### Trend Tests Example Data Setup

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Sets up example data for various trend tests. Ensure factor labels are ordered correctly for dose-response relationships.

```R
x <- c(106, 114, 116, 127, 145,
       110, 125, 143, 148, 151,
       136, 139, 149, 160, 174)
g <- gl(3,5)
levels(g) <- c("A", "B", "C")
```

--------------------------------

### Example Data Setup and Multiple Tests

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates setting up sample data and applying various ordered alternative tests like Chacko's, Cuzick's, and Jonckheere-Terpstra. Ensure factor levels are ordered correctly for dose-response.

```R
## Example from Sachs (1997, p. 402)
x <- c(106, 114, 116, 127, 145,
       110, 125, 143, 148, 151,
       136, 139, 149, 160, 174)
g <- gl(3,5)
levels(g) <- c("A", "B", "C")

## Chacko's test
chackoTest(x, g)

## Cuzick's test
cuzickTest(x, g)

## Johnson-Mehrotra test
johnsonTest(x, g)

## Jonckheere-Terpstra test
jonckheereTest(x, g)

## Le's test
leTest(x, g)

## Spearman type test
spearmanTest(x, g)

## Murakami's BWS trend test
bwsTrendTest(x, g)

## Fligner-Wolfe test
flignerWolfeTest(x, g)

## Shan-Young-Kang test
shanTest(x, g)
```

--------------------------------

### Example Data Setup and Friedman Test

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

This snippet demonstrates how to set up a data matrix for analysis and perform a Friedman test, which is a precursor to all-pairs comparisons.

```R
y <- matrix(c(
 3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92,
 23.19, 26.74, 10.91, 25.24, 33.52, 25.45, 18.85, 20.45,
 26.67, 4.44, 7.94, 4.04, 4.4, 4.23, 4.36, 29.41, 30.72,
 32.92, 28.23, 23.35, 12, 38.87, 33.12, 39.15, 28.06, 38.23,
 26.65),nrow=6, ncol=6,
 dimnames=list(1:6, LETTERS[1:6]))
 print(y)
 friedmanTest(y)
```

--------------------------------

### Data Preparation and Friedman Test Example

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates data setup for a blocked experiment and performs a Friedman test. This is a precursor to all-pairs comparisons.

```R
## Sachs, 1997, p. 675
## Six persons (block) received six different diuretics
## (A to F, treatment).
## The responses are the Na-concentration (mval)
## in the urine measured 2 hours after each treatment.
##
 y <- matrix(c(
 3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92,
 23.19, 26.74, 10.91, 25.24, 33.52, 26.67, 4.44, 7.94, 4.04,
 4.4, 4.23, 4.36, 29.41, 30.72, 32.92, 28.23, 23.35, 12,
 38.87, 33.12, 39.15, 28.06, 38.23,
 26.65),nrow=6, ncol=6,
 dimnames=list(1:6, LETTERS[1:6]))
 print(y)
 friedmanTest(y)
```

--------------------------------

### Example Data and Multiple Trend Tests

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Sets up example data and demonstrates the usage of various trend tests, including Murakami's BWS Trend Test.

```R
## Example from Sachs (1997, p. 402)
x <- c(106, 114, 116, 127, 145,
       110, 125, 143, 148, 151,
       136, 139, 149, 160, 174)
g <- gl(3,5)
levels(g) <- c("A", "B", "C")

## Chacko's test
chackoTest(x, g)

## Cuzick's test
cuzickTest(x, g)

## Johnson-Mehrotra test
johnsonTest(x, g)

## Jonckheere-Terpstra test
jonckheereTest(x, g)

## Le's test
leTest(x, g)

## Spearman type test
spearmanTest(x, g)

## Murakami's BWS trend test
bwsTrendTest(x, g)

## Fligner-Wolfe test
flignerWolfeTest(x, g)

## Shan-Young-Kang test
shanTest(x, g)

```

--------------------------------

### Install PMCMRplus on Windows

Source: https://cran.r-project.org/web/packages/PMCMRplus/readme/README.html

Use this command to install the PMCMRplus package and its dependencies from CRAN on Windows systems.

```r
install.packages("PMCMRplus")
```

