The perception of scatterplots

Four experiments investigated the perception of correlations from scatterplots. All graphic properties, other than error variance, that have been shown to affect subjective but not objective correlation (r) were held constant. Participants in Experiment 1 ranked 21 scatterplots according to the magnitude of r. In Experiments 2 and 3, participants made yes/no judgments to indicate whether a scatterplot was high (signal) or low (noise). Values of r for signal and noise scatterplots varied across participants. Differences between correlations for signal and for noise scatterplots were constant in r in Experiment 2, and constant in r2 in Experiment 3. Standard deviations of the ranks in Experiment 1 and d' values in Experiments 2 and 3 showed that discriminability increased with the magnitude of r. In Experiment 4, faculty and graduate students in psychology and sociology made point estimates of r for single scatterplots. Estimates were negatively accelerated functions of objective correlation.     

Applications of a computer algebra system in introductory statistics

Maple, a computer algebra system, is employed in introductory statistics courses to promote conceptual learning by students of statistical principles without direct use of mathematics. Maple’s symbolic computation, graphic display, and animation capabilities support an integrated set of procedures for active study of sampling distributions and concepts related to samples, populations, and statistical decision making, error, and power. Students select parameter values for one-line commands and examine the effects of alternatives on computer-generated graphical representations of distributions. The 20 procedures written to support active student exploration of basic statistical concepts are described, and examples of exercises to support their use are provided.     

THE PERCEPTION OF PEARSON PRODUCT MOMENT CORRELATIONS FROM BIVARIATE SCATTERPLOTS

Perceptions about the Pearson product moment correlation, r , from bivariate scatterplots were investigated through the use of a questionnaire. It was found that subjects who are relatively sophisticated in psychometric techniques tend to underestimate the magnitude of r , with most pronounced disparity in the range .2 < |r| < .6. Additionally, estimates of r from specially designed scatterplots indicated that subjects (1) correctly estimated the effects of range restriction, (2) underestimated the effects of attenuating outliers, (3) incorrectly reduced estimates of r when the regression slope was relatively high or low, and (4) often failed to consider the effects of removing the middle third of the data. Several implications of these generally conservative estimations are discussed.     

Some simple procedures for handling missing data in multivariate analysis

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 research was supported by NIH Special Research Resources Grant RR-3. The author expresses his gratitude to Robert I. Jennrich and the referees for their suggestions.     

Adaption-innovation typology and right-left hemispheric preferences

The authors of this article illustrate the results of an Italian research in which the correlation between the Kirton Adaption-Innovation Inventory (KAI) and Torrance's Solat C Test has been tested. Previous studies in this domain of cognitive style and individual preferences showed encouraging findings, although data were obtained with a small sample (Torrance and Horng, 1980). In this research the two measures were applied to a sample (N = 216) of high school students, heterogeneous for sex and subject of study. The Italian findings support the existence of a correlation between KAI and Solat form C, and this is valid also for KAI subtraits O, E and R. Although the correlation exists and shows that the two measures are related, it is not large enough to demonstrate that they are measuring the same thing. Nevertheless, some issues are questioned about the correlations and a new variable (δ = right-left scores) is described in order to obtain a stronger and more reliable correlation with KAI total score. The KAI subtrait's correlations with left-right preferences are available for the Italina sample.     

Statistical power analyses using G<Superscript>*</Superscript>Power 3.1: Tests for correlation and regression analyses

G^*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses. In the new version, we have added procedures to analyze the power of tests based on (1) single-sample tetrachoric correlations, (2) comparisons of dependent correlations, (3) bivariate linear regression, (4) multiple linear regression based on the random predictor model, (5) logistic regression, and (6) Poisson regression. We describe these new features and provide a brief introduction to their scope and handling.     

Development and reliability of a Brazilian Portuguese version of the MCMI-III

This paper describes the methodology used to translate the MCMI-III into Brazilian Portuguese and presents results from a reliability study conducted in Brazil with the translated instrument. The sample was comprised of 222 Brazilian college students. Test-retest correlations between first and second testings (over a period of 7 to 14 days) ranged from .70 to .93 across 27 scales. Cronbach's alpha coefficients ranged from .54 to .87. The procedures described in this paper represent preliminary steps in the development of a Brazilian Portuguese translation of the MCMI-III. Further studies are needed to obtain reliability data with a clinical sample, evaluate the diagnostic validity of the scales, and derive appropriate base rates for the Brazilian population.     

Using a computer simulation to teach attitude surveying

An interactive computer program that simulates, for teaching purposes, the procedures involved in carrying out an attitude survey is described. Students make decisions about the content and length of an attitude questionnaire, as well as about the procedures to be used to sample the population. Students’ inferences about the population characteristics can be compared with the actual characteristics (predetermined by the instructor) to provide students with an indication of the merits of the alternatives they chose.     

