granova (version 2.0.1)

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 generated for the data in hand, etc. The graphic may be called 'elemental' or 'natural' because it is built upon the key question that drives one-way ANOVA.

Usage

granova.1w(data, 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. Data points (jittered) for groups are displayed (vertical axis) with respect to respective group means. One-way ANOVA residuals can be displayed (set resid=TRUE) as a rug plot (on right margin); the standard deviation of the residuals, when squared, is just the mean square within, which corresponds to area of blue square. The conventional F statistic is just a ratio of the between to the within mean squares, or variances, each of which corresponds to areas of squares in the graphic. The blue square, centered on the grand mean vertically and zero for the X-axis, corresponds to mean square within (with side based on [twice] the pooled standard deviation); the red square corresponds to the mean square between, also centered on the grand mean. Use of effects to locate the groups in the order of the observed means, from left to right (by increasing size) yields this 'elemental' graphic for this commonly used statistical method.

Groups need not be of the same sizes, nor do data need to reflect any particular distributional characteristics. Skewness, outliers, clustering of data points, and various other features of the data may be seen in this graphic, possibly identified using point labels. Trimmed means (20%) can also be displayed if desired. Finally, by redisplaying the response data in two or more versions of the graphic it can be useful to visualize various effects of non-linear data transformations. (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

data(arousal)
#Drug A
granova.1w(arousal[,1:2], h.rng = 1.6, v.rng = 0.5, top.dot = .35)

#########################

library(MASS)
wt.gain <- anorexia[, 3] - anorexia[, 2]
granova.1w(wt.gain, group = anorexia[, 1], size.line = -3)

##########################

data(poison)
##Note violation of constant variance across groups in following graphic.
granova.1w(poison$SurvTime, group = poison$Group, ylab = "Survival Time")
##RateSurvTime = SurvTime^-1
granova.1w(poison$RateSurvTime, group = poison$Group, 
ylab = "Survival Rate = Inverse of Survival Time")

##Nonparametric version: RateSurvTime ranked and rescaled
##to be comparable to RateSurvTime; 
##note labels as well as residual (rug) plot below.
granova.1w(poison$RankRateSurvTime, group = poison$Group, 
ylab = "Ranked and Centered Survival Rates",
main = "One-way ANOVA display, poison data (ignoring 2-way set-up)", 
res = TRUE)