--------------------------------

### Install PMCMRplus using Binary Packages on Ubuntu

Source: https://cran.r-project.org/web/packages/PMCMRplus/readme/README.html

Command to install the PMCMRplus R package using precompiled binary deb packages on Ubuntu, provided the CRAN2deb4ubuntu PPA is added.

```bash
sudo apt-get install r-cran-pmcmrplus
```

--------------------------------

### Example Usage of qcochran

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates how to use the qcochran function to find a specific quantile.

```R
qcochran(0.05, 7, 3)
```

--------------------------------

### Example usage of qmandelk

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Example of calculating an upper-tail quantile for Mandel's k distribution with specified parameters.

```R
qmandelk(0.005, 7, 3, lower.tail=FALSE)
```

--------------------------------

### Example Usage of pdgrubbs

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates how to use the pdgrubbs function to calculate a probability.

```R
pdgrubbs(0.62, 7, 1E4)
```

--------------------------------

### Data Preparation and Friedman Test Example

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates how to create a matrix for response data and perform a Friedman test. This is often a precursor to post-hoc multiple comparisons.

```R
## Sachs, 1997, p. 675
## Six persons (block) received six different diuretics
## (A to F, treatment).
## The responses are the Na-concentration (mval) 
## in the urine measured 2 hours after each treatment.
##
 y <- matrix(c(
 3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92,
 23.19, 26.74, 10.91, 25.24, 33.52, 25.45, 18.85, 20.45,
 26.67, 4.44, 7.94, 4.04, 4.4, 4.23, 4.36, 29.41, 30.72,
 32.92, 28.23, 23.35, 12, 38.87, 33.12, 39.15, 28.06, 38.23,
 26.65),nrow=6, ncol=6,
 dimnames=list(1:6, LETTERS[1:6]))
 print(y)
 friedmanTest(y)
```

--------------------------------

### Install/Update PMCMRplus from Source on Linux

Source: https://cran.r-project.org/web/packages/PMCMRplus/readme/README.html

Commands to update or install the PMCMRplus package from source on Linux systems. Ensure external libraries like libgmp and libmpfr are installed first if compilation errors occur.

```r
# update PMCMRplus
update.packages("PMCMRplus")
```

```r
# or install
install.packages("PMCMRplus")
```

--------------------------------

### Example: Dunnett Quantile and Distribution

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates the usage of qDunnett and pDunnett for calculating quantiles and p-values for Dunnett's test with specified parameters. Note the use of set.seed for reproducibility.

```R
## Table gives 2.34 for df = 6, m = 2, one-sided
set.seed(112)
qval <- qDunnett(p = 0.05, n0 = 3, n = rep(3,2))
round(qval, 2)
set.seed(112)
pDunnett(qval, n0=3, n = rep(3,2), lower.tail = FALSE)
```

```R
## Table gives 2.65 for df = 20, m = 4, two-sided
set.seed(112)
qval <- qDunnett(p = 0.05/2, n0 = 5, n = rep(5,4))
round(qval, 2)
set.seed(112)
2 * pDunnett(qval, n0= 5, n = rep(5,4), lower.tail= FALSE)
```

--------------------------------

### Data Setup and Basic Tests in PMCMRplus

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Initializes a matrix for Na-concentration data and performs Friedman's test and Skillings-Mack test. Ensure data is correctly formatted as a matrix.

```R
y <- matrix(c(
3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92,
23.19, 26.74, 10.91, 25.24, 33.52, 25.45, 18.85, 20.45,
26.67, 4.44, 7.94, 4.04, 4.4, 4.23, 4.36, 29.41, 30.72,
32.92, 28.23, 23.35, 12, 38.87, 33.12, 39.15, 28.06, 38.23,
26.65),nrow=6, ncol=6,
dimnames=list(1:6, LETTERS[1:6]))
print(y)
friedmanTest(y)
skillingsMackTest(y)
```

