Estimation of sampling error variance in the meta-analysis of correlations: Use of average correlation in the homogeneous case.

The estimate of the population correlation used in the formula for sampling error variance of a correlation is typically the observed correlation, but in meta-analysis the average of the observed correlations can be used. For the case in which there is no variation in the study population correlations or sample sizes and the number of studies is very large, the authors found that use of the average correlation estimator is more accurate than use of the traditional, individual correlation estimator, except in those rare cases in which the uncorrected population correlation is greater than .60. For typical sample sizes, when the uncorrected population correlation is between -.40 and .40, there is virtually no error in the meta-analysis credibility interval based on the average correlation estimator. On the other hand, the amount of the error in the individual correlation estimator is qualitatively important if the sample is 25 or less and the population correlation is less than .40. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Unbiased estimation of sampling variance of correlations.

In a recent article, P. E. Spector and E. L. Levine (1987) asserted that the estimate of sampling error variance used in validity generalization studies is biased when the number of correlations is relatively small. In addition, Spector and Levine maintained that the bias is such that the sampling error variance estimate seriously overestimates the actual variance of observed correlations. A partial replication of Spector and Levine's study showed that the alleged bias was due to a distributional artifact and that the sampling error estimate is not seriously biased. We review evidence from several Monte Carlo studies indicating that the sampling error estimate is quite accurate. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Intraclass correlation estimates in a school-based smoking prevention study. Outcome and mediating variables, by sex and ethnicity

Most school-based smoking prevention studies employ designs in which schools or classrooms are assigned to different treatment conditions while observations are made on individual students. This design requires that the treatment effect be assessed against the between-school variance. However, the between-school variance is usually larger than the variance that would be obtained if students were individually randomized to different conditions. Consequently, the power of the test for a treatment effect is reduced, and it becomes difficult to detect important treatment effects. To assess the potential loss of power or to calculate appropriate sample sizes, investigators need good estimates of the intraclass correlations for the variables of interest. The authors calculated intraclass correlations for some common outcome variables in a school-based smoking prevention study, using a three-level model-i.e., students nested within classrooms and classrooms nested within schools. The authors present the intraclass correlation estimates for the entire data set, as well as separately by sex and ethnicity. They also illustrate the use of these estimates in the planning of future studies.     

Work values: Genetic and environmental influences.

The Minnesota Importance Questionnaire (MIQ), measuring work values, was administered to 23 monozygotic and 20 dizygotic reared-apart twin pairs to test the hypothesis that genetic factors are associated with work values. Both univariate and multivariate analyses were performed. In the univariate analysis, intraclass correlations were computed to estimate the proportion of variability in work values associated with genetic factors for each of the 20 MIQ scales and for the 6 higher-order work value scales. The multivariate analysis used maximum likelihood estimation to separate the genetic and environmental factors for the correlated higher-order scales. Results from both analyses indicated that, on average, 40% of the variance in measured work values was related to genetic factors, whereas approximately 60% of the variance was associated with environmental factors and error variance. Implications for job enrichment and motivation theories are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Inheritance of teat number and its relationship to maternal traits in swine

The relationship of teat number to seven measures of female reproduction was evaluated in the University of Nebraska Gene Pool population. Teat number was recorded for 7,513 pigs, ovulation rate for 2,794 gilts and litter size and weight at birth and weaning (42 days) for 789 gilts. Paternal half-sib and full-sib analyses were used to estimate heritabilities for each trait and to estimate the genetic and phenotypic correlations of teat number with the measures of reproduction. The direct response to selection for ovulation rate and the correlated response in teat number were also evaluated from the regressions of line differences (Select-Control) on generation number (10 generations of selection) and cumulative selection differential for ovulation rate. The paternal half-sib heritabililty for teat number was .32, and the paternal half-sib heritabilities for ovulation rate and the litter traits were similar to previous estimates from this population. Most of the genetic and phenotypic correlations with teat number were negative and all were nonsignificant. The realized heritability for ovulation rate was .46 +/- .10. The regression of response in teat number on generation number number was .08 +/- .03 (P < .10). An estimate of .44 was obtained for the realized genetic correlation of teat number with ovulation rate.     

In vitro study of enzymatic degradation of biological tissues fixed by glutaraldehyde or epoxy compound

RATIONALE AND OBJECTIVES: The authors performed this study to clarify and systematize the large number of variances and correlations observable with variance-component models of receiver operating characteristic (ROC) index estimates. MATERIALS AND METHODS: The authors present a variance-component model for ROC index estimates (and for differences between estimates) and show correspondences between the method of experimental replication and the random components in the model. The authors introduce a notation that identifies both the method of replication and, when examining estimate differences, the estimate pairing scheme. RESULTS: For models with three factors (modality, reader, case sample), the authors delineated four methods of replication and eight pairing schemes for generating estimate differences. For each of the resulting 32 replication-pairing combinations, the authors gave expressions for the variance of the difference and for the correlation between the two ROC index estimates. CONCLUSION: The variance-component approach is a useful statistical tool for modeling different sources of variation that contribute to the overall variance of ROC data and index estimates derived from those data.     

