granova.contr {granova} | R Documentation |
Provides graphic displays that shows data and effects for a priori contrasts in ANOVA contexts; also corresponding numerical results.
granova.contr(resp, con, ngrp = nrow(con), npg = length(resp)/ngrp, jj = 1)
resp |
Vector of scores for all equally sized groups. |
con |
Matrix of column contrasts with dimensions (number of groups [G]) x (number of contrasts) [generally G X G-1]. |
ngrp |
Numeric; the number of rows = number 'cells' or groups [G]; default = nrows(resp) . |
npg |
Numeric; default is length(resp)/ngrp . If the number of contrasts is NOT equal to the number
of groups less one (i.e., to df 'among'), then npg must be set equal to the number in each group
(presumed equal for all groups). The default npg setting assumes con has one fewer column than
the number of rows. |
jj |
Numeric; controls jitter and confers the possibility of
controlling the amount of jitter in the panel plots for the contrasts Default is 1. |
Function provides graphic displays of contrast effects for so-called a priori 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. resp). The matrix of contrast vectors con
should have G rows (the number of groups), and a number of columns equal to the number of a priori contrasts, at most G-1. If
the number of columns of con
is G-1, then the number per group, or cell size, is taken to be length(resp)/G
, where G = nrow(con)
.
If the number of columns of con
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.
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. |
Robert M. Pruzek RMPruzek@yahoo.com
James E. Helmreich James.Helmreich@Marist.edu
granova.1w
, granova.2w
, granova.ds
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], con = dat6) #Polynomial Contrasts granova.contr(rat[,1],con = contr.poly(6)) #based on random data (not run) resp <- rt(64, 5) granova.contr(resp, con = contr.helmert(8))