--------------------------------

### Data Preparation and Multiple Tests in PMCMRplus

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

This example demonstrates how to prepare data and apply several non-parametric tests from the PMCMRplus package, including the global Friedman test, Demsar's many-one test, Exact many-one test, Nemenyi's many-one test, and the House test. It assumes 'A' is the control group.

```R
y <- matrix(c(
 3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92,
 23.19, 26.74, 10.91, 25.24, 33.52, 25.45, 18.85, 20.45,
 26.67, 4.44, 7.94, 4.04, 4.4, 4.23, 4.36, 29.41, 30.72,
 32.92, 28.23, 23.35, 12, 38.87, 33.12, 39.15, 28.06, 38.23,
 26.65),nrow=6, ncol=6,
 dimnames=list(1:6, LETTERS[1:6]))

 ## Global Friedman test
 friedmanTest(y)

 ## Demsar's many-one test
 summary(frdManyOneDemsarTest(y=y, p.adjust = "bonferroni",
 alternative = "greater"))

 ## Exact many-one test
 summary(frdManyOneExactTest(y=y, p.adjust = "bonferroni",
 alternative = "greater"))

 ## Nemenyi's many-one test
 summary(frdManyOneNemenyiTest(y=y, alternative = "greater"))

 ## House test
 frdHouseTest(y, alternative = "greater")
```

--------------------------------

### Check/Install GMP and MPFR Development Libraries on Ubuntu/Debian

Source: https://cran.r-project.org/web/packages/PMCMRplus/readme/README.html

Commands to check for and install the GMP and MPFR development header files required for compiling R packages on Ubuntu and Debian-based systems.

```bash
dpkg -p libgmp-dev
```

```bash
dpkg -p libmpfr-dev
```

```bash
sudo apt-get install libgmp-dev
```

```bash
sudo apt-get install libmpfr-dev
```

--------------------------------

### Example Data for Quade's Test

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Sets up a matrix of Na-concentration data for six persons receiving six different diuretics, used for demonstrating Quade's test.

```R
y <- matrix(c(
3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92,
23.19, 26.74, 10.91, 25.24, 33.52, 25.45, 18.85, 20.45,
26.67, 4.44, 7.94, 4.04, 4.4, 4.23, 4.36, 29.41, 30.72,
32.92, 28.23, 23.35, 12, 38.87, 33.12, 39.15, 28.06, 38.23,
26.65),nrow=6, ncol=6,
dimnames=list(1:6, LETTERS[1:6]))
print(y)
```

--------------------------------

### Perform AD-Test, BWS-Test, Kruskal-Test, and Median Test

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates how to perform several statistical tests using sample data. Includes examples for Anderson-Darling, Bickel-Rosenberg-Schach, Kruskal-Wallis (with different distribution approximations), and Median tests. Also shows how to compare results with base R functions.

```R
x <- c(2.9, 3.0, 2.5, 2.6, 3.2) # normal subjects
y <- c(3.8, 2.7, 4.0, 2.4)      # with obstructive airway disease
z <- c(2.8, 3.4, 3.7, 2.2, 2.0) # with asbestosis
g <- factor(x = c(rep(1, length(x)),
                   rep(2, length(y)),
                   rep(3, length(z))),
             labels = c("ns", "oad", "a"))
dat <- data.frame(
   g = g,
   x = c(x, y, z))

## AD-Test
adKSampleTest(x ~ g, data = dat)

## BWS-Test
bwsKSampleTest(x ~ g, data = dat)

## Kruskal-Test
## Using incomplete beta approximation
kruskalTest(x ~ g, dat, dist="KruskalWallis")
## Using chisquare distribution
kruskalTest(x ~ g, dat, dist="Chisquare")

## Not run:
## Check with kruskal.test from R stats
kruskal.test(x ~ g, dat)

## End(Not run)
## Using Conover's F
kruskalTest(x ~ g, dat, dist="FDist")

## Not run:
## Check with aov on ranks
anova(aov(rank(x) ~ g, dat))
## Check with oneway.test
oneway.test(rank(x) ~ g, dat, var.equal = TRUE)

## End(Not run)

## Median Test asymptotic
medianTest(x ~ g, dat)

## Median Test with simulated p-values
set.seed(112)
medianTest(x ~ g, dat, simulate.p.value = TRUE)
```

