Interval estimates of the Pearson, Kendall tau-a and Spearman correlations are reviewed and an improved standard error for the Spearman correlation is proposed. The sample size required to yield a confidence interval having the desired width is examined. A two-stage approximation to the sample size requirement is shown to give accurate results.

Corrections of correlations for range restriction (i.e., selection) and unreliability are common in psychometric work. The current rule of thumb for determining the order in which to apply these corrections looks to the nature of the reliability estimate (i.e., restricted or unrestricted). While intuitive, this rule of thumb is untenable when the correction includes the variable upon which selection is made, as is generally the case. Using classical test theory, we show that it is the nature of the range restriction, not the nature of the available reliability coefficient, that determines the sequence for applying corrections for range restriction and unreliability.

It is commonly held that even where questionnaire response is poor, correlational studies are affected only by loss of degrees of freedom or precision. We show that this supposition is not true. If the decision to respond is correlated with a substantive variable of interest, then regression or analysis of variance methods based upon the questionnaire results may be adversely affected by self-selection bias. Moreover such bias may arise even where response is 100%. The problem in both cases arises where selection information is passed to the score indirectly via the disturbance or individual effects, rather than entirely via the observable explanatory variables. We suggest tests for the ensuing self-selection bias and possible ways of handling the ensuing problems of inference.

Using variance stabilizing transformations, this note describes approximate solutions to the ranking and selection problem of selecting the best binomial population or the bivariate normal population with the largest correlation coefficient.

The validity of a test is often estimated in a nonrandom sample of selected individuals. To accurately estimate the relation between the predictor and the criterion we correct this correlation for range restriction. Unfortunately, this corrected correlation cannot be transformed using Fisher's Z transformation, and asymptotic tests of hypotheses based on small or moderate samples are not accurate. We developed a Fisher r to Z transformation for the corrected correlation for each of two conditions: (a) the criterion data were missing due to selection on the predictor (the missing data were MAR); and (b) the criterion was missing at random, not due to selection (the missing data were MCAR). The two Z transformations were evaluated in a computer simulation. The transformations were accurate, and tests of hypotheses and confidence intervals based on the transformations were superior to those that were not based on the transformations.

The scoring of response vectors to give maximum test-retest correlation is investigated. Simple sufficiency arguments show that the form of the best scores is very restricted. A general method is given for finding the best scores, deriving the best scores for the normal factor model, and showing by calculation of several particular cases that for a standard model for binary response it is easy to approximate the best scores.

We derive an analytic model of the inter-judge correlation as a function of five underlying parameters. Inter-cue correlation and the number of cues capture our assumptions about the environment, while differentiations between cues, the weights attached to the cues, and (un)reliability describe assumptions about the judges. We study the relative importance of, and interrelations between these five factors with respect to inter-judge correlation. Results highlight the centrality of the inter-cue correlation. We test the model’s predictions with empirical data and illustrate its relevance. For example, we show that, typically, additional judges increase efficacy at a greater rate than additional cues.

Corrections of correlations for range restriction (i.e., selection) and unreliability are common in psychometric work. The current rule of thumb for determining the order in which to apply these corrections looks to the nature of the reliability estimate (i.e., restricted or unrestricted). While intuitive, this rule of thumb is untenable when the correction includes the variable upon which selection is made, as is generally the case. Using classical test theory, we show that it is the nature of the range restriction, not the nature of the available reliability coefficient, that determines the sequence for applying corrections for range restriction and unreliability.

For analyses with missing data, some popular procedures delete cases with missing values, perform analysis with “missing value” correlation or covariance matrices, or estimate missing values by sample means. There are objections to each of these procedures. Several procedures are outlined here for replacing missing values by regression values obtained in various ways, and for adjusting coefficients (such as factor score coefficients) when data are missing. None of the procedures are complex or expensive.

This article demonstrates that Freeman's theta, a measure of association between a nominal variable and an ordinal variable, has a sampling distribution identical with the sampling distribution of Mann-Whitney's U.

A comprehensive statistical framework is presented which encompasses a wide range of existing nonparametric methods. The basic strategy, referred to as linear assignment (LA), depends on a simple index of correspondence defined between two object sets that have been matched in some a priori manner. In this broad sense, LA can be interpreted as a general correlational technique. A variety of extensions are discussed along with the attendant problems of significance testing and the construction of normalized descriptive indices.

This study aimed to explore the genetic variability present in tamarind fruits. A survey and collection of twenty-nine tamarind accessions from the Bastar region of Chhattisgarh was conducted, focusing on morphological traits, biochemical properties, and mineral content. The analysis revealed significant variation in fruit characteristics, including pod weight (91.1–528.3 g), pod length (4.11–15.39 cm), pulp weight (32.88–275.68 g), number of seeds (26–237), seed weight (23.14–214.08 g), pulp percentage (26.43–52.18%), vitamin C content (54.5–92 mg/100 g), phenolic content (51.53–296.4 mg GAE/g fw), flavonoid content (75.91–280.88 mg QE/ 100 g fw), acidity (5.3–12.60%), reducing sugars (24.67–68.29%), total sugars (24.89–78.87%), calcium (0.15–1.28%), and iron content (26.6–125.7 ppm) across different accessions. Based on the overall evaluation, five accessions B21, B26, B15, B25, and B7 with the best combination of desirable fruit traits, were identified as the most promising. Additionally, five sweet accessions with acidity levels below 6% were identified (B26, B21, B15, B12, B11). Principal component analysis (PCA) was applied, identifying five principal components that accounted for 86.73% of the total variability. Correlation analysis showed a significant positive relationship between pod weight and pulp weight (r = 0.93), shell weight (r = 0.70), number of seeds (r = 0.89), and seed weight (r = 0.89). The biplot of PC1 and PC2 illustrated the distribution of accessions across all four quadrants, with B27, B8, B26, B29, B14, B18, and B13 displaying distinct differences from one another.