Jan Vegelius

Measures of Ecological Association

SummarySix criteria suitable for measures of ecological coexistence are proposed. For twenty such measures are examined whether they satisfy these criteria or not. Four of them satisfy all six criteria. Three of them, suggested by Ochiai, Dice and Jaccard are recommended. For them asymptotic standard errors are given. An example is given with asymptotic confidence intervals for the three measures recommended.

Influence of height, weight and obesity on risk of breast cancer in an unselected Swedish population.

A number of recent studies have shown an association between breast-cancer risk and height, weight and dietary habits, especially fat consumption. In the present study, height and weight were determined for 179 consecutive, unselected, breast-cancer patients and age-matched controls selected from a computerized population register. Height and weight for these two groups were compared, including two different indices for overweight (Quetelets index and Brocas index). Comparisons were repeated after subdivision into pre- and postmenopausal women. In all calculations, the mean values of patients and controls were very similar and without significant difference. It therefore seems improbable that increased height and weight or obesity constitute risk factors for breast cancer. Earlier studies may have shown differences as the result of selection mechanisms not present in this study.

On Generalizations Of The G Index And The Phi Coefficient To Nominal Scales.

If the same categories are used for two nominal scale variables, this information should be used in similarity measures between those variables. Two such similarity measures, one proposed by Goodman & Kruskal and one (kappa) by Cohen, are examined. Two alternative coefficients, called C and S are further proposed. They are found to be generalizations of the G index and the phi coefficient respectively. Both of them seem to have many desirable characteristics, e.g., they are both E-coefficients. They may also be used as measures of similarity between persons classifying into categories defined beforehand.

Reproductive history and risk of breast cancer. A case‐control study in an unselected swedish populations

Variables in reproductive histories were studied in 179 consecutively detected, unselected breast cancer patients and age‐matched controls selected from a computerized population register. The comparison between patients and controls showed no significant difference in age at menarche, age at first birth, age at menopause or number of children. A subdivision into pre‐ and postmenopausal women yielded no further information. These results are at variance with most earlier reports, possibly because the controls here were selected from the whole female population instead of hospitalized patients. Our data do not support the view that it is possible to define groups at high risk for breast cancer on the basis of reproductive histories.

Measures of similarity between distributions

Eleven criteria are suggested as suitable for measures of similarity between distributions. For seven measures it is discussed whether they satisfy these measures or not. Two measures, the proportional similarity and the Hellinger coefficient satisfy all the eleven criteria.

On the Utility of the E-Correlation Coefficient Concept in Psychological Research

The term correlation coefficient has been defined in various ways. In this article the E-(correlation) coefficient concept is considered. Six characteristics of an E-coefficient are mentioned. For 23 similarity measures of interval, ordinal, dichotomous, and nominal data is considered whether they are E-coefficients or not. Finally, the importance of the concept is discussed.

On Generalizations of the G Index

The G* index of agreement, introduced by Lienert as a generalization of the G index is shown to have some deficiencies. It cannot, for example, be used in a Q-factor analysis. An alternative index, roz , is proposed for ordinal scales with fixed neutral (zero-) points. The roz index can be used for measuring both person similarity and item similarity. It fulfills the demands of a normalized scalar product and can thus be applied in a Q- or an R-factor analysis.

On the Applicability of Truncated Component Analysis Based on Correlation Coefficients for Nominal Scales

The possibility of using component analysis for nominal data is discussed. Particularly, two nomi nal scale correlation coefficients are applicable, namely, Tschuprows coefficient and the J index. The reason is that they are E-correlation coeffi cients; that is, they satisfy the requirements of a scalar product between normalized vectors in a Eu clidean space. Some characteristics of these coeffi cients are described. The contingency coefficient and Cramérs V are shown not to be applicable in a component analysis. An example of a truncated component analysis on artifical nominal data is in cluded with both the J index and Tschuprows coef ficient.

The J-Index as a Measure of Nominal Scale Response Agreement

Some characteristics of Huberts Г, as a measure of nominal scale response agreement, are shown, including the characteristic that in a contingency table with equal frequencies its value will normally not be zero. By making a slight modification of its definition, some of these characteristics can be eliminated. As another alternative, the J-index is suggested. It is closely related to Г but does not have the same problematic characteristics. Some asymptotic variance formulas for the J-index are given, together with a numerical example.

On the Weighted G Index.

The G index of agreement does not permit the use of various weights for its various items. The weighted G index described here, makes it possible to use unequal weights. The weighted G index satisfies the requirements of a scalar product between normalized vectors, and a Q component analysis may, therefore, be based on it. It is also invariant over item reflection.