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Impact of Differential Item Functioning on Subsequent Statistical Conclusions Based on Observed Test Score Data
Zhen Li,Bruno D. Zumbo
Psicológica , 2009,
Abstract: This simulation study investigated the impact of differential item functioning (DIF) on the Type I error rate and effect size of the independent samples t-test on the observed total test scores. Five studies were conducted: studies one to three investigated the impact of unidirectional DIF (i.e., DIF amplification) on the Type I error rate and effect size of the independent sample t-test, studies four and five investigated the DIF cancellation effects on the Type I error rate, and effect size of the independent sample t-test. The Type I error rate and effect size were defined in terms of latent population means rather than observed sample means. The results showed that the amplification and cancellation effects among uniform DIF items did transfer to test level. These findings highlight the importance of screening DIF before conducting any further statistical analysis.
Hazards in Choosing Between Pooled and Separate- Variances t Tests
Donald W. Zimmerman,Bruno D. Zumbo
Psicológica , 2009,
Abstract: If the variances of two treatment groups are heterogeneous and, at the same time, sample sizes are unequal, the Type I error probabilities of the pooledvariances Student t test are modified extensively. It is known that the separate-variances tests introduced by Welch and others overcome this problem in many cases and restore the probability to the nominal significance level. In practice, however, it is not always apparent from sample data whether or not the homogeneity assumption is valid at the population level, and this uncertainty complicates the choice of an appropriate significance test. The present study quantifies the extent to which correct and incorrect decisions occur under various conditions. Furthermore, in using statistical packages, such as SPSS, in which both pooled-variances and separate-variances t tests are available, there is a temptation to perform both versions and to reject H0 if either of the two test statistics exceeds its critical value. The present simulations reveal that this procedure leads to incorrect statistical decisions with high probability.
A New Nonparametric Levene Test for Equal Variances
David W. Nordstokke,Bruno D. Zumbo
Psicológica , 2010,
Abstract: Tests of the equality of variances are sometimes used on their own to compare variability across groups of experimental or non-experimental conditions but they are most often used alongside other methods to support assumptions made about variances. A new nonparametric test of equality of variances is described and compared to current 'gold standard' method, the median-based Levene test, in a computer simulation study. The simulation results show that when sampling from either symmetric or skewed population distributions both the median based and nonparametric Levene tests maintain their nominal Type I error rate; however, when one is sampling from skewed population distributions the nonparametric test has more statistical power.
The Robustness of Validity and Efficiency of the Related Samples t-Test in the Presence of Outliers
Martha J. Jennings,Bruno D. Zumbo,James F. Joula
Psicológica , 2002,
Abstract: The performance of the related samples t-test (a one-sample t-test applied to the difference scores) given data which are essentially normal but contain outliers is largely unknown. In this Monte Carlo study the robustness of validity and efficiency for both the paired and one-sample ttests are investigated. The Type I error rate and power of these tests given a normal underlying population are compared with the performance of these tests given a systematic range of outlier contamination in the underlying population. Sample sizes of 8, 16, 32, 64, and 128 are included in the design. Robustness of validity results are explored using regression models. Robustness of efficiency results are expressed using a proposed fairly stringent criterion for power. The results indicate that the t-test demonstrates fairly stringent robustness of validity for the range of symmetric contamination explored. When contamination is asymmetric the Type I error rate becomes inflated as the proportion of contamination increases. If robustness of validity is intact, power is not greatly affected when medium or large effect sizes are examined. This is not necessarily true for small effect sizes and the problems are further exacerbated when sample sizes are also small. Finally, a model with practical relevance for data analysts confronted with outlier contaminated data is developed using a novel index of contamination. This model is compared with a model using skewness and kurtosis values as disributional measures.
Bias in Estimation and Hypothesis Testing of Correlation
Donald W. Zimmerman,Bruno D. Zumbo,Richard H. Williams
Psicológica , 2003,
Abstract: This study examined bias in the sample correlation coefficient, r, and its correction by unbiased estimators. Computer simulations revealed that the expected value of correlation coefficients in samples from a normal population is slightly less than the population correlation, ρ, and that the bias is almost eliminated by an estimator suggested by R.A. Fisher and is more completely eliminated by a related estimator recommended by Olkin and Pratt. Transformation of initial scores to ranks and calculation of the Spearman rank correlation, rS, produces somewhat greater bias. Type I error probabilities of significance tests of zero correlation based on the Student t statistic and exact tests based on critical values of rS obtained from permutations remain fairly close to the significance level for normal and several non-normal distributions. However, significance tests of non-zero values of correlation based on the r to Z transformation are grossly distorted for distributions that violate bivariate normality. Also, significance tests of non-zero values of rS based on the r to Z transformation are distorted even for normal distributions.
