Methods to test for equality of two normal distributions

Statistical tests for two independent samples under the assumption of normality are applied routinely by most practitioners of statistics. Likewise, presumably each introductory course in statistics treats some statistical procedures for two independent normal samples. Often, the classical two-sample model with equal variances is introduced, emphasizing that a test for equality of the expected values is a test for equality of both distributions as well, which is the actual goal. In a second step, usually the assumption of equal variances is discarded. The two-sample t test with Welch correction and the F test for equality of variances are introduced. The first test is solely treated as a test for the equality of central location, as well as the second as a test for the equality of scatter. Typically, there is no discussion if and to which extent testing for equality of the underlying normal distributions is possible, which is quite unsatisfactorily regarding the motivation and treatment of the situation with equal variances. It is the aim of this article to investigate the problem of testing for equality of two normal distributions, and to do so using knowledge and methods adequate to statistical practitioners as well as to students in an introductory statistics course. The power of the different tests discussed in the article is examined empirically. Finally, we apply the tests to several real data sets to illustrate their performance. In particular, we consider several data sets arising from intelligence tests since there is a large body of research supporting the existence of sex differences in mean scores or in variability in specific cognitive abilities.     

Bayesian analysis of dynamic magnetic resonance breast images

Summary.  We describe an integrated methodology for analysing dynamic magnetic resonance images of the breast. The problems that motivate this methodology arise from a collaborative study with a tumour institute. The methods are developed within the Bayesian framework and comprise image restoration and classification steps. Two different approaches are proposed for the restoration. Bayesian inference is performed by means of Markov chain Monte Carlo algorithms. We make use of a Metropolis algorithm with a specially chosen proposal distribution that performs better than more commonly used proposals. The classification step is based on a few attribute images yielded by the restoration step that describe the essential features of the contrast agent variation over time. Procedures for hyperparameter estimation are provided, so making our method automatic. The results show the potential of the methodology to extract useful information from acquired dynamic magnetic resonance imaging data about tumour morphology and internal pathophysiological features.     

Moderators of the relationship between daily work stressors and mood

Consistent with recent data showing a relationship between daily stress and mood, the authors investigated whether job specific factors would moderate the relationship between daily work stress and daily mood. Forty-three subjects from one teaching hospital initially completed questionnaires assessing the hypothesized moderator variables (emotional and informational support from the supervisor, job involvement, co-worker satisfaction, supervision satisfaction, and satisfaction with the meaningfulness of work). Thereafter, they completed questionnaires at the end of each workday assessing the number and negative perception of daily work stress and daily mood. After controlling for the effects of the different number of days for which data were available for each subject, the results showed that job involvement and all three facets of job satisfaction (supervision, co-worker, and work itself) moderated the relationship between the negative perception of daily work stress and mood. Neither emotional nor informational support from the supervisor moderated this relationship. Likewise, none of these variables moderated the relationship between the number of daily work events and mood. The results are discussed in terms of further research on daily work stress, and expanding and refining the focus on moderator variables.     

Spatial and non-spatial model-based protection procedures for the release of business microdata

In this paper we discuss methodology for the safe release of business microdata. In particular we extend the model-based protection procedure of Franconi and Stander (2002, The Statistician 51: 1–11) by allowing the model to take account of the spatial structure underlying the geographical information in the microdata. We discuss the use of the Gibbs sampler for performing the computations required by this spatial approach. We provide an empirical comparison of these non-spatial and spatial disclosure limitation methods based on the Italian sample from the Community Innovation Survey. We quantify the level of protection achieved for the released microdata and the error induced when various inferences are performed. We find that although the spatial method often induces higher inferential errors, it almost always provides more protection. Moreover the aggregated areas from the spatial procedure can be somewhat more spatially smooth, and hence possibly more meaningful, than those from the non-spatial approach. We discuss possible applications of these model-based protection procedures to more spatially extensive data sets.     

A comment on “A theoretical basis for perturbation methods” by Krishnamurty Muralidhar and Rathindra Sarathy

Statistics and Computing -     

Effects of short-term role overload on marital interactions

This paper examines the effect of role overload on marital interactions using a within-person, time series approach. It is proposed that role overload is indirectly related to marital interactions most strongly via anxiety but also via depression. Twenty-three couples completed daily reports of overload, depression and anxiety and weekly reports of their own and their spouse's marital behaviour over 4 months. After controlling for autocorrelation, role overload was found to affect directly both depression and anxiety, but its effect on anxiety was much stronger than that on depression. Anxiety predicted withdrawal from marital interactions, but not anger, and depression predicted anger, but not withdrawal. Also, spouses' perceptions of their partners' behaviour reflected the partners' self-reported behaviour, and spouses' perceptions predicted their own behaviour.     

Practical reason or metapreferences? an undogmatic defense of kantian morality

This article presents the thesis that a critique of decisions is not necessarily (except in the trivial sense) a critique of preferences. This thesis runs contrary to the fundamental assumption in economic theory that a critique of decisions will always simultaneously be a critique of (subjective) preferences, since decision behavior is after all a manifestation of preferences. If this thesis is right, then the paradigm of so-called instrumental rationality is in serious trouble, not for external reasons but because of imminent inconsistencies. The thesis is developed in five parts: I. A preliminary remark to the economic theory of rationality in general. II. The cooperation problem as a challenge to the economic theory of rationality. III. An account of the most interesting attempt to save the theory. IV. A critique of that attempt. V. And the conclusion: practical reason is concerned with actions and not with preferences.