Research pertaining to the distortion of the squared canonical correlation coefficient has traditionally been limited to the effects of sampling error and associated correction formulas. The purpose of this study was to compare the degree of attenuation of the squared canonical correlation coefficient under varying conditions of score reliability. Monte Carlo simulation methodology was used to fulfill the purpose of this study. Initially, data populations with various manipulated conditions were generated (N = 100,000). Subsequently, 500 random samples were drawn with replacement from each population, and data was subjected to canonical correlation analyses. The canonical correlation results were then analyzed using descriptive statistics and an ANOVA design to determine under which condition(s) the squared canonical correlation coefficient was most attenuated when compared to population Rc2 values. This information was analyzed and used to determine what effect, if any, the different conditions considered in this study had on Rc2. The results from this Monte Carlo investigation clearly illustrated the importance of score reliability when interpreting study results. As evidenced by the outcomes presented, the more measurement error (lower reliability) present in the variables included in an analysis, the more attenuation experienced by the effect size(s) produced in the analysis, in this case Rc2. These results also demonstrated the role between and within set correlation, variable set size, and sample size played in the attenuation levels of the squared canonical correlation coefficient.
The present study examined the factor structure and measurement invariance of the revised version of the Athletic Coping Skills Inventory (ACSI-28), following adjustment of the wording of items such that they were appropriate to assess Coping Skills in an educational setting. A sample of middle school students (n = 1,037) completed the revised inventory. An initial confirmatory factor analysis led to the hypothesis of a better fitting model with two items removed. Reliability of the subscales and the instrument as a whole was acceptable. Items were examined for sex invariance with differential item functioning (DIF) using item response theory, and five items were flagged for significant sex non-invariance. Following removal of these items, comparison of the mean differences between male and female coping scores revealed that there was no significant difference between the two groups. Further examination of the generalizability of the coping construct and the potential transfer of psychosocial skills between athletic and academic settings are warranted.
This study examined the bias and precision of four residualized variable validity estimates (C0, C1, C2, C3) across a number of study conditions. Validity estimates that considered measurement error, correlations among error scores, and correlations between error scores and true scores (C3) performed the best, yielding no estimates that were practically significantly different than their respective population parameters, across study conditions. Validity estimates that considered measurement error and correlations among error scores (C2) did a good job in yielding unbiased, valid, and precise results. Only in a select number of study conditions were C2 estimates unable to be computed or produced results that had sufficient variance to affect interpretation of results. Validity estimates based on observed scores (C0) fared well in producing valid, precise, and unbiased results. Validity estimates based on observed scores that were only corrected for measurement error (C1) performed the worst. Not only did they not reliably produce estimates even when the level of modeled correlated error was low, C1 produced values higher than the theoretical limit of 1.0 across a number of study conditions. Estimates based on C1 also produced the greatest number of conditions that were practically significantly different than their population parameters.
Previous research implementing stratification on the propensity score has generally relied on using five strata, based on prior theoretical groundwork and minimal empirical evidence as to the suitability of quintiles to adequately reduce bias in all cases and across all sample sizes. This study investigates bias reduction across varying number of strata and sample sizes via a large-scale simulation to determine the adequacy of quintiles for bias reduction under all conditions. Sample sizes ranged from 100 to 50,000 and strata from 3 to 20. Both the percentage of bias reduction and the standardized selection bias were examined. The results show that while the particular covariates in the simulation met certain criteria with five strata that greater bias reduction could be achieved by increasing the number of strata, especially with larger sample sizes. Simulation code written in R is included.
The advent of the Internet has increased access to information and impacted many aspects of life, including politics. The present study utilized Pew Internet & American Life survey data from the November 2008 presidential election time period to investigate the degree to which political blog reading predicted online political discussion, online political participation, whether or not a person voted, and voting choice, over and above the predication that could be explained by demographic measures of age, education level, gender, income, marital status, race/ethnicity, and region. Ordinary least squares hierarchical regression revealed that political blog reading was positively and statistically significantly related to online political discussion and online political participation. Hierarchical logistic regression analysis indicated that the odds of a political blog reader voting were 1.98 the odds of a nonreader voting, but vote choice was not predicted by reading political blogs. These results are interpreted within the uses and gratifications framework and the understanding that blogs add an interpersonal communication aspect to a mass medium. As more people use blogs and the nature of the blog-reading audience shifts, continuing to track and describe the blog audience with valid measures will be important for researchers and practitioners alike. Subsequent potential effects of political blog reading on engagement, discussion, and participation will be important to understand as these effects could impact the political landscape of this country and, therefore, the world.
The aim of this study was to validate an instrument that can be used by instructors or social scientist who are interested in evaluating statistics anxiety. The psychometric properties of the English version of the Statistical Anxiety Scale (SAS) was examined through a confirmatory factor analysis of scores from a sample of 323 undergraduate social science majors enrolled in colleges and universities in the United States. In previous studies, the psychometric properties of the Spanish and Italian versions of the SAS were validated; however, the English version of the SAS had never been assessed. Inconsistent with previous studies, scores on the English version of the SAS did not produce psychometrically acceptable values of validity. However, the results of this study suggested the potential value of a revised two-factor model SAS to measure statistics anxiety. Additionally, the Attitudes Towards Statistics (ATS) scale was used to examine the convergent and discriminant validities of the two-factor SAS. As expected, the correlation between the two factors of the SAS and the two factors of the ATS uncovered a moderately negative correlation between examination anxiety and attitudes towards the course. Additionally, the results of a structural regression model of attitudes towards statistics as a predictor of statistics anxiety suggested that attitudes towards the course and attitudes towards the field of statistics moderately predicts examination anxiety with attitudes towards the course having the greatest influence. It is recommended that future studies examine the relationship between attitudes towards statistics, statistics anxiety, and other variables such as academic achievement and instructional style.
