The reliability of a test score is usually underestimated and the deflation may be profound, 0.40 - 0.60 units of reliability or 46 - 71%. Eight root sources of the deflation are discussed and quantified by a simulation with 1,440 real-world datasets: (1) errors in the measurement modelling, (2) inefficiency in the estimator of reliability within…

This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component--and in particular for the first principal…

Researchers are combining self-reports from mobile surveys with passive data collection using sensors and apps on smartphones increasingly more often. While smartphones are commonly used in some groups of individuals, smartphone penetration is significantly lower in other groups. In addition, different operating systems (OSs) limit how mobile data…

Studies analyzing clustered data sets using both multilevel models (MLMs) and ordinary least squares (OLS) regression have generally concluded that resulting point estimates, but not the standard errors, are comparable with each other. However, the accuracy of the estimates of OLS models is important to consider, as several alternative techniques…

Power analysis is a fundamental prerequisite for conducting scientific research. Without power analysis the researcher has no way of knowing whether the sample size is large enough to detect the effect he or she is looking for. This paper demonstrates how psychometric factors such as measurement error and equating error affect the power of…

Bayesian statistical approaches to mixed treatment comparisons (MTCs) are becoming more popular because of their flexibility and interpretability. Many randomized clinical trials report multiple outcomes with possible inherent correlations. Moreover, MTC data are typically sparse (although richer than standard meta-analysis, comparing only two…

We extend a unified and easy-to-use approach to measurement error and missing data. In our companion article, Blackwell, Honaker, and King give an intuitive overview of the new technique, along with practical suggestions and empirical applications. Here, we offer more precise technical details, more sophisticated measurement error model…

Building on previous arguments for why educational researchers should not provide effect-size estimates in the face of statistically nonsignificant outcomes (Robinson & Levin, 1997), Onwuegbuzie and Levin (2005) proposed a 3-step statistical approach for assessing group differences when multiple outcome measures are individually analyzed…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of "Explorations in Statistics" explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive…

A new form of composition of the indicators employed to generate the United Nations Human Development Index (HDI) is presented here. This form of composition is based on the assumption that random errors affect the measurement of each indicator. This assumption allows for replacing the vector of evaluations according to each indicator by vectors…

Using detailed individual-level data from public universities in the state of Ohio, I estimate the effect of various institutional expenditures on the probability of graduating from college. Using a competing risks regression framework, I find differential impacts of expenditure categories across student characteristics. I estimate that student…

Background: The appropriateness of the "Diagnostic and Statistical Manual of Mental Disorders-Fourth Edition" (DSM-IV) nosology for classifying preschool mental health disturbances continues to be debated. To inform this debate, we investigate whether preschool psychopathology shows differentiation along diagnostically specific lines…

Statistics are an essential tool for making proper judgement decisions. It is concerned with probability distribution models, testing of hypotheses, significance tests and other means of determining the correctness of deductions and the most likely outcome of decisions. Measures of central tendency include the mean, median and mode. A second…