This article introduces an innovative sampling scheme, the median sampling (MS), utilizing individual observations over time to efficiently estimate the mean of a process characterized by a symmetric (non-uniform) probability distribution. The mean estimator based on MS is not only unbiased but also boasts enhanced precision compared to its simple…

Data in social and behavioral sciences typically contain measurement errors and do not have predefined metrics. Structural equation modeling (SEM) is widely used for the analysis of such data, where the scales of the manifest and latent variables are often subjective. This article studies how the model, parameter estimates, their standard errors…

Data in social and behavioral sciences typically contain measurement errors and do not have predefined metrics. Structural equation modeling (SEM) is widely used for the analysis of such data, where the scales of the manifest and latent variables are often subjective. This article studies how the model, parameter estimates, their standard errors…

In multisite trials, learning about treatment effect variation across sites is critical for understanding where and for whom a program works. Unadjusted comparisons, however, capture "compositional" differences in the distributions of unit-level features as well as "contextual" differences in site-level features, including…

In multisite trials, learning about treatment effect variation across sites is critical for understanding where and for whom a program works. Unadjusted comparisons, however, capture "compositional" differences in the distributions of unit-level features as well as "contextual" differences in site-level features, including…

Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups' test score distributions from such data. Because…

We consider here the problem of calculating the moments of binomial random variables. It is shown how formulae for both the raw and the central moments of such random variables may be obtained in a recursive manner utilizing Stirling numbers of the first kind. Suggestions are also provided as to how students might be encouraged to explore this…

The paper shows how to find the min and max extreme interval values for the exponential and triangular distributions from the min and max uniform extreme interval values. Tables are provided to show the min and max extreme interval values for the uniform, exponential, and triangular distributions for different probabilities and observation sizes.

The extreme interval values and statistics (expected value, median, mode, standard deviation, and coefficient of variation) for the smallest (min) and largest (max) values of exponentially distributed variables with parameter ? = 1 are examined for different observation (sample) sizes. An extreme interval value g[subscript a] is defined as a…

Apprentice and trainee data are reported by the State and Territory Training Authorities to the National Centre for Vocational Education Research (NCVER) on a quarterly basis, starting at the September quarter of 1994. The set of data submitted that quarter is referred to as Collection 1. The sets of data submitted in subsequent quarters are…

Benford's law of the "first digits" states that in spite of intuitively expected equal frequency of 1/9 of the decimal digits r = 1, ... , 9 appearance on the first place of any number, various empirical studies show another pattern of these frequencies distribution, which is log[subscript 10](1 + 1/r). The article considers this law and other…

Written by a social worker for social work students, this is a nuts and bolts guide to statistics that presents complex calculations and concepts in clear, easy-to-understand language. It includes numerous examples, data sets, and issues that students will encounter in social work practice. The first section introduces basic concepts and terms to…