granova (version 1.3)

granova.1w: Graphic display for one-way ANOVA

Description

Graphic to display data for a one-way analysis of variance, and also to help understand how ANOVA works, how the F statistic is computed, etc. The graphic may be called 'elemental' or 'natural' because it is built around the key question that drives one-way ANOVA.

Usage

granova.1w(yy, group = NULL, dg = 2, h.rng = 1.25, v.rng = 0.2, 
   box = FALSE, jj = 1, kx = 1, px = 1, size.line = -2.5, 
   top.dot = 0.15, trmean = FALSE, resid = FALSE, dosqrs = TRUE, 
   ident = FALSE, pt.lab = NULL, xlab = NULL, ylab = NULL, 
   main = NULL, ...)

Value

Returns a list with two components:grandsumContains the basic ANOVA statistics: the grandmean, the degrees of freedom and mean sums of squares between and within groups, the F statistic, F probability and the ratio between the sum of squares between groups and the total sum of squares.statsContains a table of statistics by group: the size of each group, the contrast coefficients used in plotting the groups, the weighted means, means, and 20% trimmed means, and the group variances and standard deviations.

Details

The central idea of the graphic is to use the fact that a one way analysis of variance F statistic is the ratio of two variances each of which can usefully be presented graphically. In particular, the sum of squares between (among) can be represented as the sum of products of so-called effects (each being a group mean minus the grand mean) and the group means; when these effects are themselves plotted against the group means a straight line necessarily ensues. The group means are plotted as red triangles along this line. Additionally, data points are displayed (re: vertical axis) with respect to these group means for each group. Once this elemental plot has been generated the one-way ANOVA residuals can be displayed as a rug plot (on the right margin), whence it is recognized that the pooled standard deviation of the residuals, when squared, is just the mean square within. The conventional F statistic is just a ratio of the between to the within mean squares, or variances, and it is straightforward to represent each variance as the area of a square in the graphic. Specifically, the blue square, centered on the grand mean vertically and zero for the X-axis, corresponds to the mean square within (with side based on [twice] the pooled standard deviation); the second square corresponds to the mean square between, and is also centered on the grand mean. The ratio of the areas of these squares is the F-statistic. By using effects to locate the groups in the order of the observed means, from left to right for smallest to largest, an 'elemental' graphic is defined for this commonly used statistical method.

Groups need not be of the same sizes, nor do data need to reflect any particular distributional characteristics. But skewness, outliers, clustering of scores, and various other features of the data can often be readily seen in this framework. Trimmed means (20%) can also be displayed if desired. Finally, by redisplaying the response data in two or more versions of the graphic it will often be possible to visualize the effects of transformations. Finally, individual points can be labeled in the graphic (ident=TRUE).

References

Fundamentals of Exploratory Analysis of Variance, Hoaglin D., Mosteller F. and Tukey J. eds., Wiley, 1991.

See Also

granova.2w, granova.contr, granova.ds

Examples

library(MASS)
wt.gain <- anorexia[,3] - anorexia[,2]
granova.1w(wt.gain, group = anorexia[,1], size.line = -3)
#
attach(ChickWeight)
CW0 <- subset(ChickWeight, Time==0)[,c(1,4)]
granova.1w(yy = CW0[,1], group = CW0[,2], jj = 2)
#
CW21 <- subset(ChickWeight, Time==21)[,c(1,4)]
granova.1w(yy = CW21[,1], group = CW21[,2])