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This paper compares the Pearson Chi-Square and Kolmogorov goodness-of-fit tests with respect to validity under the following conditions: (1) the N independent observations are tabulated and arranged into k mutually exclusive groups that are equally probable under the hypothesis to be tested; and (2) both N and k are "small"; i.e., not greater than 50. A random sampling experiment was performed, and the results show that in general for the conditions considered, the Pearson test is more valid than the Kolmogorov test. [ABSTRACT FROM AUTHOR]

When an experiment is run with a factorial layout and some of the factors are random effects, there may not be an exact test for some effect of interest. This paper considers three statistics that could be used to test that hypothesis using a ratio of linear combinations of independent Chi-square statistics. The common case, utilizing four Chi-square statistics, is examined for a number of configurations of nuisance parameters. Both the power and the probability of a type I error are used in the comparison. Two statistics appear to be equally good over a large region and, in certain situations, the statistics involving the subtraction of Chi-square statistics is shown to be more stable. [ABSTRACT FROM AUTHOR]

This paper deals with a multivariate extension of Friedman's chi[sup 2, sub tau]-test. A rank permutation distribution and the large sample properties of the criterion are studied. The asymptotic relative efficiency (A.R.E.) for a sequence of translation alternatives is studied and bounds are given for certain special cases. It is shown that, under specified conditions, the A.R.E. of this test with respect to the likelihood ratio test is largest, when the block dispersion matrices differ and can be greater than unity when the differences are large. [ABSTRACT FROM AUTHOR]

Ellison has shown that the Wald-Wolfowitz tolerance limits for a normal distribution, x + lambda s, are good only to 0(n/N[sup 2]), rather than to 0(1/N[sup 2]). Here x is distributed normally with mean mu and variance sigma[sup 2]/N while s[sup 2]/sigma[sup 2] is distributed as chi[sup 2, sub n]/n independently of x. Thus, for n much greater than N[sup 2] the usual values of lambda are incorrect; Ellison has proposed an alternative in this case. This paper derives new lambda's which have two advantages over the Wald-Wolfowitz and the Ellison limits. First, they are shown to be better approximations. Secondly, they are easily calculated in the sense that only tables of the normal and chi[sup 2] distributions are required and the solution of a non-linear equation is not required. [ABSTRACT FROM AUTHOR]

This article presents a study of the learning of verbal material congruent and incongruent with attitudes. The aim was to select Ss with rather strongly held attitudes and to have them learn verbal materials consistent and inconsistent with these attitudes. The Allport-Vernon Study of Values was given to 319 students in elementary psychology classes and those items pertaining to religious or political-economic attitudes were scored. WA Form R-PE 6 (S) was given to the same groups. Twenty-two Ss were found who met the arbitrary criteria for being designated as Religious (R) S, and 21 Ss for being designated as Political-Economic S. Resulted data are evaluated in two ways, by Chi Square and by the t-test. The evidence summarized in this report suggests that it is easier for Religious Ss to learn paired associates in which the response word is a religious one than it is for them to learn paired associates in which the response word has a political economic meaning. The reverse finding was obtained for Ss with strong political-economic values.

Several authors have considered point and interval estimation of the exponential scale parameter, σ, on the basis of subsets of the order statistics. In this paper, we suggest a procedure for finding approximate confidence intervals for σ in large samples, using k sample quantiles of a random sample of size n. The procedure is based on a simple chi-square approximation to the distribution of the asymptotically best linear estimate of σ. We compare this procedure with the one given by Ogawa (1962) based on an approximating t-distribution. We find that the interval based on the chi-square approximarion is easier to calculate, and performs better when k is small and n is large. [ABSTRACT FROM AUTHOR]

Recently the U. S. Water Resources Council has proposed standardization of the analysis of peak flood discharges by fitting a Pearson Type III distribution to the logarithms of the data. This action has served to draw attention to the inadequacy of available tables of percentage points of the Pearson Type III distribution and the need for better tables. Many tables of percentage points of the related chi-square distribution are available in the literature, perhaps the most comprehensive being those published by the author in 1964. These could be used to obtain percentage points of the Pearson Type III distribution, but it would be much more convenient to have a table from which percentage points of the latter distribution could be read directly for uniformly spaced values of the skewness coefficient. The author has therefore, by a modification of the programs used to compute his 1964 tables of percentage points of the chi-square distribution, obtained percentage points, corresponding to cumula. tire probability P = .0001, .0005, .001, .005, .01, .02, .025, .04, .05, .1(.1).9, .95, .96, .975, .98, .99, .995, .999, .9995, .9999, of the standardized Pearson Type III distribution with skewness α[sub 3] ≡ γ[sub 1] = 0.0(0.1)9.0. This paper includes the five-decimal-place table, accurate to within a unit in the last place, together with a description of the method of computation and a discussion of possible applications, including the estimation of the return periods of floods. Space has been conserved by giving results only at intervals of 0.2 in &alpha[sub 3] for &alpha[sub 3] > 4.8; the intermediate values, if needed, can be obtained by interpolation. [ABSTRACT FROM AUTHOR]

