Hierarchical linear modeling as an example for measuring change over time in a leadership development evaluation context

One of the difficulties in evaluating leadership development is measuring whether and how people change over the time period of the leadership development initiative. Even when change over time is an inherent part of the design and evaluation of leadership development, events may occur outside of the control of evaluators that limit the effectiveness of adequately and accurately assessing change over time. With data from a leadership development initiative designed to account for change over time, this article suggests hierarchical linear modeling (HLM) as a multilevel methodological technique to assess change over time in a leadership development context. This article will use real change over time data from a leadership development initiative and discuss the logic and rationale of HLM. We use HLM as an example of a multilevel methodological tool to investigate typical change over time questions in leadership development evaluation.     

A slacks-based inefficiency measure for a two-stage system with bad outputs

We model the performance of DMUs (decision-making units) using a two-stage network model. In the first stage of production DMUs use inputs to produce an intermediate output that becomes an input to a second stage where final outputs are produced. Previous black box DEA models allowed for non-radial scaling of outputs and inputs and accounted for slacks in the constraints that define the technology. We extend these models and build a performance measure that accounts for a network structure of production. We use our method to estimate the performance of Japanese banks, which use labor, physical capital, and financial equity capital in a first stage to produce an intermediate output of deposits. In the second stage, those deposits become an input in the production of loans and securities investments. The network estimates reveal greater bank inefficiency than do the estimates that treat the bank production process as a black box with all production taking place in a single stage.     

Class,race, and the disposal of urban waste: Locations of landfills,incinerators, and sewage treatment plants

This study compared the socioeconomic status, racial composition, and ethnic composition of 49 randomly selected U.S. cities with those of the census tracts containing the solid waste disposal facilities and sewage treatment plants for those cities. Contrary to the environmental racism and classism hypotheses, residents of tracts with landfills or incinerators had higher incomes and were less likely to be minority group members than residents of the cities that generated the refuse—although they did have somewhat lower education levels. There were few differences between the population characteristics of the cities and the census tracts that contained their sewage treatment plants. Possible explanations for these findings are discussed.     

A Sample Size Formula for a Non-Central t Test

An elementary method of proof of the mode, median, and mean inequality is given for skewed, unimodal distributions of continuous random variables. A proof of the inequality for the gamma, F, and beta random variables is sketched.     

Editor's Report

There are two common methods for statistical inference on 2 × 2 contingency tables. One is the widely taught Pearson chi-square test, which uses the well-known χ²statistic. The chi-square test is appropriate for large sample inference, and it is equivalent to the Z-test that uses the difference between the two sample proportions for the 2 × 2 case. Another method is Fisher’s exact test, which evaluates the likelihood of each table with the same marginal totals. This article mathematically justifies that these two methods for determining extreme do not completely agree with each other. Our analysis obtains one-sided and two-sided conditions under which a disagreement in determining extreme between the two tests could occur. We also address the question whether or not their discrepancy in determining extreme would make them draw different conclusions when testing homogeneity or independence. Our examination of the two tests casts light on which test should be trusted when the two tests draw different conclusions.