N. Clayton Silver

A Monte Carlo Evaluation of Tests for Comparing Dependent Correlations

Abstract The authors conducted a Monte Carlo simulation of 8 statistical tests for comparing dependent zero-order correlations. In particular, they evaluated the Type I error rates and power of a number of test statistics for sample sizes (Ns) of 20, 50, 100, and 300 under 3 different population distributions (normal, uniform, and exponential). For the Type I error rate analyses, the authors evaluated 3 different magnitudes of the predictor-criterion correlations (py,x1 = py,x2=.1, .4, and .7). For the power analyses, they examined 3 different effect sizes or magnitudes of discrepancy between py,x2 and py,x2 (values of .1, .3, and .6). They conducted all of the simulations at 3 different levels of predictor intercorrelation (px1,x2 = .1, .3, and .6). The results indicated that both Type I error rate and power depend not only on sample size and population distribution, but also on (a) the predictor intercorrelation and (b) the effect size (for power) or the magnitude of the predictor-criterion correlations (for Type I error rate). When the authors considered Type I error rate and power simultaneously, the findings suggested that O. J. Dunn and V. A. Clarks (1969) z and E. J. Williamss (1959) t have the best overall statistical properties. The findings extend and refine previous simulation research and as such, should have greater utility for applied researchers.

Sex differences in color preferences among an elderly sample.

The purpose of the study was to assess differences in color preferences between the sexes. A sample of 193 retirees were asked to report their favorite colors. The pattern of frequencies for preferred color differed as a function of sex. Blue was chosen as the most preferred color by both sexes. Women preferred black and purple more than men did. Moreover, the men preferred red over pink, whereas the women preferred red and pink equally. The rank order of color preferences for this elderly group were very similar to the findings of Silver, et al. who sampled young adults in 1988.

The Impact of Color on Warnings Research

Researchers have examined a variety of attributes that influence a warnings ability to communicate important product hazards. These attributes include font type, signal words, and the use of icons. One attribute that has been noticeably absent from the warnings literature is color. Therefore, the purpose of the present study was to determine the appropriateness of achromatic stimuli in product warning research. Thirty-three undergraduate students rated color and achromatic versions of twelve labels. These labels varied across four levels of product class and three levels of signal word. All labels were evaluated on six attributes: salience, readability, hazardousness, likelihood of injury, carefulness, and familiarity. A composite variable called “perceived hazard” was formed from the averaged ratings of hazardousness, carefulness, and likelihood of injury. Moreover, an additional variable “perceived readability” was composed of the mean ratings of readability and saliency. Results showed that color labels were perceived as more readable and hazardous than achromatic labels. Implications for warning research are discussed.

A FORTRAN 77 Program for Comparing Dependent Correlations.

Suppose that a researcher is interested in determining whether the correlation between job satisfaction and salary is larger than between job satisfaction and supervisor ratings within the same sample. This would constitute a test of dependent correlations with one element in common (ρ12 = ρ23). May and Hittner (1997) and Hittner, May, and Silver (2003) performed Monte Carlo simulations on a number of statistical tests for examining this hypothesis and found that Williams’s (1959) t, Dunn and Clark’s (1969) z, Steiger’s (1980) modification of Dunn and Clark’s z using average correlations, a similar modification of Dunn and Clark’s z using average Fisher zs, and Meng, Rosenthal, and Rubin’s (1992) z were all fairly equal in terms of controlling Type I error and power. As a second example, consider the case in which a researcher is interested in determining whether the correlation between job satisfaction and salary is smaller at Time 1 than 1 year later (e.g., after a 6% raise is given across the board). This example calls for a test of dependent correlations with zero elements in common (ρ12 = ρ34). Silver, Hittner, and May (2004) performed a Monte Carlo simulation on four different procedures for testing this hypothesis and found that Dunn and Clark’s (1969) z, Steiger’s (1980) modification of Dunn and Clark’s z using average correlations, and the modification of Dunn and Clark’s z using average Fisher zs were all fairly equal in terms of controlling Type I error and power. Unfortunately, these hypothesis tests are computationally tedious and cannot readily be computed by most statistical packages. Although Hittner and May (1998) created a SAS program for testing dependent correlations, their program only tests the null hypothesis of ρ12 = ρ23. Moreover it is possible to perform tests of dependent correlations using structural equation modeling methods (Cheung & Chan, 2004), however, many researchers may not be familiar with these techniques. Hence, DEPCOR provides a user-friendly means for obtaining the procedures advocated by Hittner et al. (2003) and Silver et al. (2004) for testing dependent correlations.

Testing Dependent Correlations with Nonoverlapping Variables: A Monte Carlo Simulation.