--------------------------------

### K-Sample Rank Test Examples

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates the usage of k-sample rank tests including AD-Test, BWS-Test, Kruskal-Test, and Median Test with different distribution assumptions and simulation options.

```R
## Hollander & Wolfe (1973), 116.
## Mucociliary efficiency from the rate of removal of dust in normal
## subjects, subjects with obstructive airway disease, and subjects
## with asbestosis.
x <- c(2.9, 3.0, 2.5, 2.6, 3.2) # normal subjects
y <- c(3.8, 2.7, 4.0, 2.4)      # with obstructive airway disease
z <- c(2.8, 3.4, 3.7, 2.2, 2.0) # with asbestosis
g <- factor(x = c(rep(1, length(x)),
                   rep(2, length(y)),
                   rep(3, length(z))), 
             labels = c("ns", "oad", "a"))
dat <- data.frame(
   g = g,
   x = c(x, y, z))

## AD-Test
adKSampleTest(x ~ g, data = dat)

## BWS-Test
bwsKSampleTest(x ~ g, data = dat)

## Kruskal-Test
## Using incomplete beta approximation
kruskalTest(x ~ g, dat, dist="KruskalWallis")
## Using chisquare distribution
kruskalTest(x ~ g, dat, dist="Chisquare")

## Not run: 
## Check with kruskal.test from R stats
kruskal.test(x ~ g, dat)

## End(Not run)
## Using Conover's F
kruskalTest(x ~ g, dat, dist="FDist")

## Not run: 
## Check with aov on ranks
anova(aov(rank(x) ~ g, dat))
## Check with oneway.test
oneway.test(rank(x) ~ g, dat, var.equal = TRUE)

## End(Not run)

## Median Test asymptotic
medianTest(x ~ g, dat)

## Median Test with simulated p-values
set.seed(112)
medianTest(x ~ g, dat, simulate.p.value = TRUE)
```

--------------------------------

### Shirley's Williams Test Example

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates Shirley's one-sided test using a look-up table for reaction times of mice.

```R
## Example from Shirley (1977)
## Reaction times of mice to stimuli to their tails.
x <- c(2.4, 3, 3, 2.2, 2.2, 2.2, 2.2, 2.8, 2, 3,
 2.8, 2.2, 3.8, 9.4, 8.4, 3, 3.2, 4.4, 3.2, 7.4, 9.8, 3.2, 5.8,
 7.8, 2.6, 2.2, 6.2, 9.4, 7.8, 3.4, 7, 9.8, 9.4, 8.8, 8.8, 3.4,
 9, 8.4, 2.4, 7.8)
g <- gl(4, 10)

## Shirley's test
## one-sided test using look-up table
shirleyWilliamsTest(x ~ g, alternative = "greater")
```

--------------------------------

### Steel's Test Example (Sachs)

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates Steel's test for comparing multiple groups against a control, using data from Sachs (1997). Requires the kSamples package.

```R
x <- c(106, 114, 116, 127, 145,
110, 125, 143, 148, 151,
136, 139, 149, 160, 174)
g <- gl(3,5)
levels(g) <- c("0", "I", "II")

## Steel's Test
steelsKSampleTest(x ~ g, alternative = "greater")
```

--------------------------------

### Check/Install GMP and MPFR Development Libraries on Fedora/Redhat

Source: https://cran.r-project.org/web/packages/PMCMRplus/readme/README.html

Commands to check for and install the GMP and MPFR development header files required for compiling R packages on Fedora, Redhat, CentOS, and similar distributions.

```bash
dnf info gmp-devel
```

```bash
dnf info mpfr-devel
```

```bash
sudo dnf install gmp-devel
```

```bash
sudo dnf install mpfr-devel
```