Toward using confidence intervals to compare correlations.

Confidence intervals are widely accepted as a preferred way to present study results. They encompass significance tests and provide an estimate of the magnitude of the effect. However, comparisons of correlations still rely heavily on significance testing. The persistence of this practice is caused primarily by the lack of simple yet accurate procedures that can maintain coverage at the nominal level in a nonlopsided manner. The purpose of this article is to present a general approach to constructing approximate confidence intervals for differences between (a) 2 independent correlations, (b) 2 overlapping correlations, (c) 2 nonoverlapping correlations, and (d) 2 independent R2s. The distinctive feature of this approach is its acknowledgment of the asymmetry of sampling distributions for single correlations. This approach requires only the availability of confidence limits for the separate correlations and, for correlated correlations, a method for taking into account the dependency between correlations. These closed-form procedures are shown by simulation studies to provide very satisfactory results in small to moderate sample sizes. The proposed approach is illustrated with worked examples. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Unsquared genetic correlations.

Demonstrates that correlations commonly used to provide an estimate of the ratio of genotypic to phenotypic variance require restrictive (and probably unreasonable) assumptions. When these assumptions are violated, the correlation in question will provide a biased estimate of the desired ratio. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Intraclass correlations: There's more there than meets the eye.

Methods of calculating intraclass correlations (ICC) are well established and understood in psychological research. Several issues relating to the process of determining reliability have, on the other hand, been only lightly treated. The present paper examines 2 issues regarding the use of ICCs: (a) the real vs theoretical limits of ICCs and procedures for applying significance tests when using these measures and (b) sources of unreliability in the data. The real limits of some ICCs are not 0 and +1.00 (the theoretical limits), but exceed both –2.00 and +1.00. Even when within the theoretical limits, the ICC values may not always reflect the reliability of the measure. Under certain conditions, one can obtain moderately high ICC values that are not significantly different from zero, suggesting that researchers calculate the significance of the target variance before calculating the intraclass r. Three sources of unreliability are also identified: patterns of both positive and negative correlations among judges, limited variance in the data matrix, and no correlations among judges. A method of determining the significance of the Judge?×?Target interaction and for demonstrating how that procedure can be used to aid in the identification of sources of unreliability, is detailed. (13 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A model for interpreting genetic correlations with estimates of parameters.

Presents a general additive model for kinship correlational structures which includes genetic, environmental, covariance, and measurement error components. The properties and assumptions of the model and other models which are viewed as special cases are discussed. A procedure is described for estimating the model parameters from sample correlation coefficients. The procedure results in numerical estimates of the ratio of genetic to environmental variance, estimates of the correlation between genetic and environmental factors, and estimates of the correlation between environments. A simple procedure for partitioning a correlation coefficient into its variance components is suggested. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An analysis of correlations corrected for attenuation and range restriction.

An empirical attempt at demonstrating the bias in correlation coefficients that are corrected for both attenuation and range restriction was recently presented by R. Lee et al (see record 1983-02451-001). Using asymptotic methods, the present article analytically derives properties of the double-corrected correlation. It is shown that the double-corrected correlation is negatively biased. This negative bias decreases with increasing sample size and/or selection ratio. An expression for the standard error of the corrected correlation, useful for confidence interval estimation, is presented. Although the standard error of the corrected correlation is larger than that of the uncorrected correlation, the increase is proportionately smaller than the respective increase in the point estimate. Findings represent progress toward the request for full information about corrected correlations set forth in the Standards for Educational and Psychological Tests. (12 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Estimation of genetic parameters for growth, feed consumption, and conformation traits for double-muscled Belgian blue bulls performance-tested in Belgium

