On the minimum expected quantity for the validity of the chi-squared test in 2 2 2 tables

A 2 2 2 contingency table can often be analysed in an exact fashion by using Fisher's exact test and in an approximate fashion by using the chi-squared test with Yates' continuity correction, and it is traditionally held that the approximation is valid when the minimum expected quantity E is E S 5. Unfortunately, little research has been carried out into this belief, other than that it is necessary to establish a bound E>E*, that the condition E S 5 may not be the most appropriate (Martín Andrés et al., 1992) and that E* is not a constant, but usually increasing with the growth of the sample size (Martín Andrés & Herranz Tejedor, 1997). In this paper, the authors conduct a theoretical experimental study from which they ascertain that E* value (which is very variable and frequently quite a lot greater than 5) is strongly related to the magnitude of the skewness of the underlying hypergeometric distribution, and that bounding the skewness is equivalent to bounding E (which is the best control procedure). The study enables estimating the expression for the above-mentioned E* (which in turn depends on the number of tails in the test, the alpha error used, the total sample size, and the minimum marginal imbalance) to be estimated. Also the authors show that E* increases generally with the sample size and with the marginal imbalance, although it does reach a maximum. Some general and very conservative validity conditions are E S 35.53 (one-tailed test) and E S 7.45 (two-tailed test) for alpha nominal errors in 1% h f h 10%. The traditional condition E S 5 is only valid when the samples are small and one of the marginals is very balanced; alternatively, the condition E S 5.5 is valid for small samples or a very balanced marginal. Finally, it is proved that the chi-squared test is always valid in tables where both marginals are balanced, and that the maximum skewness permitted is related to the maximum value of the bound E*, to its value for tables with at least one balanced marginal and to the minimum value that those marginals must have (in non-balanced tables) for the chi-squared test to be valid.     

Time series count data regression

The count data model studied in the paper extends the Poisson model by al-lowing for overdispersion and serial correlation. Alternative approaches to esti-mate nuisance parameters, required for the correction of the Poisson maximum likelihood covariance matrix estimator and for a quasi-likelihood estimator, are studied. The estimators are evaluated by finite sample Monte Carlo experi-mentation. It is found that the Poisson maximum likelihood estimator with corrected covariance matrix estimators provide reliable inferences for longer time series. Overdispersion test statistics are wellbehaved, while conventional portmanteau statistics for white noise have too large sizes. Two empirical illustrations are included.     

Pan-European groupings: A case study in paint manufacture

This complete Case Study, including Teaching Notes, won the 1991 EFMD Case Writing Competition Prize on a European theme, as well as receiving much praise from the judges. The Case concerns a group of four different European paint manufacturers co-operating in an EC Economic Interest Grouping to improve their economic position in European markets. The co-ordination of raw material purchasing policies was the first area of joint action; they obtained significant discounts straight away. Then they could begin to think about competing together against the big paint multinationals established in Europe. Later, talks started on joint investment and technology transfer.Lluis Renart and Francesco Parés have written a stimulating Case Study with Teaching Notes of value to business students and managers wishing to test out their analytical abilities.     

Women’s Employment Status,Coercive Control,and Intimate Partner Violence in Mexico

Findings from previous studies examining the relation between women’s employment and the risk of intimate partner violence have been mixed. Some studies find greater violence toward women who are employed, whereas others find the opposite relation or no relation at all. I propose a new framework in which a woman’s employment status and her risk of violent victimization are both influenced by the level of control exercised by her partner. Controlling men will actively prevent women from working and are also more likely to physically harm their partners. Using a statistical model in which the effect of omitted characteristics on women’s employment and their risk of violence are allowed to be correlated reverses the estimated association between employment and violence. The final results show that employment reduces women’s risk of violence. Data for the study are drawn from a sample of over 30,000 Mexican women in intimate relationships. The findings have broad implications given the increase in female labor force participation in many parts of the world.     

Homogamy by education and migration status in Monterrey,Mexico: changes and continuities over time

This paper reviews changes in homogamy by migration status and educational level in Monterrey, Mexico, through the analysis of marriage patterns for two cohorts of men born in 1905–1934 and 1940–1969. Results show a significant increase in educational homogamy, as well as in homogamy by rural origins. The changes suggest that education has played an increasingly important role in the process of mate selection, although certain particularistic characteristics, such as being a rural immigrant, are still important in marriage formation. The paper concludes with a discussion of the implications of these findings for the relationship between homogamy and social stratification.

Control charts for monitoring the median in non-negative asymmetric data

Statistical Methods & Applications - Control charts are commonly used for monitoring the mean of processes. However, there are practical applications in which asymmetric data are the standard....     

Uncertainty and Sensitivity Analysis in Assessment of the Thyroid Cancer Risk Related to Chernobyl Fallout in Eastern France

The increase in the thyroid cancer incidence in France observed over the last 20 years has raised public concern about its association with the 1986 nuclear power plant accident at Chernobyl. At the request of French authorities, a first study sought to quantify the possible risk of thyroid cancer associated with the Chernobyl fallout in France. This study suffered from two limitations. The first involved the lack of knowledge of spontaneous thyroid cancer incidence rates (in the absence of exposure), which was especially necessary to take their trends into account for projections over time; the second was the failure to consider the uncertainties. The aim of this article is to enhance the initial thyroid cancer risk assessment for the period 1991-2007 in the area of France most exposed to the fallout (i.e., eastern France) and thereby mitigate these limitations. We consider the changes over time in the incidence of spontaneous thyroid cancer and conduct both uncertainty and sensitivity analyses. The number of spontaneous thyroid cancers was estimated from French cancer registries on the basis of two scenarios: one with a constant incidence, the other using the trend observed. Thyroid doses were estimated from all available data about contamination in France from Chernobyl fallout. Results from a 1995 pooled analysis published by Ron et al. were used to determine the dose-response relation. Depending on the scenario, the number of spontaneous thyroid cancer cases ranges from 894 (90% CI: 869-920) to 1,716 (90% CI: 1,691-1,741). The number of excess thyroid cancer cases predicted ranges from 5 (90% UI: 1-15) to 63 (90% UI: 12-180). All of the assumptions underlying the thyroid cancer risk assessment are discussed.