The authors conducted a Monte Carlo simulation of 4 test statistics for comparing dependent correlations with no variables in common. Empirical Type I error rates and power estimates were determined for K. Pearson and L. N. G. Filons (1898) z, O. J. Dunn and V. A. Clarks (1969) z, J. H. Steigers (1980) original modification of Dunn and Clarks z, and Steigers modification of Dunn and Clarks z using a backtransformed average z procedure for sample sizes of 10, 20, 50, and 100 under 3 different population distributions. For the Type I error rate analyses, the authors evaluated 3 different magnitudes of the predictor-criterion correlations (ρ12 = ρ34 = .10, .30, and .70). Likewise, for the power analyses, 3 different magnitudes of discrepancy or effect sizes between correlations with no variables in common (ρ12 and ρ34) were examined (values of .10, .40, and .60). All of the analyses were conducted at 3 different levels of predictor intercorrelation. Results indicated that the choice as to which test statistic is optimal, in terms of power and Type I error rate, depends not only on sample size and population distribution but also on (a) the predictor intercorrelations and (b) the effect size (for power) or the magnitude of the predictor-criterion correlations (for Type I error rate). For the conditions examined in the present study, Pearson and Filons z had inflated Type I error rates when the predictor-criterion correlations were low to moderate. Dunn and Clarks z and the 2 Steiger procedures had similar, but conservative, Type I error rates when the predictor-criterion correlations were low. Moreover, the power estimates were similar among the 3 procedures.

Adjudicated Mexican American Adolescents: The Effects of Familial Emotional Support on Self-Esteem, Emotional Well-Being, and Delinquency

This article examines relationships between familial emotional support, self-esteem, emotional well-being, and delinquency in 58 adjudicated Mexican American adolescents who were on probationary status with the juvenile justice system. Results indicated that maternal emotional support was negatively correlated with delinquency, and positively correlated with emotional well-being. In addition, regression analyses revealed that familial emotional support significantly predicted delinquency and emotional well-being, with maternal emotional support accounting for most of the total variance. Unlike previous findings in the general delinquency research, familial emotional support was unrelated to self-esteem. These results offer several insights into the nature and effects of Mexican American familial emotional support on an adolescents behavioral and emotional adjustment.

Initial Reliability and Validity of the Life Satisfaction Scale for Problem Youth in a Sample of Drug Abusing and Conduct Disordered Youth

Responses to Life Satisfaction Scale for Problem Youth (LSSPY) items were examined in a sample of 193 substance abusing and conduct disordered adolescents. In responding to the LSSPY, youth endorse their percentage of happiness (0 to 100%) in twelve domains (i.e., friendships, family, school, employment/work, fun activities, appearance, sex life/dating, use of drugs, use of alcohol, money/material possessions, transportation, control of ones life). Results indicated that the LSSPY yielded three factor structures (i.e., Social Satisfaction, External Obligations Satisfaction, Substance Use Satisfaction), demonstrated good initial psychometric properties, and appears to be a useful instrument in the evaluation of treatment outcome in problem youth. Males were more satisfied in the Social and External Obligations domains than females, although no gender differences were indicated in Substance Use Satisfaction. Caucasian, African-American, and Hispanic youths responded to LSSPY items similarly. Future directions are discussed in light of these results.

The Interaction of Signal Word and Color on Warning Labels: Differences in Perceived Hazard

Previous research has examined the connoted hazard of various colors and signal words separately. The purpose of the present research was to examine the interaction of signal words and colors. A sample of 30 undergraduates rated the perceived hazard of 105 signal word/color combinations printed in specific hazard colors. of the colors used, red conveyed the highest level of perceived hazard followed by orange, black, green, and blue. There were significant differences among the signal words which were grouped into three different hazard level categories. High hazard words conveyed significantly more hazard than moderate and low hazard words. Likewise, moderate hazard words conveyed significantly more hazard than low hazard word group. More importantly, however, it was noted that a signal word such as DEADLY connoted less hazard when printed in green than red ink. Implications for warning design are discussed.

Signal Word and Color Specifications for Product Warnings: An Isoperformance Application:

Recent work in the area of color and warnings has indicated that the level of hazard communicated by signal words varies as a function of the color in which they are printed. These findings suggest that signal word and color combinations create a continuum of perceived hazard. Although individual experiments advance the understanding of how color affects the perception of product hazard, explicit data do not always provide label designers and product manufacturers with the tools necessary to successfully apply them. To explore how color and signal words can be jointly used, the present effort applied the isoperformance technique to the problem of specifying signal word and color combinations. This technique identifies combinations of variables that produce equal (iso) levels of warning (performance). Using perceived hazard data from 30 participants, signal words and colors were systematically grouped into categories that conveyed equal levels of hazard. How the isoperformance technique might serve as a tool for label designers is described.

Interaction of Warning Label Features: Determining the Contributions of Three Warning Characteristics

Warning label features such as signal words, typefaces, and color, have largely been evaluated independently of one another. Despite the statistically significant findings resulting from virtually every experiment involving these warning features, the literature has yet to address the larger issue of how these features interact when all three are present. The present effort evaluated the interaction of three different warning features to identify the extent to which each feature contributes to the perception of product hazard. These features included: signal word, legibility, and color. A sample of 34 participants rated the level of perceived hazard associated with labels that depicted the factorial combinations of two products, three signal words (DANGER, CAUTION, NOTICE), two levels of legibility (Helvetica and Arabia), and four colors (red, orange, green, and black). The data revealed significant main effects for each factor and a significant three-way interaction. The interaction indicated that in conditions of reduced legibility, color may be the only source of hazard information. Consumer product warning design implications are discussed.