A note on moran's measure of multiple rank correlation

A measure of multiple rank correlation,T _y.12 ², is proposed for the situation with no tied observations in the variables. The measure is a weighted average of two squared Kendall taus. It is shown thatT _y.12 ² is equivalent to a statistic previously proposed by Moran and thus a new interpretation is given to Moran's statistic.The author wishes to thank Nancy Anderson, Willard Larkin, and Kent Norman for their helpful comments.     

A note on methods of indexing associative relatedness

A method of indexing response relations among stimulus words on a word association test is presented utilizing the concept of mathematical sets. Two coefficients of associative relatedness are proposed and some relationships between these and a number of other coefficients are given.     

A note on the unbiased estimation of the intraclass correlation

The intraclass correlation,, is a parameter featured in much psychological research. Two commonly used estimators of, the maximum likelihood and least squares estimators, are known to be negatively biased. Olkin and Pratt (1958) derived the minimum variance unbiased estimator of the intraclass correlation, but use of this estimator has apparently been impeded by the lack of a closed form solution. This note briefly reviews the unbiased estimator and gives a FORTRAN 77 subroutine to calculate it.The first author was supported by an All-University Fellowship from the University of Southern California.     

A note on multiple and canonical correlation for a singular covariance matrix

A weaker generalized inverse (Rao's g-inverse; Graybill's c-inverse) can be used in place of the Moore-Penrose generalized inverse to obtain multiple and canonical correlations from singular covariance matrices.The author expresses his gratitude to a referee for his suggestions.     

A cautionary note on using internal cross validation to select the number of clusters

A highly popular method for examining the stability of a data clustering is to split the data into two parts, cluster the observations in Part A, assign the objects in Part B to their nearest centroid in Part A, and then independently cluster the Part B objects. One then examines how close the two partitions are (say, by the Rand measure). Another proposal is to split the data into k parts, and see how their centroids cluster. By means of synthetic data analyses, we demonstrate that these approaches fail to identify the appropriate number of clusters, particularly as sample size becomes large and the variables exhibit higher correlations.The authors express their thanks to the Sol C. Snider Entrepreneurial Center, Wharton School, for support of this project.     

A note on notes: note taking and containment

In extreme situations of massive projective identification, both the analyst and the patient may come to share a fantasy or belief that his or her own psychic reality will be annihilated if the psychic reality of the other is accepted or adopted (Britton 1998). In the example of' Dr. M and his patient, the paradoxical dilemma around note taking had highly specific transference meanings; it was not simply an instance of the generalized human response of distracted attention that Freud (1912) had spoken of, nor was it the destabilization of analytic functioning that I tried to describe in my work with Mr. L. Whether such meanings will always exist in these situations remains a matter to be determined by further clinical experience. In reopening a dialogue about note taking during sessions, I have attempted to move the discussion away from categorical injunctions about what analysis should or should not do, and instead to foster a more nuanced, dynamic, and pair-specific consideration of the analyst's functioning in the immediate context of the analytic relationship. There is, of course, a wide variety of listening styles among analysts, and each analyst's mental functioning may be affected differently by each patient whom the analyst sees. I have raised many questions in the hopes of stimulating an expanded discussion that will allow us to share our experiences and perhaps reach additional conclusions. Further consideration may lead us to decide whether note taking may have very different meanings for other analysts and analyst-patient pairs, and whether it may serve useful functions in addition to the one that I have described.     

A short note on the maximal point‐biserial correlation under non‐normality

The aim of this paper is to derive the maximal point‐biserial correlation under non‐normality. Several widely used non‐normal distributions are considered, namely the uniform distribution, t‐distribution, exponential distribution, and a mixture of two normal distributions. Results show that the maximal point‐biserial correlation, depending on the non‐normal continuous variable underlying the binary manifest variable, may not be a function of p (the probability that the dichotomous variable takes the value 1), can be symmetric or non‐symmetric around p = .5, and may still lie in the range from ?1.0 to 1.0. Therefore researchers should exercise caution when they interpret their sample point‐biserial correlation coefficients based on popular beliefs that the maximal point‐biserial correlation is always smaller than 1, and that the size of the correlation is always further restricted as p deviates from .5.