--------------------------------

### Kruskal-Wallis Test Examples

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates the usage of the kruskalTest function with different p-value distribution options. Includes checks against base R functions for verification.

```R
## Hollander & Wolfe (1973), 116.
## Mucociliary efficiency from the rate of removal of dust in normal
## subjects, subjects with obstructive airway disease, and subjects
## with asbestosis.
x <- c(2.9, 3.0, 2.5, 2.6, 3.2) # normal subjects
y <- c(3.8, 2.7, 4.0, 2.4)      # with obstructive airway disease
z <- c(2.8, 3.4, 3.7, 2.2, 2.0) # with asbestosis
g <- factor(x = c(rep(1, length(x)),
                   rep(2, length(y)),
                   rep(3, length(z))),
             labels = c("ns", "oad", "a"))
dat <- data.frame(
   g = g,
   x = c(x, y, z))

## AD-Test
adKSampleTest(x ~ g, data = dat)

## BWS-Test
bwsKSampleTest(x ~ g, data = dat)

## Kruskal-Test
## Using incomplete beta approximation
kruskalTest(x ~ g, dat, dist="KruskalWallis")
## Using chisquare distribution
kruskalTest(x ~ g, dat, dist="Chisquare")

## Not run: 
## Check with kruskal.test from R stats
kruskal.test(x ~ g, dat)

## End(Not run)
## Using Conover's F
kruskalTest(x ~ g, dat, dist="FDist")

## Not run: 
## Check with aov on ranks
anova(aov(rank(x) ~ g, dat))
## Check with oneway.test
oneway.test(rank(x) ~ g, dat, var.equal = TRUE)

## End(Not run)

## Median Test asymptotic
medianTest(x ~ g, dat)

## Median Test with simulated p-values
set.seed(112)
medianTest(x ~ g, dat, simulate.p.value = TRUE)

```

--------------------------------

### Friedman Test and Post-Hoc Tests in R

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates the usage of friedmanTest and various post-hoc all-pairs comparison tests for a matrix of data. Includes examples for exact tests, Conover's, Nemenyi's, Miller's, Siegel-Castellan's, and Nemenyi's test using a formula interface.

```R
## Sachs, 1997, p. 675
## Six persons (block) received six different diuretics
## (A to F, treatment).
## The responses are the Na-concentration (mval)
## in the urine measured 2 hours after each treatment.
##
y <- matrix(c(
3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92,
23.19, 26.74, 10.91, 25.24, 33.52, 25.45, 18.85, 20.45,
26.67, 4.44, 4.04, 4.4, 4.23, 4.36, 29.41, 30.72,
32.92, 28.23, 23.35, 12, 38.87, 33.12, 39.15, 28.06, 38.23,
26.65),nrow=6, ncol=6,
 dimnames=list(1:6, LETTERS[1:6]))
print(y)
friedmanTest(y)

## Eisinga et al. 2017
frdAllPairsExactTest(y=y, p.adjust = "bonferroni")

## Conover's test
frdAllPairsConoverTest(y=y, p.adjust = "bonferroni")

## Nemenyi's test
frdAllPairsNemenyiTest(y=y)

## Miller et al.
frdAllPairsMillerTest(y=y)

## Siegel-Castellan
frdAllPairsSiegelTest(y=y, p.adjust = "bonferroni")

## Irrelevant of group order?
x <- as.vector(y)
g <- rep(colnames(y), each = length(x)/length(colnames(y)))
b <- rep(rownames(y), times = length(x)/length(rownames(y)))
xDF <- data.frame(x, g, b) # grouped by colnames

frdAllPairsNemenyiTest(xDF$x, groups = xDF$g, blocks = xDF$b)
o <- order(xDF$b) # order per block increasingly
frdAllPairsNemenyiTest(xDF$x[o], groups = xDF$g[o], blocks = xDF$b[o])
o <- order(xDF$x) # order per value increasingly
frdAllPairsNemenyiTest(xDF$x[o], groups = xDF$g[o], blocks = xDF$b[o])

## formula method (only works for Nemenyi)
frdAllPairsNemenyiTest(x ~ g | b, data = xDF)

```

--------------------------------

### Williams Test Example

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates the application of Williams' test for comparing treatment means against a zero dose control. Requires data and a factor defining treatment groups.

```R
## Example from Sachs (1997, p. 402)
x <- c(106, 114, 116, 127, 145,
110, 125, 143, 148, 151,
136, 139, 149, 160, 174)
g <- gl(3,5)
levels(g) <- c("0", "I", "II")

## Williams Test
williamsTest(x ~ g)
```

--------------------------------

### Anderson-Darling All-Pairs Test Example

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Performs the Anderson-Darling all-pairs comparison test using a formula interface. The p-value adjustment method is set to 'holm'.

```R
out <- adAllPairsTest(count ~ spray, InsectSprays, p.adjust="holm")
summary(out)
summaryGroup(out)
```