Some properties of r equivalent: a simple effect size indicator

One version of r equivalent, calculated from Fisher's exact test p values and recommended for small samples, is considered "a more realistic . . . [and] a more accurate estimate of the population correlation than . . . the sample correlation, r sample" (R. Rosenthal & D. B. Rubin, 2003, p. 494). Small sample properties of r sample and of two effect size estimators (r equivalent* and r hybrid) that use r equivalent were examined: r sample is preferable to r equivalent* (defined as r equivalent used without restrictions) in terms of bias and mean squared error (MSE); r hybrid (defined as r equivalent only when r sample = 1.0) is generally preferable to r equivalent*, and preferable to r sample in terms of MSEs, except when population correlations are very large. Conditions favoring r sample over r equivalent* and r hybrid in meta-analyses are noted.     

How Many Subjects Does It Take To Do A Regression Analysis

Numerous rules-of-thumb have been suggested for determining the minimum number of subjects required to conduct multiple regression analyses. These rules-of-thumb are evaluated by comparing their results against those based on power analyses for tests of hypotheses of multiple and partial correlations. The results did not support the use of rules-of-thumb that simply specify some constant (e.g., 100 subjects) as the minimum number of subjects or a minimum ratio of number of subjects (N) to number of predictors (m). Some support was obtained for a rule-of-thumb that N ≥ 50 + 8 m for the multiple correlation and N ≥104 + m for the partial correlation. However, the rule-of-thumb for the multiple correlation yields values too large for N when m ≥ 7, and both rules-of-thumb assume all studies have a medium-size relationship between criterion and predictors. Accordingly, a slightly more complex rule-of thumb is introduced that estimates minimum sample size as function of effect size as well as the number of predictors. It is argued that researchers should use methods to determine sample size that incorporate effect size.     

Transmission of religious beliefs in college students

The aim of the current study was to assess factors contributing to the generational transmission of religious beliefs in a sample of college students. Participants were 92 students from a small Catholic university in the southeastern United States. Students were surveyed in school regarding family relationships, communication, and religious values. Overall, results indicated that children’s and parents’ religious beliefs were significantly correlated. Furthermore, children were fairly accurate reporters of their parents’ religious beliefs. Some gender differences were found in the strength of the correlations between parents’ and children’s beliefs. Additionally, explicit communication, implicit communication, and perception of parents’ beliefs predicted children’s beliefs. The current study holds clinical and developmental significance by examining the manner in which religiosity is expressed within the familial milieu of emerging adults.     

Gender Differences in the Association of Intimate Partner Violence and Relationship Values among College Students

Although research has indicated that cognitions and situational factors play a role in relationship satisfaction and aggression, few studies have investigated the association between intimate partner violence (IPV) and relationship values. We addressed this gap by measuring college students’ perpetration of and victimization by four types of IPV; namely, physical violence, sexual violence, threats, and psychological aggression over the past year. One-way ANOVAs and multiple regression analyses were used to measure the association between IPV and the endorsement of relationship values. The results suggest that past IPV perpetration and victimization correlated with the current endorsement of relationship values for males more than females. In general, male perpetrators rated relationship values such as security, investment, others’ approval, and daily conflict as less important than non-perpetrators. Although male victimization explained significant variance in security, investment, and others’ approval, the results were somewhat mixed as to whether victimization related to higher or lower ratings of relationship values, with the majority of the results suggesting an inverse correlation between relationship value endorsement and IPV experience. Future research can investigate mediating factors in the relationship between IPV and relationship value endorsement, as well as look at how IPV and relationship values influence decisions concerning relationship maintenance.     

Validity and reliability of perceptually-based scales during exhausting runs in trained male runners

The purposes of this study were to test the validity of a recent scale based on the estimation of a time of exhaustion (entitled Estimated Time Limit scale) to predict a time limit (Tlim) and to regulate exercise intensity and to investigate the reliability of the Estimated Time Limit scale and the Ratings of Perceived Exertion (RPE) scale. 14 male runners performed one incremental test, one constant velocity test at 85% of Maximal Aerobic Velocity (MAV), one constant duration test and one retest of 15 min. on an outdoor track. The difference between Estimated Time Limit values obtained during the incremental test at 85% MAV and measured Tlim values during the constant velocity test were examined, the velocities at ETL = 13 (i.e., 15 min.) obtained during the incremental test were compared with measured velocities during the constant duration test or the retest (only the best performance was used), and RPE and Estimated Time Limit values during the constant duration test were compared with those measured during retest. The results have shown a nonsignificant correlation between Estimated Time Limit values at 85% MAV and measured Tlim values during constant velocity test. There was a significant correlation (p < .02, r = .64) between velocities at ETL= 13 and measured velocities. However, the slope and y intercept value of this regression were significantly different from those of the identity line. There was no significant difference between constant duration test and retest for the values of RPE and Estimated Time Limit with high correlations (between r = .77 and .99 for RPE scale, and r = .74 and .99 for Estimated Time Limit scale). Moreover, the regression lines were close to the identity line. The RPE and Estimated Time Limit scales are reliable, but the lack of validity for the Estimated Time Limit scale suggests that more studies must be performed before using this scale to predict Tlim and regulate exercise intensity in male runners.     