This paper is concerned primarily with the method of moments in dissecting a mixture of two normal distributions. In the general case, with two means, two standard deviations, and a proportionality factor to be estimated, the first five sample moments are required, and it becomes necessary to find a particular solution of a ninth degree polynomial equation that was originally derived by Karl Pearson [10]. A procedure which circumvents solution of the nonic equation and thereby considerably reduces the total computational effort otherwise required, is presented. Estimates obtained in the simpler special case in which the two standard deviations are assumed to be equal, are employed as first approximations in an iterative method for simultaneously solving the basic system of moment equations applicable in the more general case in which the two standard deviations are unequal. Conditional maximum likelihood and conditional minimum chi-square estimation subject to having the first four sample moments equated to corresponding population moments, are also considered. An illustrative example is included. [ABSTRACT FROM AUTHOR]

A technique previously developed for interpreting measures of association for fourfold tables based on markovian assumptions is here extended to derive measures of second order association. Transition rates between the states represented by [ABSTRACT FROM AUTHOR]

This study examines student participation in formal organizations. The five social participation categories were the four quartiles for the sample, labeled as None, Low, Middle--in the order of increasing participation. Chapin Social Participation Scale reports the reliability coefficient as .887. Social adjustment was measured by the Washburne Social Adjustment Inventory. The chi square was employed to test for statistically significant relationships between participation scores and various background factors such as age, employment and marital status. The data for the study were collected from a random sample of students in a large midwestern university. Of the background factors studied, sex, age, marital status, and military status are significantly related to social participation. Women participate more than do men. The older the student, the less likely he is to participate. Among men, traveling time to campus and mode of travel are related significantly to social participation. Women who participate date significantly more than do low participants or non-participants. Men in the middle and low participant categories are more active in sports than those in the high or non-participant categories. Place of residence is an important factor in social participation. For the females, however, the mean social adjustment scores increased with decreased participation.

Focuses on an experimental study of the effect of character and personality in public speaking. Historic studies on effectiveness of oral persuasion; Use of chi-square test for the analysis.

As a result of an opinion poll among the students at Grinnell College a sex difference was noted. This investigation was designed to test the significance of this difference and to seek the cause for it. It was found to be significant when tested by chi-square, and the chief reason seemed to be in underlying attitudes of (a) greater emotionality of response on the part of women and (b) greater interest in the war and world events on the part of men. [ABSTRACT FROM AUTHOR]

The article presents a study on leadership as related to Bernreuter personality measures. The purpose of the present study is to attempt to pick out the individual items on the inventory which show a significant difference in the responses of the leaders and the non-leaders. Also an analysis of the "traits" which appear to determine these differences in response is made. To a lesser extent we are interested in the validity of the trait scales and the appropriateness of the names applied to them. The subjects are 81 college women -- 36 leaders and 45 nonleaders. The increase in the number of non-leaders is due to the inclusion of some day students. The exclusion of day students in the previous study was found not materially to change the results. The first step is the tabulation of the responses made by the two groups to each of the 125 items on the inventory. The items which appear to show a difference in response are selected from the total list. The application of the Chi-Square Test reveals that few of the 125 items in the Inventory show a significant difference in the responses of the leaders and non-leaders

Explores the use of statistical tests for decision-making in regional geographical construction in the United States. Chi square; Variance analysis; Relationship between regional constructs and the areal dispersion of selected traits within regional frames.

The article presents a comparative analysis of MMPI profiles of black and white psychiatric patients. An analysis was conducted wherein corrected chi-square was computed for each item on the race criterion in each sample. Eight factors comprising 53 of 58 items were derived in the psychiatric patient sample. The black psychiatric patient more often than the white psychiatric patient characterized herself as an individual who, although considering herself morally conscientious, was unable to affect her environment, as she felt manipulated by powerful external agents. Ten factors comprising 56 of 65 items were derived in the prison sample. The black prison inmate more often than the white prison inmate characterized himself as having intense feelings, and as conscientious, self-confident, sensitive to self and others. Item-level comparisons have value for further investigations, as scale scores conceal racial differences and as many discriminating items are not keyed so that scale-level comparisons do not utilize all available data.

Looks on the use of Chi square for testing regional geographical boundaries. Absolute frequency of a geographic area; Validity of the statistical test; Use of acres as a unit of mensuration.