--------------------------------

### Check Kruskal-Test with R's kruskal.test

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

This example demonstrates how to verify the results of kruskalTest against the standard kruskal.test function from the R stats package. It is commented out with '## Not run:' and should be executed manually if needed.

```R
## Check with kruskal.test from R stats
kruskal.test(x ~ g, dat)
```

--------------------------------

### Comparing Power Estimation for One-Way ANOVA

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Compares power estimation for one-way ANOVA using R's built-in functions and the PMCMRplus package. This example demonstrates how to calculate necessary parameters like Cohen's f and R-squared for comparison.

```R
groupmeans <- c(120, 130, 140, 150)
SEsq <- 500  # within-variance
n <- 10
k <- length(groupmeans)
df <- n * k - k
SSQ.E <- SEsq * df
SSQ.A <- n * var(groupmeans) * (k - 1)
sd.errfn <- sqrt(SSQ.E / (n * k - 1))
R2 <- c("R-squared" = SSQ.A / (SSQ.A + SSQ.E))
cohensf <- sqrt(R2 / (1 - R2))
names(cohensf) <- "Cohens f"

## R stats power function
power.anova.test(groups = k,
                 between.var = var(groupmeans),
                 within.var = SEsq,
                 n = n)

## pwr power function
pwr.anova.test(k = k, n = n, f = cohensf, sig.level=0.05)
```

--------------------------------

### Check Kruskal-Test with aov on ranks

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

This example shows how to compare the Kruskal-Test results with an ANOVA performed on the ranks of the data. It is part of a 'Not run' block and requires manual execution.

```R
## Check with aov on ranks
anova(aov(rank(x) ~ g, dat))
```

--------------------------------

### Chen's Test Example with Default p-value Adjustment

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates the usage of chenJanTest for analyzing dose-response data with the default p-value adjustment method. This is useful for identifying the minimum effective dose in experiments.

```R
y <- c(0.2, 6.2, 0.3, 0.3, 4.9, 1.8, 3.9, 2, 0.3, 2.5, 5.4, 2.3, 12.7,
-0.2, 2.1, 6, 1.8, 3.9, 1.1, 3.8, 2.5, 1.3, -0.8, 13.1, 1.1,
12.8, 18.2, 3.4, 13.5, 4.4, 6.1, 2.8, 4, 10.6, 9, 4.2, 6.7, 35,
9, 12.9, 2, 7.1, 1.5, 10.6)
groups <- gl(4,11, labels = c("0", "0.25", "0.5", "1.0"))
blocks <- structure(rep(1:11, 4), class = "factor",
levels = c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11"))

summary(chenJanTest(y, groups, blocks, alternative = "greater"))
```

--------------------------------

### Grubbs Double Outlier Test Example

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Example of performing Grubbs double outlier test on a subset of Pentosan data, testing for a 'less' alternative hypothesis.

```R
data(Pentosan)
labMeans <- tapply(dat$value, dat$lab, mean)
doubleGrubbsTest(x = labMeans, alternative = "less")
```

--------------------------------

### Update PMCMRplus or All Packages

Source: https://cran.r-project.org/web/packages/PMCMRplus/readme/README.html

Commands to update the PMCMRplus package specifically or all installed R packages.

```r
# update PMCMRplus
update.packages("PMCMRplus")
```

```r
# or update all
update.packages()
```

--------------------------------

### Shirley-Williams Test Example

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Performs a one-sided Shirley-Williams test using a lookup table. Requires a formula interface for data and group specification.

```R
x <- c(2.4, 3, 3, 2.2, 2.2, 2.2, 2.2, 2.8, 2, 3,
 2.8, 2.2, 3.8, 9.4, 8.4, 3, 3.2, 4.4, 3.2, 7.4, 9.8, 3.2, 5.8,
 7.8, 2.6, 2.2, 6.2, 9.4, 7.8, 3.4, 7, 9.8, 9.4, 8.8, 8.8, 3.4,
 9, 8.4, 2.4, 7.8)
g <- gl(4, 10)
shirleyWilliamsTest(x ~ g, alternative = "greater")
```

--------------------------------

### Compare with BWStest Package Implementation (Less Alternative)

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Compares the 'less' alternative hypothesis result with the implementation in the BWStest package.

```R
BWStest::bws_test(x=x[g==1], y=x[g==2], alternative = "less")
```