Efficiency of graphical perception

The term graphical perception refers to the part played by visual perception in analyzing graphs. Computer graphics have stimulated interest in the perceptual pros and cons of different formats for displaying data. One way of evaluating the effectiveness of a display is to measure the efficiency (as defined by signal-detection theory) with which an observer extracts information from the graph. We measured observers' efficiencies in detecting differences in the means or variances of pairs of data sets sampled from Gaussian distributions. Sample size ranged from 1 to 20 for viewing times of 0.3 or 1 sec. The samples were displayed in three formats: numerical tables, scatterplots, and luminance-coded displays. Efficiency was highest for the scatterplots (approximately equal to 60% for both means and variances) and was only weakly dependent on sample size and exposure time. The pattern of results suggests parallel perceptual computation in which a constant proportion of the available information is used. Efficiency was lowest for the numerical tables and depended more strongly on sample size and viewing time. The results suggest serial processing in which a fixed amount of the available information is processed in a given time.     

Novel methods for analyzing multifaceted personality scales: sense of coherence and depression as an example

Multifaceted personality scales assess multiple related facets or dimensions and, as such, they are typically made up of correlated subscales. In some cases, the degree of correlation among subscales can be so high as to render the use of standard procedures for evaluating a subscale's relative importance (e.g., beta weights or bivariate correlations) dubious. In such cases of high predictor multicollinearity, researchers are faced with few viable options and, in response, many turn to multiple regression when examining predictor-criterion associations (for example, interpreting semipartial correlations and incremental variance estimates). In an effort to broaden researchers' options and thereby allow for greater interpretive clarity, z tests for comparing dependent zero-order correlations and R. G. Malgady's (1987) methods for comparing two dependent semipartial correlations and for comparing dependent semipartial and zero-order correlations are proposed as additional techniques for analyzing predictor (or subscale) criterion associations in the context of predictor collinearity. Worked examples of both techniques are provided, using a dataset on sense of coherence and depression. Finally, relevant computer programs for implementing the aforementioned techniques are noted.     

Generating multivariate data from nonnormal distributions: Mihal and Barrett revisited

An algorithm described by Graybill (1969) factors a population correlation matrix, R, into an upper and lower triangular matrix, T and T′, such that R=T′T. The matrix T is used to generate multivariate data sets from a multinormal distribution. When this algorithm is used to generate data for nonnormal distributions, however, the sample correlations are systematically biased downward. We describe an iterative technique that removes this bias by adjusting the initial correlation matrix. R, factored by the Graybill algorithm. The method is illustrated by simulating a multivariate study by Mihal and Barrett (1976). Large-N simulations indicate that the iterative technique works: multivariate data sets generated with this approach successfully model both the univariate distributions of the individual variables and their multivariate structure (as assessed by intercorrelation and regression analyses).     

German version of the Kuwait University Anxiety Scale: psychometric parameters

A German translation of the Kuwait University Anxiety Scale, written originally in Arabic, was prepared. A sample of 207 men and women German college students was recruited. Coefficient alpha was .88, whereas the item-remainder correlations ranged from .21 to .63, denoting good internal consistency. The correlation of the scale with the German form of the Trait Anxiety Scale was .76, indicating high criterion-related validity. Three factors were identified: General, Somatic, and Cognitive/Affective Anxiety. German students scored lower (less anxious) than students from the U.S. and 18 Arab countries. The sex difference was not significant for the German sample.     

Personality and aesthetic preference in Spain and England: two studies relating sensation seeking and openness to experience to liking for paintings and music

In two studies, one employing Spanish students and the other English students, questionnaire measures of Sensation Seeking and Openness to Experience were correlated with liking for major music types, several short music excerpts, and eight categories of painting (presented as slides). Inter‐correlations between music preference measures, painting preference, and personality are reported. In both samples, the Sensation Seeking Scale (Form V) and, particularly, the Experience Seeking sub‐scale were associated with a factor contrasting liking for ‘hard rock’ music and ‘violent–abstract’ art with liking for ‘neutral–realistic’ art and ‘easy listening’ music. Several substantial relationships between aesthetics measures and Openness to Experience (from the NEO‐PI‐R) were also found, though mostly in the English sample. The results reinforce the view that personality dimensions such as Sensation Seeking and Openness are important influences on aesthetic judgment. Copyright © 2000 John Wiley & Sons, Ltd.