The current study evaluated the performance of traditional versus modern MDTs in the estimation of fixed-effects and variance components for data missing at the second level of an hierarchical linear model (HLM) model across 24 different study conditions. Variables manipulated in the analysis included, (a) number of Level-2 variables with missing data, (b) percentage of missing data, and (c) Level-2 sample size. Listwise deletion outperformed all other methods across all study conditions in the estimation of both fixed-effects and variance components. The model-based procedures evaluated, EM and MI, outperformed the other traditional MDTs, mean and group mean substitution, in the estimation of the variance components, outperforming mean substitution in the estimation of the fixed-effects as well. Group mean substitution performed well in the estimation of the fixed-effects, but poorly in the estimation of the variance components. Data in the current study were modeled as missing completely at random (MCAR). Further research is suggested to compare the performance of model-based versus traditional MDTs, specifically listwise deletion, when data are missing at random (MAR), a condition that is more likely to occur in practical research settings.
This study examined science achievement growth across elementary and middle school and parent school involvement using the Early Childhood Longitudinal Study – Kindergarten Class of 1998 – 1999 (ECLS-K). The ECLS-K is a nationally representative kindergarten cohort of students from public and private schools who attended full-day or half-day kindergarten class in 1998 – 1999. The present study’s sample (N = 8,070) was based on students that had a sampling weight available from the public-use data file. Students were assessed in science achievement at third, fifth, and eighth grades and parents of the students were surveyed at the same time points. Analyses using latent growth curve modeling with time invariant and varying covariates in an SEM framework revealed a positive relationship between science achievement and parent involvement at eighth grade. Furthermore, there were gender and racial/ethnic differences in parents’ school involvement as a predictor of science achievement. Findings indicated that students with lower initial science achievement scores had a faster rate of growth across time. The achievement gap between low and high achievers in earth, space and life sciences lessened from elementary to middle school. Parents’ involvement with school usually tapers off after elementary school, but due to parent school involvement being a significant predictor of eighth grade science achievement, later school involvement may need to be supported and better implemented in secondary schooling.
Understanding student achievement in science is important as there is an increasing reliance of the U.S. economy on math, science, and technology-related fields despite the declining number of youth seeking college degrees and careers in math and science. A series of structural equation models were tested using the scores from a statewide science exam for 276 students from a suburban north Texas public school district at the end of their 5th grade year and the latent variables of spatial ability, motivation to learn science and science-related attitude. Spatial ability was tested as a mediating variable on motivation and attitude; however, while spatial ability had statistically significant regression coefficients with motivation and attitude, spatial ability was found to be the sole statistically significant predictor of science achievement for these students explaining 23.1% of the variance in science scores.
The present study examined the structural construct validity of the LoTi Digital-Age Survey, a measure of teacher instructional practices with technology in the classroom. Teacher responses (N = 2840) from across the United States were used to assess factor structure of the instrument using both exploratory and confirmatory analyses. Parallel analysis suggests retaining a five-factor solution compared to the MAP test that suggests retaining a three-factor solution. Both analyses (EFA and CFA) indicate that changes need to be made to the current factor structure of the survey. The last two factors were composed of items that did not cover or accurately measure the content of the latent trait. Problematic items, such as items with crossloadings, were discussed. Suggestions were provided to improve the factor structure, items, and scale of the survey.
Covariate quality has been primarily theory driven in propensity score matching with a general adversity to the interpretation of group prediction. However, effect sizes are well supported in the literature and may help to inform the method. Specifically, I index can be used as a measure of effect size in logistic regression to evaluate group prediction. As such, simulation was used to create 35 conditions of I, initial bias and sample size to examine statistical differences in (a) post-matching bias reduction and (b) treatment effect sensitivity. The results of this study suggest these conditions do not explain statistical differences in percent bias reduction of treatment likelihood after matching. However, I and sample size do explain statistical differences in treatment effect sensitivity. Treatment effect sensitivity was lower when sample sizes and I increased. However, this relationship was mitigated within smaller sample sizes as I increased above I = .50.
The common practice for testing measurement invariance is to constrain parameters to be equal over groups, and then evaluate the model-data fit to reject or fail to reject the restrictive model. Posterior predictive checking (PPC) provides an alternative approach to evaluating model-data discrepancy. This paper explores the utility of PPC in estimating measurement invariance. The simulation results show that the posterior predictive p (PP p) values of item parameter estimates respond to various invariance violations, whereas the PP p values of item-fit index may fail to detect such violations. The current paper suggests comparing group estimates and restrictive model estimates with posterior predictive distributions in order to demonstrate the pattern of misfit graphically.