For 1,442 Belgian Blue bulls performance-tested at the Centre de Sélection de la Race Blanc-Bleue Belge, nine traits were observed: height at withers at 7 mo, height at withers at 13 mo, weight at 7 mo, weight at 13 mo, average feed consumption of concentrates, average daily gain, average feed consumption of concentrates per average daily gain, average feed consumption of concentrates per mean metabolic weight, and price per kilogram of live weight. This price is based on muscle conformation and is therefore used as muscle conformation score. Restricted maximum likelihood with a derivative-free algorithm was used to estimate (co)variance components because there were different models and missing values per trait. Estimates of heritabilities were above .50 except for average feed consumption per average daily gain (.16) and average feed consumption per mean metabolic weight (.33). Estimates of genetic and phenotypic correlations between height at withers and weight traits were positive and moderate to high. Average daily gain showed a negative genetic correlation with weight at 7 mo (-.68) but had positive correlations with height at withers at 13 mo and weight at 13 mo (.22 and .43). Muscle conformation expressed as price per kilogram of live weight was related to low average feed consumption per average daily gain. Average feed consumption showed high correlations with weight at 7 mo and weight at 13 mo. Average feed consumption per average daily gain had a high negative genetic correlation with average daily gain (-.89).     

Genetic and environmental factors in relative body weight and human adiposity

We review the literature on the familial resemblance of body mass index (BMI) and other adiposity measures and find strikingly convergent results for a variety of relationships. Results from twin studies suggest that genetic factors explain 50 to 90% of the variance in BMI. Family studies generally report estimates of parent-offspring and sibling correlations in agreement with heritabilities of 20 to 80%. Data from adoption studies are consistent with genetic factors accounting for 20 to 60% of the variation in BMI. Based on data from more than 25,000 twin pairs and 50,000 biological and adoptive family members, the weighted mean correlations are .74 for MZ twins, .32 for DZ twins, .25 for siblings, .19 for parent-offspring pairs, .06 for adoptive relatives, and .12 for spouses. Advantages and disadvantages of twin, family, and adoption studies are reviewed. Data from the Virginia 30,000, including twins and their parents, siblings, spouses, and children, were analyzed using a structural equation model (Stealth) which estimates additive and dominance genetic variance, cultural transmission, assortative mating, nonparental shared environment, and special twin and MZ twin environmental variance. Genetic factors explained 67% of the variance in males and females, of which half is due to dominance. A small proportion of the genetic variance was attributed to the consequences of assortative mating. The remainder of the variance is accounted for by unique environmental factors, of which 7% is correlated across twins. No evidence was found for a special MZ twin environment, thereby supporting the equal environment assumption. These results are consistent with other studies in suggesting that genetic factors play a significant role in the causes of individual differences in relative body weight and human adiposity.     

Estimating test norms via multiple matrix sampling.

Compared estimates of a population mean and variance obtained by examinee sampling and multiple matrix sampling (MMS), using a computer-simulated database. Variables were number of observations and item subtest sizes. Results indicate that MMS provided as good estimates of a population mean and variance as examinee sampling. The estimate of population variance, however, became more stable as number of items in each subtest increased. (French abstract) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A test of two refinements in procedures for meta-analysis.

This study used Monte Carlo simulation to examine the increase in accuracy resulting from 2 statistical refinements of the interactive Schmidt-Hunter procedures for meta-analysis: the use of the mean correlation instead of individual correlations in the estimation of sampling error variance, and a procedure that takes into account the nonlinear nature of the range-restriction correction. In all of the cases examined, these refinements increased the accuracy of the interactive procedure in estimating the variance of population correlations and resulted in more accuracy than other procedures examined. The use of the mean correlation in the sampling error variance formula also increased the accuracy of variance estimates for the multiplicative and Taylor Series procedures. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Assessment of ecologic regression in the study of lung cancer and indoor radon

Ecologic regression studies conducted to assess the cancer risk of indoor radon to the general population are subject to methodological limitations, and they have given seemingly contradictory results. The authors use simulations to examine the effects of two major methodological problems that affect these studies: measurement error and misspecification of the risk model. In a simulation study of the effect of measurement error caused by the sampling process used to estimate radon exposure for a geographic unit, both the effect of radon and the standard error of the effect estimate were underestimated, with greater bias for smaller sample sizes. In another simulation study, which addressed the consequences of uncontrolled confounding by cigarette smoking, even small negative correlations between county geometric mean annual radon exposure and the proportion of smokers resulted in negative average estimates of the radon effect. A third study considered consequences of using simple linear ecologic models when the true underlying model relation between lung cancer and radon exposure is nonlinear. These examples quantify potential biases and demonstrate the limitations of estimating risks from ecologic studies of lung cancer and indoor radon.     