--------------------------------

### Tamhane-Dunnett Test Example with ANOVA Object

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Performs Tamhane-Dunnett's test on residuals from an ANOVA model. Assumes data is normally distributed with unequal variances.

```R
set.seed(245)
mn <- c(1, 2, 2^2, 2^3, 2^4)
x <- rep(mn, each=5) + rnorm(25)
g <- factor(rep(1:5, each=5))

fit <- aov(x ~ g - 1)
shapiro.test(residuals(fit))
bartlett.test(x ~ g - 1)
anova(fit)
## works with object of class aov
summary(tamhaneDunnettTest(fit, alternative = "greater"))
```

--------------------------------

### Nemenyi's All-Pairs Test

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Performs Nemenyi's all-pairs comparison test for Friedman rank sums. No specific p-value adjustment is shown in this example.

```R
## Nemenyi's test
 frdAllPairsNemenyiTest(y=y)
```

--------------------------------

### Ordered Alternatives Tests in R

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Demonstrates various tests for ordered alternatives using sample data. Ensure factor labels for 'g' are ordered increasingly from zero-dose control to the highest dose level.

```r
x <- c(106, 114, 116, 127, 145,
       110, 125, 143, 148, 151,
       136, 139, 149, 160, 174)
g <- gl(3,5)
levels(g) <- c("A", "B", "C")

## Chacko's test
chackoTest(x, g)

## Cuzick's test
cuzickTest(x, g)

## Johnson-Mehrotra test
johnsonTest(x, g)

## Jonckheere-Terpstra test
jonckheereTest(x, g)

## Le's test
leTest(x, g)

## Spearman type test
spearmanTest(x, g)

## Murakami's BWS trend test
bwsTrendTest(x, g)

## Fligner-Wolfe test
flignerWolfeTest(x, g)

## Shan-Young-Kang test
shanTest(x, g)
```

--------------------------------

### Compare with BWStest Package Implementation (Greater Alternative)

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Compares the 'greater' alternative hypothesis result with the implementation in the BWStest package.

```R
BWStest::bws_test(x=x[g==1], y=x[g==2], alternative = "greater")
```

--------------------------------

### Data Preparation and Global Friedman Test

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Prepares sample data in a matrix format and performs a global Friedman test. This is a foundational step before conducting pairwise comparisons.

```R
y <- matrix(c(
 3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92,
 23.19, 26.74, 10.91, 25.24, 33.52, 25.45, 18.85, 20.45,
 26.67, 4.44, 7.94, 4.04, 4.4, 4.23, 4.36, 29.41, 30.72,
 32.92, 28.23, 23.35, 12, 38.87, 33.12, 39.15, 28.06, 38.23,
 26.65),nrow=6, ncol=6,
 dimnames=list(1:6, LETTERS[1:6]))

 ## Global Friedman test
 friedmanTest(y)
```

--------------------------------

### Perform Dunn's All-Pairs Comparison Test

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Conduct Dunn's all-pairs comparison test with Dunn's original Bonferroni p-adjustment method using kwAllPairsDunnTest.

```R
## Dunn's all-pairs comparison test
ans <- kwAllPairsDunnTest(count ~ spray, data = InsectSprays,
                             p.adjust.method = "bonferroni")
summary(ans)
```

--------------------------------

### Perform Grubbs Outlier Test

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

This snippet shows how to perform Grubbs' single outlier test on a numeric vector. Ensure the data is pre-processed as needed, for example, by calculating group means.

```R
data(Pentosan)
dat <- subset(Pentosan, subset = (material == "A"))
labMeans <- tapply(dat$value, dat$lab, mean)
grubbsTest(x = labMeans, alternative = "two.sided")
```

--------------------------------

### Compare Friedman Test with friedman.test

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Compares the results of the `friedmanTest` function with the base R `friedman.test` function for verification.

```R
## check with friedman.test from R stats
friedman.test(RoundingTimes)
```

--------------------------------

### Chen's Test Example with SD1 p-value Adjustment

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Illustrates using chenJanTest with the 'SD1' p-value adjustment method, which is specifically designed for accounting for alpha-error inflation in dose-response trend tests.

```R
summary(chenJanTest(y, groups, blocks, alternative = "greater", p.adjust = "SD1"))
```

--------------------------------

### NPMTest: All-Pairs Comparisons for Simply Ordered Mean Ranksums

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Performs Nashimoto and Wright's all-pairs comparison procedure for simply ordered mean ranksums. Supports different methods including look-up, bootstrap, and asymptotic tests.

```APIDOC
## All-Pairs Comparisons for Simply Ordered Mean Ranksums

### Description
Performs Nashimoto and Wright's all-pairs comparison procedure for simply ordered mean ranksums. 

### Usage
```R
NPMTest(x, ...)

