The inability of students to become proficient in algebra seems to be widespread in American schools. One of the reasons often cited for this inability is that instruction seldom builds on prior knowledge. Research suggests that teacher effectiveness is the most critical controllable variable in improving student achievement. This report details a…

A selection of statistical problems commonly encountered in psychological or psychiatric research concerning correlation coefficients are re-evaluated in the light of recently developed simplifications in the forms of the distribution theory of the intraclass correlation coefficient, of the product-moment correlation coefficient, and the Spearman…

Relative to given scale properties of each of two paired variables, a program for identification and computation of the following indices of relationship is provided: phi, Spearman rank order, Kendall's Tau, Pearson's product moment, biserial, and point biserial. (Author/RC)

Various cases of unequal variances and unequal sample sizes from a normal and a skewed population were used to empirically obtain the probability of a Type I error and the power for the permutation t-test as compared to Student's t-test and the Mann-Whitney U-test. Empirical results showed differences for different sample sizes, variance ratios,…

A general method of devising stepwise multiple testing procedures with fixed experimentwise error is applied to the problem of non-parametric randomized block design with ordered alternatives. In addition, the method is applied to other models with ordered alternatives. (Author)

A computer program for two-group nonparametric discriminant analysis is presented. Based on Bayes' Theorem for probability revision, the statistical rationale for this program uses the calculation of maximum likelihood estimates of group membership. The program compares the Bayesian procedure to the standard Linear Discriminant Function.…

This Digest presents a discussion of the assumptions of multiple regression that is tailored to the practicing researcher. The focus is on the assumptions of multiple regression that are not robust to violation, and that researchers can deal with if violated. Assumptions of normality, linearity, reliability of measurement, and homoscedasticity are…

Asymptotic distribution theory of Brogden's form of biserial correlation coefficient is derived and large sample estimates of its standard error obtained. Its relative efficiency to the biserial correlation coefficient is examined. Recommendations for choice of estimator of biserial correlation are presented. (Author/JKS)

Fisher's exact probability test is severely conservative when interpreted with reference to conventional alpha levels due to the discontinuity of the sampling distribution for 2 x 2 tables. An adjustment of the cell frequencies is proposed that results in a correction for continuity with appropriate alpha protection and increased power. (Author)

Inference procedures appropriate for the analysis of nominal and ordinal data are discussed. Matching models are shown to be useful under certain constraints. (JKS)

A study was conducted using generated data sets that contained specified amounts of error to determine empirically which of two large sample approximations for the coefficient of concordance or weighted average tau was more appropriate for various numbers of judges and numbers of objects. (CTM)

It is demonstrated that for polytomous items the monotone likelihood ratio (MLR) holds for the partial credit model. MLR does not necessarily hold if the slopes of the item response functions vary over items or item steps. MLR also does not hold for the graded response model. (Author/SLD)

Combined several developments in statistics and item response theory to develop a procedure for analysis of dichotomously scored test data. This version of nonparametric item response analysis, as illustrated through simulation and with data from other studies, marginalizes the role of the ability parameter theta. (SLD)