Application of an autoregressive process to estimate genetic parameters and breeding values for daily milk yield in a tropical herd of Lucerna cattle and in United States Holstein herds

The objectives of this study were to estimate from test day records the genetic and environmental (co)variance components, correlations, and breeding values to increase genetic gain in milk yield of Lucerna and US Holstein cattle. The effects of repeated observations (within cow) were explained by first-order autoregressive processes within and across lactations using an animal model. Estimates of variance components and correlation coefficients between test days were obtained using derivative-free REML methodology. The autoregressive structure significantly reduced the model error component by disentangling the short-term environmental effects. The additional information and the more heterogeneous environmental variances between lactations in the multiple-lactation test day model than in the first lactation model provided substantially larger estimates of additive genetic variance (0.62 kg2 for Lucerna; 14.73 kg2 for Holstein), heritability (0.13 for Lucerna; 0.42 for Holstein), and individual genetic merit. Rank correlations of breeding values from multiple lactations and from first lactations ranged from 0.18 to 0.37 for females and from 0.73 to 0.89 for males, respectively. Consequently, more selection errors and less genetic gain would be expected from selection decisions based on an analysis of first lactation only, and greater accuracy would be achieved from multiple lactations. Results indicated that substantial genetic gain was possible for milk yield in the Lucerna herd (34 kg/yr). Estimates of genetic variance for Holsteins were larger than previously reported, which portends more rapid genetic progress in US herds also; under our assumptions, increases would be from 173 to 197 kg/yr.     

Bias in validity generalization variance estimates: A reply to Hoben Thomas.

In a recent article H. Thomas (see record 1989-10691-001) derived the expected value of the true validity variance estimate used in validity generalization studies. Based on computations of the expected values for certain scenarios, Thomas made a number of critical assertions regarding the variance estimate. This article shows that Thomas's arguments regarding deficiencies in the variance estimate used in the validity generalization studies are misleading. Contrary to Thomas's extremely negative assessment of the situation, there is no really convincing reason to doubt or abandon the estimates of true validity variance obtained in applied research from the Callender-Osborn and other closely related methods. Rather, there is strong evidence to indicate that populations of true validities with meaningful differences in mean and variance can be reliably distinguished, provided that a sufficient amount of base data are available. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Least squares interval mapping of quantitative trait loci under the infinitesimal genetic model in outbred populations

Genetic marker and phenotypic data for a quantitative trait were simulated on 20 paternal half-sib families with 100 progeny to investigate properties of within-family-regression interval mapping of a postulated single quantitative trait locus (QTL) in a marker interval under the infinitesimal genetic model, which has been the basis of the application of quantitative genetics to genetic improvement programs, and to investigate use of the infinitesimal model as null hypothesis in testing for presence of a major QTL. Genetic effects on the marked chromosome were generated based on a major gene model, which simulated a central biallelic QTL, or based on 101 biallelic QTL of equal effect, which approximated the infinitesimal model. The marked chromosome contained 0, 3.3%, 13.3%, or 33.3% of genetic variance and heritability was 0.25 or 0.70. Under the polygenic model with 3.3% of genetic variance on the marked chromosome, which corresponds to the infinitesimal model for the bovine, significant QTL effects were found for individual families. Correlations between estimates of QTL effects and true chromosome substitution effects were 0.29 and 0.47 for heritabilities of 0.25 and 0.70 but up to 0.85 with 33.3% of polygenic variance on the marked chromosome. These results illustrate the potential of marker-assisted selection even under the infinitesimal genetic model. Power of tests for presence of QTL was substantially reduced when the polygenic model with 3.3% of genetic variance on the chromosome was used as a null hypothesis. The ability to determine whether genetic variance on a chromosome was contributed by a single QTL of major effect or a large number of QTL with minor effects, corresponding to the infinitesimal model, was limited.     

Sulfur distribution in bacteriorhodopsin from multiple wavelength anomalous diffraction near the sulfur K-edge with synchrotron x-ray radiation

Estimates of variance components for test day records in an animal model that considered multiple traits over multiple lactations were calculated using REML methodology. Test day records were classified into 11 periods within first and later lactations. Missing ancestors in the relationship matrix were classified in genetic groups. Data were collected from Costa Rican dairy farms. Estimates of components for total and additive genetic variance were clearly heterogeneous during the lactation. Heritabilities for traits in later parities were slightly higher than those for traits in first parity. Heritabilities were highest for records of midlactation. Phenotypic and genetic correlations for adjacent test days were close to 1. Phenotypic correlations were lower than genetic correlations. Heterogeneity of variances during the lactation suggests the adequacy of the multiple-trait test day model to describe milk yield during the lactation. When missing ancestors were allocated to a single base population instead of genetic groups, the estimates of residual variance were lower, and the estimates of genetic variance and genetic correlations were higher. When standardized records were used instead of actual test day records, the estimates of residual and total variance were lower, and the estimates of genetic variance were higher. Consequently, estimates of heritability and genetic correlations were also higher. Use of standardized data obtained by interpolation procedures is not advised for estimation of genetic variance components in a test day model.