Diversity analysis: Richness versus evenness.

Richness and evenness, two important components of diversity, have been the subject of numerous studies exploring their potential dependence or lack thereof. The results have been contradictory and inconclusive, but tending to indicate only a low (positive or negative) correlation. While such reported studies have been based on particular data sets and species abundance distributions, the present article provides the results of a study using randomly generated abundance distributions and hence more generalizable findings and valid statistical results.

Measurement of market (industry) concentration based on value validity.

As measures of concentration, especially for market (industry) concentration based on market shares, a variety of different measures or indices have been proposed. However, the various indices, including the two most widely used ones, the concentration ratio and the Herfindahl-Hirschman index (HHI), lack an important property: the value-validity property. An alternative index with this and other desirable properties is introduced.

Hick's law equivalent for reaction time to individual stimuli.

Hick's law, one of the few law-like relationships involving human performance, expresses choice reaction time as a linear function of the mutual information between the stimulus and response events. However, since this law was first proposed in 1952, its validity has been challenged by the fact that it only holds for the overall reaction time (RT) across all the stimuli, and does not hold for the reaction time (RT ) for each individual stimulus. This paper introduces a new formulation in which RT is a linear function of (1) the mutual information between the event that stimulus i occurs and the set of all potential response events and (2) the overall mutual information for all stimuli and responses.

Relationship between concentration ratio and Herfindahl-Hirschman index: A re-examination based on majorization theory.

While the two most widely used measures of market (industrial) concentration, the -firm concentration ratio and the Herfindahl-Hirschman index , have no precise functional relationship, they can be related by means of boundary formulations. Such bounds and potential relationships, which have been considered in some earlier reported studies, are being re-examined, corrected, and reformulated in this paper. The underlying analysis uses a different approach based on majorization theory and the results are supported by computer simulation.

An Alternative Interpretation of the Linearly Weighted Kappa Coefficients for Ordinal Data.

When two (or more) observers are independently categorizing a set of observations, Cohen's kappa has become the most notable measure of interobserver agreement. When the categories are ordinal, a weighted form of kappa becomes desirable. The two most popular weighting schemes are the quadratic weights and linear weights.

Evenness indices once again: critical analysis of properties.

Various properties have been advocated for biological evenness indices, with some properties being clearly desirable while others appear questionable. With a focus on such properties, this paper makes a distinction between properties that are clearly necessary and those that appear to be unnecessary or even inappropriate. Based on Euclidean distances as a criterion, conditions are introduced in order for an index to provide valid, true, and realistic representations of the evenness characteristic (attribute) from species abundance distributions.

On a general class of chi-squared goodness-of-fit statistics.

A class of chi-squared goodness-of-fit statistics is presented as being based on the so-called divergence of one probability distribution from another. A still more general class of goodness-of-fit statistics is then presented by eliminating some of the restrictions required of divergence-based statistics. This most general class of statistics includes, as particular cases, a variety of statistics used in the published literature.

Weighted specific-category kappa measure of interobserver agreement.

When two observers classify a sample of items using the same categorical scale, and when different disagreements are differentially weighted, the weighted Kappa (Kw) by Cohen may serve as a measure of interobserver agreement. We propose a Kappa-based weighted measure (K(ws)) of agreement on some specific category s, with Kw being a weighted average of all K(ws)s. Therefore, while Cohen's Kw is a summary measure of the overall agreement, the proposed K(ws) provides a measure of the extent to which the observers agree on the specific categories, with both measures being suitable for ordinal categories because of the weights being used.