This small collection of functions provides what we call elemental graphics for display of analysis of variance results, David C. Hoaglin, Frederick Mosteller and John W. Tukey (1991, ISBN:978-0-471-52735-0), Paul R. Rosenbaum (1989) doi:10.2307/2684513, Robert M. Pruzek and James E. Helmreich https://jse.amstat.org/v17n1/helmreich.html.
The term elemental derives from the fact that each function is aimed at construction of graphical displays that afford direct visualizations of data with respect to the fundamental questions that drive the particular analysis of variance methods. These functions can be particularly helpful for students and non-statistician analysts. But these methods should be quite generally helpful for work-a-day applications of all kinds, as they can help to identify outliers, clusters or patterns, as well as highlight the role of non-linear transformations of data.
This package has been written by Robert M. Pruzek and James E. Helmreich. Frederic Bertrand is now the maintainer of package and has been doing several code fixes and improvements to the package.
Installation
You can install the released version of granova from CRAN with:
install.packages("granova")You can install the development version of granova from github like so:
devtools::install_github("fbertran/granova")Example
data(arousal)Drug A
## basic example code
granova.1w(arousal[,1:2], h.rng = 1.6, v.rng = 0.5, top.dot = .35)
plot of chunk DrugA
#> $grandsum
#> Grandmean df.bet df.with MS.bet MS.with F.stat
#> 22.35 1.00 18.00 73.73 6.86 10.75
#> F.prob SS.bet/SS.tot
#> 0.00 0.37
#>
#> $stats
#> Size Contrast Coef Wt'd Mean Mean Trim'd Mean Var. St. Dev.
#> Placebo 10 -1.92 20.43 20.43 20.30 5.83 2.41
#> Drug.A 10 1.92 24.27 24.27 24.45 7.89 2.81
data(anorexia, package="MASS")
wt.gain <- anorexia[, 3] - anorexia[, 2]
granova.1w(wt.gain, group = anorexia[, 1], size.line = -3)
plot of chunk anorexia
#> $grandsum
#> Grandmean df.bet df.with MS.bet MS.with F.stat
#> 2.76 2.00 69.00 307.32 56.68 5.42
#> F.prob SS.bet/SS.tot
#> 0.01 0.14
#>
#> $stats
#> Size Contrast Coef Wt'd Mean Mean Trim'd Mean Var. St. Dev.
#> Cont 26 -3.21 -0.49 -0.45 -1.16 63.82 7.99
#> CBT 29 0.24 3.63 3.01 1.80 53.41 7.31
#> FT 17 4.50 5.15 7.26 7.91 51.23 7.16
data(poison)Note violation of constant variance across groups in following graphic.
granova.1w(poison$SurvTime, group = poison$Group, ylab = "Survival Time")
plot of chunk violation of constant variance across groups
#> $grandsum
#> Grandmean df.bet df.with MS.bet MS.with F.stat
#> 0.48 11.00 36.00 0.20 0.02 9.01
#> F.prob SS.bet/SS.tot
#> 0.00 0.73
#>
#> $stats
#> Size Contrast Coef Wt'd Mean Mean Trim'd Mean Var. St. Dev.
#> 3 4 -0.27 0.21 0.21 0.21 0.00 0.02
#> 9 4 -0.24 0.23 0.23 0.23 0.00 0.01
#> 2 4 -0.16 0.32 0.32 0.32 0.01 0.08
#> 12 4 -0.15 0.32 0.32 0.32 0.00 0.03
#> 6 4 -0.14 0.33 0.33 0.33 0.00 0.05
#> 8 4 -0.10 0.38 0.38 0.38 0.00 0.06
#> 1 4 -0.07 0.41 0.41 0.41 0.00 0.07
#> 7 4 0.09 0.57 0.57 0.57 0.02 0.16
#> 10 4 0.13 0.61 0.61 0.61 0.01 0.11
#> 11 4 0.19 0.67 0.67 0.67 0.07 0.27
#> 5 4 0.34 0.81 0.81 0.81 0.11 0.34
#> 4 4 0.40 0.88 0.88 0.88 0.03 0.16RateSurvTime = SurvTime^-1
granova.1w(poison$RateSurvTime, group = poison$Group,
ylab = "Survival Rate = Inverse of Survival Time")
plot of chunk RateSurvTime
#> $grandsum
#> Grandmean df.bet df.with MS.bet MS.with F.stat
#> 2.62 11.00 36.00 5.17 0.24 21.53
#> F.prob SS.bet/SS.tot
#> 0.00 0.87
#>
#> $stats
#> Size Contrast Coef Wt'd Mean Mean Trim'd Mean Var. St. Dev.
#> 4 4 -1.46 1.16 1.16 1.16 0.04 0.20
#> 5 4 -1.23 1.39 1.39 1.39 0.31 0.55
#> 10 4 -0.93 1.69 1.69 1.69 0.13 0.36
#> 11 4 -0.92 1.70 1.70 1.70 0.49 0.70
#> 7 4 -0.76 1.86 1.86 1.86 0.24 0.49
#> 1 4 -0.14 2.49 2.49 2.49 0.25 0.50
#> 8 4 0.09 2.71 2.71 2.71 0.17 0.42
#> 6 4 0.41 3.03 3.03 3.03 0.18 0.42
#> 12 4 0.47 3.09 3.09 3.09 0.06 0.24
#> 2 4 0.65 3.27 3.27 3.27 0.68 0.82
#> 9 4 1.64 4.26 4.26 4.26 0.06 0.23
#> 3 4 2.18 4.80 4.80 4.80 0.28 0.53Nonparametric version: RateSurvTime ranked and rescaled to be comparable to RateSurvTime; note labels as well as residual (rug) plot below.
granova.1w(poison$RankRateSurvTime, group = poison$Group,
ylab = "Ranked and Centered Survival Rates",
main = "One-way ANOVA display, poison data (ignoring 2-way set-up)",
res = TRUE)
plot of chunk Nonparametric version
#> $grandsum
#> Grandmean df.bet df.with MS.bet MS.with F.stat
#> 2.49 11.00 36.00 3.70 0.19 19.18
#> F.prob SS.bet/SS.tot
#> 0.00 0.85
#>
#> $stats
#> Size Contrast Coef Wt'd Mean Mean Trim'd Mean Var. St. Dev.
#> 4 4 -1.38 1.11 1.11 1.11 0.03 0.18
#> 5 4 -1.13 1.36 1.36 1.36 0.28 0.53
#> 10 4 -0.82 1.67 1.67 1.67 0.10 0.31
#> 11 4 -0.80 1.69 1.69 1.69 0.50 0.71
#> 7 4 -0.67 1.81 1.81 1.81 0.24 0.49
#> 1 4 -0.10 2.39 2.39 2.39 0.30 0.55
#> 8 4 0.23 2.72 2.72 2.72 0.19 0.44
#> 6 4 0.55 3.04 3.04 3.04 0.18 0.42
#> 12 4 0.61 3.09 3.09 3.09 0.05 0.22
#> 2 4 0.66 3.15 3.15 3.15 0.39 0.62
#> 9 4 1.29 3.78 3.78 3.78 0.03 0.16
#> 3 4 1.55 4.04 4.04 4.04 0.03 0.16