We briefly discuss the philosophical basis of science, causality, and scientific evidence, by introducing the hidden but most fundamental principle of science: the similarity principle. The principle's use in scientific discovery is illustrated with Simpson's paradox and other examples. In discussing the value of null hypothesis statistical…

Type I error rates in multiple regression, and hence the chance for false positive research findings, can be drastically inflated when multiple regression models are used to analyze data that contain random measurement error. This article shows the potential for inflated Type I error rates in commonly encountered scenarios and provides new…

An analysis of variance procedure for testing differences in r-squared, the coefficient of determination, across independent samples is proposed and briefly discussed. The principal advantage of the procedure is to minimize Type I error for follow-up tests of pairwise differences. (Author/JKS)

It has been shown that the degree of restriction of range taken into account in testing the hypothesis that rho equals zero, entails risks of incorrect inferences. It is argued that an alternative is to disregard the restriction of range and to use the common t-statistics proposed by regression theory. (Author/JKS)

The effects of the violation of the assumption of normality in the conditional distributions of the dependent variable, coupled with the condition of multicollinearity upon the outcome of testing the hypothesis that the regression coefficient equals zero, are investigated via a Monte Carlo study. (Author/JKS)

EXPLORE is a flexible computer program for analyzing multiple data sets. The investigator has the option of focusing on the original variables, or of selecting a reduced rank solution where original variables are summarized by a principal components analysis. (Author/JKS)

The effects of the violation of the assumption of homogeneity of regression on the Type I error rate and on the power of analysis of covariance are investigated. The results indicate that analysis of covariance is robust when sample sizes are equal. (Author/JKS)

The controversy surrounding regression methods for unbalanced factorial designs is addressed. The statistical hypotheses being tested under the various methods, as well as salient issues in the use of these methods, are discussed. The use of statistical computer packages is also discussed. (Author/JKS)

The t ratio used in testing the difference between two independent regression coefficients is generalized to the multivariate case of testing the difference between two vectors of regression coefficients. This is particularly useful in determining which of two variables best predicts a number of criterion variables. (Author/JKS)

Develops a testing procedure based on a model including treatment effects on residual variances. (Author/RC)