multcompLetters: Letter summary of similarities and differences

Description

Convert a logical vector or a vector of p-values or a correlation or distance matrix into a character-based display in which common characters identify levels or groups that are not significantly different. Designed for use with the output of functions like TukeyHSD, diststats, simint, simtest, csimint, csimtestmultcomp, friedmanmc, kruskalmcpgirmess.

Usage

multcompLetters(
  x,
  compare = "<", threshold="0.05," letters="c(letters," letters,="" "."),="" reversed="FALSE" )<="" p="">multcompLetters2(formula, x, data, ...)
multcompLetters3(z, y, x, data, ...)
multcompLetters4(object, comp, ...)

Value

An object of class 'multcompLetters', which is a list with the following components:

Letters: character vector with names = the names of the levels or groups compared and with values = character strings in which common values of the function argument "Letters" identify levels or groups that are not significantly different (or more precisely for which the corresponding element of "x" was FALSE or was converted to FALSE by "compare").
monospacedLetters: Same as "Letters" but with spaces so the individual grouping letters will line up with a monospaced type font.
LetterMatrix: Logical matrix with one row for each level compared and one column for each "Letter" in the "letter-based representation". The output component "Letters" is obtained by concatenating the column names of all columns with TRUE in that row.

multcompLetters4 will return a named list with the terms containing a object of class 'multcompLetters' as produced by multcompLetters.

Arguments

x: One of the following: (1) A square, symmetric matrix with row names. (2) A vector with hyphenated names, which identify individual items or factor levels after "strsplit". (3) An object of class "dist". If x (or x[1]) is not already of class "logical", it is replaced with do.call(compare, list(x, threshold)), which by default converts numbers (typically p-values) less than 0.05 to TRUE and everything else to FALSE. If x is a matrix, its diagonal must be or must convert to FALSE.
compare: function or binary operator; not used if class(x) is "logical".
threshold: Second (reference) argument to "compare".
Letters: Vector of distinct characters (or character strings) used to connect levels that are not significantly different. They should be recognizable when concatenated. The last element of "Letters" is used as a prefix for a reuse of "Letters" if more are needed than are provided. For example, with the default "Letters", if 53 distinct connection columns are required, they will be "a", ..., "z", "A", ..., "Z", and ".a". If 54 are required, the last one will be ".b". If 105 are required, the last one will be "..a", etc. (If the algorithm generates that many distinct groups, the display may be too busy to be useful, but the algorithm shouldn't break.)
reversed: A logical value indicating whether the order of the letters should be reversed. Defaults to FALSE.
formula: The formula used to make the test (lm, aov, glm, etc.). Like y ~ x.
data: Data used to make the test.
...: Extra arguments passed to multcompLetters.
z: Categorical variables used in the test.
y: Value of the response variable.
object: An object of class aov or lm for the time being.
comp: A object with multiple comparison or a function name to perform a multiple comparison.

Functions

multcompLetters2():
multcompLetters3(): create a compact letters display and order the letters
multcompLetters4(): create a compact letters display using a aov object

Author

Spencer Graves, Hans-Peter Piepho and Luciano Selzer

Details

Produces a "Letter-Based Representation of All- Pairwise Comparisons" as described by Piepho (2004). (The present algorithm does NOT perform his "sweeping" step.) multcompLettersx are wrapper of multcompLetters that will reorder the levels of the data so that the letters appear in a descending order of the mean. mulcompletters3 is similar to multcompletters2 except that it uses vector names to separate and the later has an formula interface. multcompLetters4 will take a aov or lm object and a comparison test and will produce all the letters for the terms and interactions.

References

Piepho, Hans-Peter (2004) "An Algorithm for a Letter-Based Representation of All-Pairwise Comparisons", Journal of Computational and Graphical Statistics, 13(2)456-466.

Examples

Run this code


##
## 1.  a logical vector indicating signficant differences
##
dif3 <- c(FALSE, FALSE, TRUE)
names(dif3) <- c("A-B", "A-C", "B-C")
dif3L <- multcompLetters(dif3)
dif3L
print(dif3L)
print(dif3L, TRUE)

##
## 2.  numeric vector indicating statistical significance
##
dif4 <- c(.01, .02, .03, 1)
names(dif4) <- c("a-b", "a-c", "b-d", "a-d")
(diff4.T <- multcompLetters(dif4))

(dif4.L1 <- multcompLetters(dif4,
       Letters=c("*", ".")))
# "Letters" can be any character strings,
# but they should be recognizable when
# concatenated.

##
## 3.  distance matrix
##
dJudge <- dist(USJudgeRatings)
dJl <- multcompLetters(dJudge, compare='>', threshold = median(dJudge))
# comparison of 43 judges;  compact but undecipherable:
dJl

x <- array(1:9, dim=c(3,3),
   dimnames=list(LETTERS[1:3], NULL) )
d3 <- dist(x)
dxLtrs <- multcompLetters(d3, compare=">", threshold=2)

d3d <- dist(x, diag=TRUE)
dxdLtrs <- multcompLetters(d3d, compare=">", threshold=2)

stopifnot(
all.equal(dxLtrs, dxdLtrs)
)

d3u <- dist(x, upper=TRUE)
dxuLtrs <- multcompLetters(d3d, compare=">", threshold=2)

stopifnot(
all.equal(dxLtrs, dxuLtrs)
)

##
## 4.  cor matrix
##
set.seed(4)
x100 <- matrix(rnorm(100), ncol=5,
               dimnames=list(NULL, LETTERS[1:5]) )
cx <- cor(x100)
cxLtrs <- multcompLetters(abs(cx), threshold=.3)


##
##5. reversed
##

dif3 <- c(FALSE, FALSE, TRUE)
names(dif3) <- c("A-B", "A-C", "B-C")
dif3L <- multcompLetters(dif3)
dif3L.R <- multcompLetters(dif3, rev = TRUE)
dif3L
dif3L.R


##
##6. multcompletters2 usage

experiment <- data.frame(treatments = gl(11, 20, labels = c("dtl", "ctrl", "treat1", 
              "treat2", "treatA2", "treatB", "treatB2",
              "treatC", "treatD", "treatA1", "treatX")),
              y = c(rnorm(20, 10, 5), rnorm(20, 20, 5), rnorm(20, 22, 5), rnorm(20, 24, 5),
               rnorm(20, 35, 5), rnorm(20, 37, 5), rnorm(20, 40, 5), rnorm(20, 43, 5),
               rnorm(20, 45, 5), rnorm(20, 60, 5), rnorm(20, 60, 5)))
exp_tukey <- TukeyHSD(exp_aov <- aov(y  ~ treatments, data = experiment))
exp_letters1 <- multcompLetters(exp_tukey$treatments[,4])
exp_letters1
#Notice lowest mean treatments gets a "e"
#Ordered letters
multcompLetters2(y ~ treatments, exp_tukey$treatments[,"p adj"], experiment)
multcompLetters2(y ~ treatments, exp_tukey$treatments[,"p adj"], experiment, reversed = TRUE)

##7. multcompletters3 usage

multcompLetters3("treatments", "y", exp_tukey$treatments[,"p adj"], experiment)

##8. multcompletters4 usage


multcompLetters4(exp_aov, exp_tukey)

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