Change In Population Mean Research Articles

Scan Statistics for Normal Data with Outliers

In this article we investigate the performance of scan statistics based on moving medians, as test statistics for detecting a local change in population mean, for one and two dimensional normal data, in presence of outliers, when the population variance is unknown. For fixed window scan statistics, both the training sample and parametric bootstrap methods are employed for one and two dimensional normal data, in presence of one or two outliers. Multiple window scan statistics are implemented via the parametric bootstrap method for one and two dimensional normal data, in presence of one or two outliers. Numerical results are presented via simulation to evaluate the power of these scan statistics for detecting the local change in the population mean, for selected parameters of the models characterizing the local change in the population mean and models characterizing the occurrence of one or two outliers in the data. When the window size where the local change of the population mean has occurred is unknown, the multiple window scan statistics, implemented via the bootstrap method, performed quite well.

Robust Scan Statistics for Detecting a Local Change in Population Mean for Normal Data

In this article we investigate the performance of robust scan statistics based on moving medians, as test statistics for detecting a local change in population mean, for one and two dimensional data. When a local change in the population mean has not occurred and outliers are not present in the data, we derive approximations for the tail probabilities of fixed window scan statistics based on moving medians. The performance of the proposed robust scan statistics are evaluated and compared to, via power calculations, the performance of scan statistics based on moving sums, that have been previously investigated in the statistical literature. Numerical results based on a simulation study, for independent and identically distributed (iid) normal observations with known variance, indicate that in presence of outliers the scan statistic based on moving medians outperform the scan statistic based on moving sums, in terms of achieving more accurately the specified probability of type I error. The performance of a multiple window scan statistic based on moving medians for detecting a local change in population mean, for one and two dimensional normal data in presence of outliers, when the size of the window where a change has occurred is unknown has been investigated as well.

The multivariate evolution of female body shape in an artificial digital ecosystem

Human bodies exemplify complex phenotypes, likely to be subject to complex evolutionary forces. Despite the importance of body shape to health, social interactions and self-esteem, our understanding of body evolution and integration remains simplistically focused on simple ratios like waist–hip ratio (WHR), and body mass index (BMI), or manipulations of one or a few traits. Evolutionary selection analyses give a multivariate perspective, but highly correlated body measures create multicollinearity problems. Here we develop an original approach mimicking Darwinian selection to study how clonal lines of bodies, allowed to vary in 24 attributes via a mutation-like process, evolve in a digital ecosystem over 8 generations. Ten of 24 traits changed by more than one |S.D.| over seven generations of selection. Analyses of selection within generations, change in population mean, and change within clonal family lines all implicate slenderness, particularly narrow waists and long legs as the most important dimension of body attractiveness. WHR did not offer any improvement on waist girth as a predictor of attractiveness. Within the most successful clonal lineages, selection favored greater shapeliness, including larger busts, in addition to slenderness. Our results reveal the complex, multivariate nature of attractiveness, and that the success of simple ratios like WHR and BMI in previous studies is probably incidental to the importance of waist girth and general slenderness. Our results also suggest that the integration of the entire body phenotype is at least as important as any one trait, and that more than one way exists to make an attractive body.

Errors in genetic theory equations

This study addresses the consequences of eliminating terms such as x(2) and x(3) from genetic equations when the variable x is known to be small. This paper indicates logically that to assign such terms a value of 0.0 requires knowing the magnitude of the coefficients for each of these terms as well as the magnitude of all other terms in a given expression. Since most genetic expressions of interest involve several unknowns, the elimination of these terms appears difficult to justify in most situations. The effects of the elimination of a single term from an expression in a classical plant breeding paper were investigated as a simple exemplifying case. In the example, the simplified equation for change in population mean with selection sometimes greatly overestimated the response to selection and in some cases also altered conclusions as to best procedure. Though simplified equations are usually much more tractable and interpretable, the bias which is introduced into the research results and the potential for propagation of such biases in subsequent studies indicates that no term can be uncritically ignored in a genetic equation. The obvious alternatives are (1) do not simplify by eliminating terms, (2) perform a complete error analysis, or (3) restrict the range of values for variables so that terms can be justifiably eliminated in the error analysis.