granovagg.1w: Elemental Graphic Display for One-Way ANOVA

In granovaGG: Graphical Analysis of Variance Using ggplot2

Elemental Graphic Display for One-Way ANOVA

Description

Graphic to display data for a one-way analysis of variance – that is for unstructured groups. Also to help understand how data play out in the context of the basic one-way model, how the F statistic is generated for the data at hand, etc. The graphic may be called 'elemental' or 'natural' because it is built upon the central question that drives one-way ANOVA (see details below).

Usage

granovagg.1w(
  data,
  group = NULL,
  h.rng = 1,
  v.rng = 1,
  jj = NULL,
  dg = 2,
  resid = FALSE,
  print.squares = TRUE,
  xlab = "default_x_label",
  ylab = "default_y_label",
  main = "default_granova_title",
  plot.theme = "theme_granova_1w",
  ...
)

Arguments

data	Dataframe or vector. If a dataframe, the two or more columns are taken to be groups of equal size (whence group is NULL). If data is a vector, group must be a vector, perhaps a factor, that indicates groups (unequal group sizes allowed with this option).
group	Group indicator, generally a factor in case data is a vector.
h.rng	Numeric; controls the horizontal spread of groups, default = 1
v.rng	Numeric; controls the vertical spread of points, default = 1.
jj	Numeric; sets horiz. jittering level of points. jj gets passed as the amount parameter to jitter. When jj = NULL (the default behavior), the degree of jitter will take on a sensible value. In addition, if pairs of ordered means are close to one another and jj = NULL, the degree of jitter will default to the smallest difference between two adjacent contrasts.
dg	Numeric; sets number of decimal points in output display, default = 2
resid	Logical; displays marginal distribution of residuals (as a 'rug') on right side (wrt grand mean), default = FALSE.
print.squares	Logical; displays graphical squares for visualizing the F-statistic as a ratio of MS-between to MS-within
xlab	Character; horizontal axis label, can be supplied by user, default = "default_x_label", which leads to a generic x-axis label ("Contrast coefficients based on group means").
ylab	Character; vertical axis label, can be supplied by user, default = "default_y_label", which leads to a generic y-axis label ("Dependent variable (response)").
main	Character; main label, top of graphic; can be supplied by user, default = "default_granova_title", which will print a generic title for graphic.
plot.theme	argument indicating a ggplot2 theme to apply to the graphic; defaults to a customized theme created for the one-way graphic
...	Optional arguments to/from other functions

Details

The one-way ANOVA graphic shows how the comparison of unstructured groups, viz. their means, entails a particular linear combination (L.C.) of the group means. In particular, we use the fact that the numerator of the one-way F statistic, the mean square between (MS.B), is a linear combination of the group means; each weight – one for each group – in the L.C. is (principally) a function of the difference between the group's mean and the grand mean, viz., (M~j~ - M..) where M~j~ denotes the jth group's mean, and M.. denotes the grand mean. The L.C. can be written as a sum of products of the form MS.B = Sum((1/df.B)(n_j (M_j - M..) M_j)) for j = 1...J. The denominator of the F-statistic, MS.W (mean square within), can be described as a 'scaling factor'. It is just the (weighted) average of the variances of the J groups (j = 1 ... J). (n~j~'s are group sizes.) The differences (M~j~ - M..) are themselves the 'effects' in the analysis. When the effects are plotted against the group means (the horizontal and vertical axes) a straight line necessarily ensues. Group means are plotted as triangles along this line. Once the means have been plotted, the data points (jittered) for the groups are displayed (vertical axis) with respect to the respective contrasts. Since the group means are just the fitted values in one-way ANOVA, and the deviations of the scores within groups are the residuals (subsetted by groups), the graphic can be seen as showing fitted vs. residual values for the line that shows the locus of ordered group means – from the smallest on the left) the the largest (on the right). If desired, the aggregate of all such residuals can be plotted (as a rug plot) on the right margin of the graphic centered on the grand mean (large green dot in 'middle'). The use of effects to locate groups this way yields what we term an 'elemental' graphic because it is based on the central question that drives one-way ANOVA.

Note that groups need not have the same size, nor do data need to reflect any particular distributional characteristics. Finally, the gray bars (one for each group) at the bottom of the graphic show the relative sizes of the group standard deviations with referene to the 'average' group s.d. (more precisely, the square root of the MS.W). This 'average' corresponds to the thin white line that runs horizontally across these bars.

Value

Returns a plot object of class ggplot. The function also provides printed output including by-group statistical summaries and information about groups that might be overplotted (if applicable):

group	group names
group means	means for each group
trimmed.mean	20% trimmed group means
contrast	Contrasts (group main effects)
variance	variances
standard.deviation	standard deviations
group.size	group sizes
overplotting information	Information about groups that, due to their close means, may be overplotted

Author(s)

Brian A. Danielak [e-mail]
Robert M. Pruzek [e-mail]

with contributions by:
William E. J. Doane [e-mail]
James E. Helmreich [e-mail]
Jason Bryer [e-mail]

References

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

Wickham, H. (2009). Ggplot2: Elegant Graphics for Data Analysis. New York: Springer.

Wilkinson, L. (1999). The Grammar of Graphics. Statistics and computing. New York: Springer.

See Also

granovagg.contr, granovagg.ds, granovaGG

Examples

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

###

data(anorexia)
wt.gain <- anorexia[, 3] - anorexia[, 2]
granovagg.1w(wt.gain, group = anorexia[, 1])

###

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

###

data(chickwts)
?chickwts # An explanation of the chickwts dataset
with(chickwts, granovagg.1w(weight, group = feed)) # Modeling weight as explained by feed type

granovaGG documentation built on Nov. 23, 2023, 9:08 a.m.