Painless Posterior Sampling: Bayesian Bootstrapped Correlation Coefficients

We propose the Bayesian bootstrap (BB) as a generic, simple, and accessible method for sampling from the posterior distribution of various correlation coefficients that are commonly used in the social-behavioral sciences. In a series of examples, we demonstrate how the BB can be used to estimate Pearson's, Spearman's, Gaussian rank, Kendall's tau, and polychoric correlations. We also describe an approach based on a region of practical equivalence to evaluate differences and null associations among the estimated correlations. Key advantages of the proposed methods are illustrated using two psychological datasets. In addition, we have implemented the methodology in the R package BBcor.

Angular similarity in test parameters

Through N-dimensional person space, the article gives measures of test parameters and item statistics, including difficulty/discriminating value of test, correlations between a pair of items, and item-total correlations with binary items using angular similarity between two vectors. Relationships between difficulty value and discriminating value of items and test were derived, including relationship between test reliability and test discriminating value. Reliability of a test as per theoretical definition in terms of length of score vectors of two parallel subtests and angle between such vectors was derived. The method was extended to find reliability of a battery of tests. Reliability and discriminating value of a Likert-type item and scale was found in terms of angular similarity without involving assumptions of continuous nature or linearity or normality for the observed variables, or the underlying variable being measured. The proposed methods also avoid test of unidimensionality or assumption of normality or bivariate normality associated with the polychoric correlations. Thus, the proposed methods are in fact nonparametric and considered as improvement over the existing ones. Reliability as a measure of association of two vectors and discrimination as a measure of distance between the vectors are likely to show a negative relationship.

Content and Correlational Analysis of a Corpus of MTV-Promoted Music Videos Aired Between 1990 and 1999

From 1990 to 1999 MTV promoted a series of 288 music videos called “Buzz Clips”, designed to highlight emerging artists and genres. Such promotion had a measurable impact on an artists’ earnings and record sales. To date, the kinds of musical and visual practices MTV promoted have not been quantitatively analyzed. Just what made some videos Buzzworthy, and others not? We applied two phases of content analysis to this corpus to determine the most common sonic and visual signifiers in Buzz Clips, then processed the results of that content analysis using polychoric correlations. Our findings show high degrees of shared variance between certain pairs of musical and visual elements observed in the sample music videos. We interpret a number of these relationships in terms of their relevance to a performer’s perceived ethnicity and gender, showing how certain audiovisual features regularly accompany white men (e.g., electric guitar) while others regularly accompany women and performers of color (e.g. drum machines).