require specific assumptions concerning the distribution function in the parent population. The need for a test which can be applied without making any such assumption is stressed. Such a statistical test is derived. The application of the test involves converting scores to rank orders. The exact probabilities may then be calculated for specified differences between samples by means of which the null hypothesis may be tested. The application of the test is simple and requires a minimum of calculation. The test loses in precision because of the conversion to rank orders but gains in generality since it may be safely used with any kind of distribution.This study was started at the Iowa Child Welfare Research Station of the State University of Iowa. I should like to express my gratitude for the help I received there.     

The minimum average correlation between equivalent sets of uncorrelated factors

A simplified proof of a lemma by Ledermann [1938], which lies at the core of the factor indeterminacy issue, is presented. It leads to a representation of an orthogonal matrixT, relating equivalent factor solutions, which is different from Ledermann's [1938] and Guttman's [1955].T is used to evaluate bounds on the average correlation between equivalent sets of uncorrelated factors. It is found that the minimum average correlation is independent of the data.This paper owes much to an unknown reviewer.     

Tables for the determination of the significance of skewness and of the significance of the difference in the skewness of two independent distributions

Several of the more popular statistics texts used in psychology are reviewed with respect to their treatment of the measurement and interpretation of skewness. Some areas in psychology where measures of skewness of distributions may yield significant information are indicated. Tables of 1%, 2% and 5% points of moment measures of skewness and tables of the 1% and 5% points of the difference in skewness of two uncorrelated distributions are presented. These tables are approximations based on the approximate normality of skewness in large samples from normal populations. The limited confidence with which these tables can be used in the absence of exact knowledge of the distribution function of the underlying statistics is indicated.The opinions expressed in this article are those of the author and are not to be interpreted as official War Department policy.     

The significance of rank difference coefficients of correlation

The coefficients of rank difference correlation that are barely significant at six different levels of significance are given forN's of 2 to 30. Most of the values were obtained by translation of Olds' tables of probabilities for various values of d ². Comparison of these data with those obtained by four other methods indicates that one method yields values more appropriate than those obtained from Olds' data for coefficients significant at the .01 level forN's from 11 to 25. This method also provides a convenient means of obtaining approximate values of coefficients significant at the .01 level forN's above 30. Need for caution in evaluating the significance of coefficients obtained from data involving tie rankings is indicated. The article concludes with recommendations as to choice of methods of determining the significance of rank difference coefficients.     

The difference between t and z and the difference it makes

Tests of the null hypothesis for comparisons involving sample means use the t test when the conditions of the z test cannot be met. The 2 tests have different rationales and can lead to different conclusions regarding significance. In the present study, the authors compared the properties of t and z in simulation runs. The differences in the results are a result of fluctuations in the t test sample variances that do not exist in the z test, and those differences lead to differences in designating the significance of comparisons.     

A theoretical framework for testing the additive difference model for dissimilarities data: Representing gambles as multidimensional stimuli

Implicit within the acceptance of most multidimensional scaling models as accurate representations of an individual's cognitive structure for a set of complex stimuli, is the acceptance of the more general Additive Difference Model (ADM). A theoretical framework for testing the ordinal properties of the ADM for dissimilarities data is presented and is illustrated for a set of three-outcome gambles. Paired comparison dissimilarity judgments were obtained for two sets of gambles. Judgments from one set were first analyzed using the ALSCAL individual differences scaling model. Based on four highly interpretable dimensions derived from this analysis, a predicted set of dimensions were obtained for each subject for the second set of gambles. The ordinal properties of the ADM necessary for interdimensional additivity and intradimensional subtractivity were then tested for each subject's second set of data via a new computer-based algorithm, ADDIMOD. The tests indicated that the ADM was rejected. Although violations of the axioms were significantly less than what would be expected by chance, for only one subject was the model clearly supported. It is argued that while multidimensional scaling models may be useful as data reduction techniques, they do not reflect the perceptual processes used by individuals to form judgments of similarity. Implications for further study of multidimensional scaling models are offered and discussed.     

Null hypothesis significance testing. On the survival of a flawed method

Null hypothesis significance testing (NHST) is the researcher's workhorse for making inductive inferences. This method has often been challenged, has occasionally been defended, and has persistently been used through most of the history of scientific psychology. This article reviews both the criticisms of NHST and the arguments brought to its defense. The review shows that the criticisms address the logical validity of inferences arising from NHST, whereas the defenses stress the pragmatic value of these inferences. The author suggests that both critics and apologists implicitly rely on Bayesian assumptions. When these assumptions are made explicit, the primary challenge for NHST--and any system of induction--can be confronted. The challenge is to find a solution to the question of replicability.     

Pigeons play the percentages: computation of probability in a bird

The ability to compute probability, previously shown in nonverbal infants, apes, and monkeys, was examined in three experiments with pigeons. After responding to individually presented keys in an operant chamber that delivered reinforcement with varying probabilities, pigeons chose between these keys on probe trials. Pigeons strongly preferred a 75% reinforced key over a 25% reinforced key, even when the total number of reinforcers obtained on each key was equated. When both keys delivered 50% reinforcement, pigeons showed indifference between them, even though three times more reinforcers were obtained on one key than on the other. It is suggested that computation of probability may be common to many classes of animals and may be driven by the need to forage successfully for nutritional food items, mates, and areas with a low density of predators.