The relation between factor loadings and biserial correlations in item analysis

The first centroid factor loadings obtained from various interitem relations are compared with item discrimination indices commonly used in item analysis. Depending upon what type of matrix is factored, the factor loadings are shown to be related to point biserial and biserial correlations.     

The polyserial correlation coefficient

The polyserial and point polyserial correlations are discussed as generalizations of the biserial and point biserial correlations. The relationship between the polyserial and point polyserial correlation is derived. The maximum likelihood estimator of the polyserial correlation is compared with a two-step estimator and with a computationally convenient ad hoc estimator. All three estimators perform reasonably well in a Monte Carlo simulation. Some practical applications of the polyserial correlation are described.By coincidence, the first author and the second and third authors learned that they were working independently on closely related problems and, consequently, decided to write a jointly authored paper.     

A note on the computation of biserialr in item validation

A method of computing biserial coefficients of correlation through the use of punch card tabulating equipment is presented. Each item is assigned a separate column and successes are punched 1. By arranging the cards on the criterion variable and obtaining progressive sums on several columns simultaneously, it is possible to obtain data for several correlations in one run of the cards through the machine.     

CTTITEM: SAS macro and SPSS syntax for classical item analysis

This article describes the functions of a SAS macro and an SPSS syntax that produce common statistics for conventional item analysis including Cronbach’s alpha, item difficulty index (p-value or item mean), and item discrimination indices (D-index, point biserial and biserial correlations for dichotomous items and item-total correlation for polytomous items). These programs represent an improvement over the existing SAS and SPSS item analysis routines in terms of completeness and user-friendliness. To promote routine evaluations of item qualities in instrument development of any scale, the programs are available at no charge for interested users. The program codes along with a brief user’s manual that contains instructions and examples are downloadable from suen.ed.psu.edu/~pwlei/plei.htm.     

Accuracy of maximum-likelihood estimates of correlation for a biserial model

Tables are given for the calculation of variances of maximum-likelihood estimates in a multiple biserial model. For the estimates of individual correlations between the dichotomized variable and each of the graduated variables additional calculation is necessary; variances for estimates of the multiple correlation and the point of dichotomy are available directly. The required formulas and notation are those of a recent paper by Hannan and Tate.Research sponsored by the National Science Foundation under grant NSF-GP219.Aero-Space Division (Applied Mathematics), Seattle, Washington.     

Modified biserial correlation coefficients

Asymptotic distribution theory of Brogden's form of biserial correlation coefficient is derived and large sample estimates of its standard error obtained. Its efficiency relative to the biserial correlation coefficient is examined. Other modifications of the statistic are evaluated, and on the basis of these results, recommendations for choice of estimator of biserial correlation are presented.Supported by the National Institute of Mental Health Specialized Research Center Grant #MH-30854 and by the National Institute of Mental Health Grant #MH-11028.     

Further validation of the psychopathic personality inventory among offenders: personality and behavioral correlates.

The Psychopathic Personality Inventory (PPI; Lilienfeld & Andrews, 1996) is a relatively new self-report measure that has shown considerable promise as an index of psychopathic traits in both nonoffender and offender samples. The present study examined the construct validity and predictive utility of the PPI by examining its association with theoretically relevant scales of the Personality Assessment Inventory (PAI; Morey, 1991) among 60 male prison inmates, and its ability to predict institutional misbehavior in an expanded sample (n = 89). As expected, correlations with the PAI scales were highest for the Antisocial Features (ANT) and Aggression (AGG) scales (rs = .68 and .57, respectively). The PPI also predicted various forms of nonviolent and physically aggressive disciplinary infractions significantly better than chance (point biserial correlations ranging from .26 to .37).     

Some applications of attribute prediction theory to psychophysics

The following development is a coordination of certain aspects of mental test methods and psychophysics. The biserial and triserial prediction equations of the Katzell-Cureton theory are utilized to reformulate the determination of absolute and differential limens from data produced by the constant method.     

The reliability of a point biserial coefficient of correlation

An attempt is made to elaborate upon Lev's results concerning the reliability of the point biserial coefficient of correlation in a manner that will be helpful to the psychological statistician. Procedures required in the use of the non-centralt tables prepared by Johnson and Welch are described as they relate to the determination of the fiducial limits for a point biserial coefficient. A normal approximation technique for the estimation of fiducial limits is also suggested. Numerical evidence is presented which shows that relative to a given level of significance the width of the fiducial interval estimated from a point biserial coefficient of any size is smaller than that of the fiducial interval corresponding to an ordinary Pearsonian coefficient of the same magnitude.     

