MRtest {midrangeMCP}

Multiple comparison procedures to the means of a factor using the studentized range and midrange distributions.

Description

MRtest applies the Means grouping based on midrange, Means Grouping based on Range, Student-Newman-Keuls based on midrange and Tukey based on midrange tests. These are new tests for multiple comparisons proposed by the authors (BATISTA, 2016), that are being published.

Usage

MRtest(
  y,
  trt = NULL,
  dferror = NULL,
  mserror = NULL,
  replication = NULL,
  alpha = 0.05,
  main = NULL,
  MCP = "all",
  ismean = FALSE
)

Arguments

y

Model (aov or lm), numeric vector containing the response variable or the mean of the treatments.

trt

Constant (y = model) or a vector containing the treatments.

dferror

Degrees of freedom of the Mean Square Error.

mserror

Mean Square Error.

replication

Number de repetitions of the treatments in the experiment. For unbalanced data should be informed the harmonic mean of repetitions. This argument should be informed only if ismean = TRUE.

alpha

Significant level. The default is alpha = 0.05.

main

Title of the analysis.

MCP

Allows choosing the multiple comparison test; the defaut is "all". This option will go perform all tests. However, the options are: the Means grouping based on midrange test ("MGM"), Means Grouping based on Range test ("MGR"), the Student-Newman-Keuls based on midrange test ("SNKM") and the Tukey based on midrange test ("TM").

ismean

Logic. If FALSE (default), the y argument represents a model (aov or lm) or a numeric vector containing the response variable. If TRUE the y argument represents the mean of treatments.

Details

The MCP argument allows you to choose various tests of multiple comparisons at once. For example, MCP = c("MGM", "MGR"), and so on.

Value

MRtest returns the print of a list of results. First, the summary of y. Second, the statistics of the test chosen. And finally, the mean group results for each test. If MRtest function is stored in an object, the results will be printed and also stored in the object.

Examples

# Simulated data (completely randomized design)

# Response variable
rv <- c(100.08, 105.66, 97.64, 100.11, 102.60, 121.29, 100.80,
        99.11, 104.43, 122.18, 119.49, 124.37, 123.19, 134.16,
        125.67, 128.88, 148.07, 134.27, 151.53, 127.31)

# Treatments
treat <- factor(rep(LETTERS[1:5], each = 4))

# Anova
res     <- anova(aov(rv~treat))
DFerror <- res$Df[2]
MSerror <- res$`Mean Sq`[2]

# Loading the midrangeMCP package
library(midrangeMCP)

# applying the tests
results <- MRtest(y = rv,
                  trt = treat,
                  dferror = DFerror,
                  mserror = MSerror,
                  alpha = 0.05,
                  main = "Multiple Comparison Procedure: MGM test",
                  MCP = c("MGM"))

# Other option for the MCP argument is "all". All tests are used.

results$Groups     # Results of the tests
results$Statistics # Main arguments of the tests
results$Summary    # Summary of the response variable

# Using the y argument as aov or lm model
res  <- aov(rv~treat)

MRtest(y = res, trt = "treat", alpha = 0.05,
       main = "Multiple Comparison Procedure: MGM test",
       MCP = c("MGM"))

# For unbalanced data: It will be used the harmonic mean of
#                       the number of experiment replicates

# Using the previous example
rv <- rv[-1]
treat <- treat[-1]

res  <- lm(rv~treat) # Linear model

# Multiple comparison procedure: MGR test
MRtest(y = res, trt = "treat", alpha = 0.05,
       main = "Multiple Comparison Procedure: MGR test",
       MCP = c("MGR"))

# Assuming that the available data are the averages
#  of the treatments and the analysis of variance

# Analysis of Variance Table

# Response: rv
#            Df Sum Sq Mean Sq F value    Pr(>F)
# treat      4 4135.2 1033.80  14.669 4.562e-05 ***
# Residuals 15 1057.1   70.47

mean.treat <- c(100.87, 105.95, 117.62, 127.97, 140.30)
treat <- factor(LETTERS[1:5])
DFerror <- 15
MSerror <- 70.47488
replic <- 4

MRtest(y = mean.treat,
       trt = treat,
       dferror = DFerror,
       mserror = MSerror,
       replication = replic,
       alpha = 0.05,
       main = "Multiple Comparison Procedure: MGM test",
       MCP = c("MGM"),
       ismean = TRUE)