Self-reported physical and mental health status and quality of life in adolescents: a latent variable mediation model
Richard Sawatzky, Pamela A Ratner, Joy L Johnson, Jacek A Kopec, Bruno D Zumbo
Health and Quality of Life Outcomes , 2010, DOI: 10.1186/1477-7525-8-17
Abstract: The data were obtained via a cross-sectional health survey of 8,225 adolescents in 49 schools in British Columbia, Canada. Structural equation modeling was applied to test the implied latent variable mediation model. The Pratt index (d) was used to evaluate variable importance.Relative to one another, self-reported mental health status was found to be more strongly associated with depressive symptoms, and self-reported physical health status more strongly associated with physical activity. Self-reported physical and mental health status and the five life domains explained 76% of the variance in global QOL. Relatively poorer mental health and physical health were significantly associated with lower satisfaction in each of the life domains. Global QOL was predominantly explained by three of the variables: mental health status (d = 30%), satisfaction with self (d = 42%), and satisfaction with family (d = 20%). Satisfaction with self and family were the predominant mediators of mental health and global QOL (45% total mediation), and of physical health and global QOL (68% total mediation).This study provides support for the validity and relevance of differentiating self-reported physical and mental health status in adolescent health surveys. Self-reported mental health status and, to a lesser extent, self-reported physical health status were associated with significant differences in the adolescents' satisfaction with their family, friends, living environment, school experiences, self, and their global QOL. Questions about adolescents' self-reported physical and mental health status and their experiences with these life domains require more research attention so as to target appropriate supportive services, particularly for adolescents with mental or physical health challenges.Health researchers and providers increasingly recognize the importance of obtaining information about adolescents' perspectives of their quality of life (QOL) [1-10]. Several instruments have been
The Influence of Web- Versus Paper-based Formats on the Assessment of Tobacco Dependence: Evaluating the Measurement Invariance of the Dimensions of Tobacco Dependence Scale
Chris G. Richardson, Joy L. Johnson, Pamela A. Ratner and Bruno D. Zumbo
Substance Abuse: Research and Treatment , 2012,
Abstract: The purpose of this study was to examine the influence of mode of administration (internet-based, web survey format versus pencil-and-paper format) on responses to the Dimensions of Tobacco Dependence Scale (DTDS). Responses from 1,484 adolescents that reported using tobacco (mean age 16 years) were examined; 354 (23.9%) participants completed a web-based version and 1,130 (76.1%) completed a paper-based version of the survey. Both surveys were completed in supervised classroom environments. Use of the web-based format was associated with significantly shorter completion times and a small but statistically significant increase in the number of missing responses. Tests of measurement invariance indicated that using a web-based mode of administration did not influence the psychometric functioning of the DTDS. There were no significant differences between the web- and paper-based groups’ ratings of the survey’s length, their question comprehension, and their response accuracy. Overall, the results of the study support the equivalence of scores obtained from web- and paper-based versions of the DTDS in secondary school settings.
The Influence of Web- Versus Paper-based Formats on the Assessment of Tobacco Dependence: Evaluating the Measurement Invariance of the Dimensions of Tobacco Dependence Scale
Chris G. Richardson,Joy L. Johnson,Pamela A. Ratner,Bruno D. Zumbo
Substance Abuse: Research and Treatment , 2009,
Abstract: The purpose of this study was to examine the influence of mode of administration (internet-based, web survey format versus pencil-and-paper format) on responses to the Dimensions of Tobacco Dependence Scale (DTDS). Responses from 1,484 adolescents that reported using tobacco (mean age 16 years) were examined; 354 (23.9%) participants completed a web-based version and 1,130 (76.1%) completed a paper-based version of the survey. Both surveys were completed in supervised classroom environments. Use of the web-based format was associated with significantly shorter completion times and a small but statistically significant increase in the number of missing responses. Tests of measurement invariance indicated that using a web-based mode of administration did not influence the psychometric functioning of the DTDS. There were no significant differences between the web- and paper-based groups’ ratings of the survey’s length, their question comprehension, and their response accuracy. Overall, the results of the study support the equivalence of scores obtained from web- and paper-based versions of the DTDS in secondary school settings.
The Robustness of Validity and Efficiency of the Related Samples t-Test in the Presence of Outliers
Zumbo B. D.,Martha J. Jennings
Psicológica , 2002,
Abstract:
Bias in Estimation and Hypothesis Testing of Correlation.
Zimmerman D. W.,Zumbo B. D.,Williams R. H.
Psicológica , 2003,
Abstract:
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