granova.contr: Graphic Display of Contrast Effect of ANOVA

In granova: Graphical Analysis of Variance

Graphic Display of Contrast Effect of ANOVA

Description

Provides graphic displays that shows data and effects for a priori contrasts in ANOVA contexts; also corresponding numerical results.

Usage

granova.contr(data, contrasts, ylab = "Outcome (response)", 
	xlab = NULL, jj = 1)

Arguments

data	Vector of scores for all equally sized groups, or a data.fame or matrix where each column represents a group.
contrasts	Matrix of column contrasts with dimensions (number of groups [G]) x (number of contrasts) [generally (G x G-1)].
ylab	Character; y axis lable.
xlab	Character vector of length number of contrast columns. To name the specific contrast being made in all but last panel of graphic. Default = NULL
jj	Numeric; controls jitter and confers the possibility of controlling the amount of jitter in the panel plots for the contrasts Default is 1.

Details

Function provides graphic displays of contrast effects for prespecified contrasts in ANOVA. Data points are displayed as relevant for each contrast based on comparing groups according to the positive and negative contrast coefficients for each contrast on the horizontal axis, against response values on the vertical axis. Data points corresponding to groups not being compared in any contrast (coefficients of zero) are ignored. For each contrast (generally as part of a 2 x 2 panel) a line segment is given that compares the (weighted) mean of the response variable for the negative coefficients versus the positive coefficients. Standardized contrasts are used, wherein the sum of (magnitudes) of negative coefficients is unity; and the same for positive coefficients. If a line is ‘notably’ different from horizontal (i.e. slope of zero), a ‘notable’ effect has been identified; however, the question of statistical significance generally depends on a sound context-based estimate of standard error for the corresponding effect. This means that while summary aov numerical results and test statistics are presented (see below), the appropriateness of the default standard error generally requires the analyst's judgment. The response values are to be input in (a stacked) form, i.e. as a vector, for all cells (cf. arg. ylab). The matrix of contrast vectors contrasts must have G rows (the number of groups), and a number of columns equal to the number of prespecified contrasts, at most G-1. If the number of columns of contrasts is G-1, then the number per group, or cell size, is taken to be length(data)/G, where G = nrow(contrasts).

If the number of columns of contrasts is less than G-1 then the user must stipulate npg, the number in each group or cell. The function is designed for the case when all cell sizes are the same, and may be most helpful when the a priori contrasts are mutually orthogonal (e.g., in power of 2 designs, or their fractional counterparts; also when specific row or column comparisons, or their interactions (see the example below based on rat weight gain data)). It is not essential that contrasts be mutually orthogonal; but mutual linear independence is required. (When factor levels correspond to some underlying continuum a standard application might use con = contr.poly(G), for G the number of groups; consider also contr.helmert(G).) The final plot in each application shows the data for all groups or cells in the design, where groups are simply numbered from 1:G, for G the number of groups, on the horizontal axis, versus the response values on the vertical axis.

Value

Two sets of numerical results are presented: Weighted cell means for positive and negative coefficients for each a priori contrast, and summary results from lm.

summary.lm	Summary results for a linear model analysis based on the R function lm (When effects are simple, as in an equal n's power of 2 design, mean differences will generally correspond to the linear regression coefficients as seen in the lm summary results.)
means.pos.neg.coeff	table showing the (weighted) means for positive and negative coefficients for each (row) contrast, and for each row, the difference between these means in the final column
means.pos.neg.coeff	Table showing the (weighted) means for positive and negative coefficients for each (row) contrast, and for each row, the difference between these means, and the standardized effect size in the final column.
contrasts	Contrast matrix used.
group.means.sds	Group means and standard deviations.
data	Input data in matrix form.

Author(s)

Robert M. Pruzek [e-mail]

James E. Helmreich [e-mail]

See Also

granova.1w, granova.2w, granova.ds

Examples

data(arousal)	
contrasts22 <- data.frame( c(-.5,-.5,.5,.5), 
	c(-.5,.5,-.5,.5), c(.5,-.5,-.5,.5) )
names(contrasts22) <- c("Drug.A", "Drug.B", "Drug.A.B")
granova.contr(arousal, contrasts = contrasts22)
	
data(rat)
dat6 <- matrix(c(1, 1, 1, -1, -1, -1, -1, 1, 0, -1, 1, 0, 1, 1, -2, 
    1, 1, -2, -1, 1, 0, 1, -1, 0, 1, 1, -2, -1, -1, 2), ncol = 5)
granova.contr(rat[,1], contrasts = dat6, ylab = "Rat Weight Gain", 
  xlab = c("Amount 1 vs. Amount 2", "Type 1 vs. Type 2", 
  "Type 1 & 2 vs Type 3", "Interaction of Amount and Type 1 & 2", 
  "Interaction of Amount and  Type (1, 2), 3"))
#Polynomial Contrasts 
granova.contr(rat[,1],contrasts = contr.poly(6))

#based on random data 
data.random <- rt(64, 5)
granova.contr(data.random, contrasts = contr.helmert(8), 
	ylab = "Random Data")

granova documentation built on March 31, 2023, 7:29 p.m.