Repeat pregnancy among urban adolescents: sociodemographic, family, and health factors

First-time adolescent mothers are at high risk for a repeat pregnancy. The present investigation, part of an ongoing longitudinal study, examined sociodemographic, family, and health factors associated with repeat Pregnancy in a clinic sample of urban, first-time adolescent mothers (ages 13 to 17 years). They were predominantly African-American and from low-income households. Repeat pregnancy within one year and between one and two years postpartum was determined from medical records. Summary statistics, point biserial correlations, and chi-square statistics were used to analyze the data. Results indicated that postpartum contraceptive method was associated with repeat pregnancy at Year 1; contraceptive use, maternal age, history of miscarriages, and postpartum contraceptive method were associated with repeat pregnancy at Year 2. It was concluded that efforts to prevent repeat pregnancies among first-time adolescent mothers should include the continuous monitoring of contraceptive use, as well as the promotion of long-acting contraceptives (e.g., medroxyprogesterone or progesterone implants). Further, counseling should be offered to adolescent mothers with a history offered miscarriages.     

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.     

On the correlation of a naturally and an artificially dichotomized variable

A method is suggested for estimating the correlation of a naturally (X) and an artificially (Y) dichotomized variable. It is assumed that a normal random variable (L) underlies the artificially dichotomized variable. The proposed correlation coefficient recovers the product moment correlation coefficient between X and L from a fourfold table of X and Y. The suggested correlation coefficient ν is contrasted with the phi correlation and the biserial η. The biserial η was proposed by Karl Pearson and is conceptually related to the new correlation coefficient. However, in addition, Pearson's biserial η invokes the assumption that the marginal distribution of L is normal, which contradicts its basic assumptions and thus does not recover the true correlation of L and X. Finally, an approximation is provided to simplify the calculation of ν and its standard error.     

A machine method for computing the biserial correlation coefficient in item validation

A method for computing the biserial correlation coefficients with the aid of punch card equipment is oultined. A numerical example and a work sheet layout is included in the presentation.This method was developed by Dr. Elmer B. Royer prior to his untimely death on April 3, 1939. It has been prepared for publication by some of his former associates, not only as a contribution to science but also as a tribute to the memory of a true scientist.     

Corrected item-test correlations

Previous papers on this subject derive the correlation between an item and the remainder of the test. This correlation is unsatisfactory because the reliability of the remainder varies inversely with the reliability of the item omitted. The present paper derives the correlation between an item and the total test, with that item replaced by a rationally equivalent item. The general formula is then modified, for dichotomus items, to give the corrected point-biserial, biserial, and Brogden biserial correlations. The results apply strictly only to factorially homogeneous tests: those in which the same trait or combination of traits is measured (apart from error) by every item.     

Fear of success and academic underachievement

Seventy-eight female and 63 male 9th-grade students were administered the revised Horner fantasy-based measure of fear of success. The point biserial correlation between scores of this measure and academic achievement was not significant.     

A comparison of generalized and modified sample biserial correlation estimators

In a recent paper, Bedrick derived the asymptotic distribution of Lord's modified sample biserial correlation estimator and studied its efficiency for bivariate normal populations. We present a more detailed examination of the properties of Lord's estimator and several competitors, including Brogden's estimator. We show that Lord's estimator is more efficient for three nonnormal distributions than a generalization of Pearson's sample biserial estimator. In addition, Lord's estimator is reasonably efficient relative to the maximum likelihood estimator for these distributions. These conclusions are consistent with Bedrick's results for the bivariate normal distribution. We also study the small sample bias and variance of Lord's estimator, and the coverage properties of several confidence interval estimates.The author would like to thank the referees for several suggestions that improved the paper.     

A frequent misunderstanding associated with point biserial and phi coefficients

The label "Pearson r" is legitimately used both for the standard Pearson r calculated on continuous variables and for its other varieties in the form of the point biserial or the phi coefficient. This fact is often ignored by psychologists and psychiatrists.     

Relationship of feeling states after exercise and Total Mood Disturbance over 10 weeks in formerly sedentary women

Changes in feeling states after exercise and changes in overall mood after a period of 10 weeks were correlated after participation in a supervised, moderate intensity resistance training program. 52 previously sedentary, asymptomatic women (M=56 yr.) participated. Point biserial correlations were calculated between the 10-wk. change on the Profile of Mood States using the Total Mood Disturbance score as the continuous variable, and positive or negative change in feeling states after exercise, assessed via the Exercise-induced Feeling Inventory, being the dichotomous variable. Correlations were significant for both the total sample (rpb=-.49) and participants with high initial Total Mood Disturbance based on a median split (rpb=-.55). Participants with positive changes in their feeling states after exercise also showed a significantly greater decrease in Total Mood Disturbance than those with negative changes. Changes in Total Mood Disturbance were not significantly correlated with changes in resting heart rate over the 10 weeks. Discussion included limitations and, after replication, possible application of the findings.     

On the standard error of the modified biserial correlation

A paradoxical implication of Kraemer's expression for the large-sample standard error of Brogden's form of the biserial correlation is identified, and a new expression is given which does not imply the paradox. However, numerical evidence is presented which calls into question the correctness of the expression.