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The Half-Half (HH) plot is a new graphical method to investigate qualitatively the shape of a regression curve. The empirical HH-plot counts observations in the lower and upper quarter of a strip that moves horizontally over the scatterplot. The plot displays jumps clearly and reveals further features of the regression curve. We prove a functional central limit theorem for the empirical HH-plot, with rate of convergence . In a simulation study, the good performance of the plot is demonstrated. The method is also applied to two case studies. The proofs and one more case study are deferred to a supplement, which is available online. [ABSTRACT FROM AUTHOR]

The analysis of screening experiments based on nonregular designs can lead to a model selection problem in which the number of variables is large, the number of trials is small, and there are constraints on model structure. Common subset selection methods do not perform well in this setting. We propose a new approach particularly well suited to screening. The method uses an intentionally nonconvergent stochastic search to generate a large set of well-fitting models, each with the same number of variables. Model selection is then viewed as a feature extraction problem from this set. An easy-to-use graphical method and an automatic approach are proposed to determine the best models. Computer code and additional supplementary materials are available online. [ABSTRACT FROM AUTHOR]

Proposes a graphical method for assessing parametric transformation of the response in a linear regression model. Examples of response formations using data from an experiment on the behavior of worsted yarns; Details of the proposed method; Application of the linearity condition to the marginal distribution of the predictors.

This paper presents theory and applications of a simple graphical method, called hazard plotting, for the analysis of multiply censored life data consisting of failure times of failed units intermixed with running times on unfailed units. Applications of the method are given for multiply censored data on service life of equipment, for strength data on an item with different failure modes, and for biological data multiply censored on both sides from paired comparisons. Theory for the hazard plotting method, which is based on the hazard function of a distribution, is developed from the properties of order statistics from Type II multiply censored samples. [ABSTRACT FROM AUTHOR]

Measures of the quality of prediction at locations on the surface of a hypersphere are presented. These measures are used to form a graphical method of assessing the overall prediction capability of an experimental design throughout the region of interest. A plot of the spherical variance and the maximum and minimum prediction variances for locations on a sphere against the radius of the sphere, a variance dispersion graph, is used to give a comprehensive picture of the behavior of the prediction variances throughout a region and hence of the quality of the predicted responses obtained with a particular design. Such plots are used to investigate and compare the prediction capabilities of certain response surface designs currently available to the researcher. [ABSTRACT FROM AUTHOR]

The sorted binary plot is a graphical method for identifying and displaying patterns in multivariate data sets. The construction requires calculation of the median for each variable measured, followed by subtraction of the medians from the values for each sample. The signs of the residuals represent a binary number for each sample. The list of binary numbers is sorted and converted to a graph by assigning distinctive symbols to 1 and 0. The sorting operation causes samples with the same binary number to form clusters. The method can be extended to three or more quantiles. It has been applied to several kinds of data. [ABSTRACT FROM AUTHOR]

A graphical method is proposed to display a number of point estimates while allowing for their differing standard errors. More generally, it can be viewed as a representation of interval estimates by points on a bivariate plot. The method exploits a familiar connection between standardized estimates and regression through the origin and has several advantages over some alternative plots used in the literature. It is particularly useful when there may be a mixture of parameters, as illustrated by the problem of "mixed ages" in fission track dating. [ABSTRACT FROM AUTHOR]

A dynamic graphical method is one in which a data analyst interacts in real time with a data display on a computer graphics terminal. Using a screen input device such as a mouse, the analyst can specify, in a visual way, points or regions on the display and cause aspects of the display to change nearly instantaneously. Brushing is a collection of dynamic methods for viewing multidimensional data. It is very effective when used on a scatterplot matrix, a rectangular array of all pairwise scatterplots of the variables. Four brushing operations-highlight, shadow highlight, delete, and label--are carried out by moving a mouse-controlled rectangle, called the brush, over one of the scatterplots. The effect of an operation appears simultaneously on all scatterplots. Three paint modes--transient, lasting, and undo--and the ability to change the shape of the brush allow the analyst to specify collections of points on which the operations are carried out. Brushing can be used in various ways or on certain types of data; these usages are called brush techniques and include the following: single-point and cluster linking, conditioning on a single variable, conditioning on two variables, subsetting with categorical variables, and stationarity probing of a time series. [ABSTRACT FROM AUTHOR]