## Default S3 method:
NPMTest(x, g, alternative = c("greater", "less"), method = c("look-up", "boot", "asympt"), nperm = 10000, ...)

## S3 method for class 'formula'
NPMTest(formula, data, subset, na.action, alternative = c("greater", "less"), method = c("look-up", "boot", "asympt"), nperm = 10000, ...)
```

### Arguments
`x` |  a numeric vector of data values, or a list of numeric data vectors.  
`g` |  a vector or factor object giving the group for the corresponding elements of `"x"`. Ignored with a warning if `"x"` is a list.  
`alternative` |  the alternative hypothesis. Defaults to `greater`.  
`method` |  a character string specifying the test statistic to use. Defaults to `"look-up"` that uses published Table values of Williams (1972).  
`nperm` |  number of permutations for the asymptotic permutation test. Defaults to `1000`. Ignored, if `method = "look-up"`.  
`formula` |  a formula of the form `response ~ group` where `response` gives the data values and `group` a vector or factor of the corresponding groups.  
`data` |  an optional matrix or data frame (or similar: see `model.frame`) containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`.  
`subset` |  an optional vector specifying a subset of observations to be used.  
`na.action` |  a function which indicates what should happen when the data contain `NA`s. Defaults to `getOption("na.action")`.  
`...` |  further arguments to be passed to or from methods.  
```

--------------------------------

### S3 Method for Formula Interface of steelsKSampleTest

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

S3 method for steelsKSampleTest using a formula interface. Allows specifying response, group, and optional arguments like subset and na.action.

```R
steelsKSampleTest(
  formula,
  data,
  subset,
  na.action,
  alternative = c("two.sided", "greater", "less"),
  ...
)
```

--------------------------------

### Fit ANOVA Model for Scheffe's Test

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Fit an ANOVA model using aov() before applying Scheffe's test. This example uses the 'chickwts' dataset to model 'weight' based on 'feed'.

```R
fit <- aov(weight ~ feed, chickwts)
shapiro.test(residuals(fit))
bartlett.test(weight ~ feed, chickwts)
anova(fit)
```

--------------------------------

### hsAllPairsTest Formula Method Signature

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Illustrates the S3 method for hsAllPairsTest when using a formula interface, specifying formula, data, and subset arguments.

```R
## S3 method for class 'formula':
hsAllPairsTest(
  formula,
  data,
  subset,
  na.action,
  alternative = c("greater", "less"),
  method = c("look-up", "boot", "asympt"),
  nperm = 10000,
  ...
)
```

--------------------------------

### Steel's Test Example (USEPA)

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Applies Steel's test to reproduction data from a Ceriodaphnia dubia chronic test, excluding a specific dose level. Useful for identifying No Observed Effect Concentrations (NOEC).

```R
x <- c(20, 26, 26, 23, 24, 27, 26, 23, 27, 24,
13, 15, 14, 13, 23, 26, 0, 25, 26, 27,
18, 22, 13, 13, 23, 22, 20, 22, 23, 22,
14, 22, 20, 23, 20, 23, 25, 24, 25, 21,
9, 0, 9, 7, 6, 10, 12, 14, 9, 13,
rep(0,10))
g <- gl(6, 10)
levels(g) <- c("Control", "3%", "6%", "12%", "25%", "50%")

## NOEC at 3%, LOEC at 6%
steelsKSampleTest(x ~ g, subset = g != "50%", alternative = "less")
```

--------------------------------

### leTest

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Performs Le's test for ordered alternatives.

```APIDOC
## leTest

### Description
Performs Le's test for ordered alternatives.

### Usage
```R
leTest(x, g, ...)
```

### Arguments
* `x`: A numeric vector of data values.
* `g`: A vector or factor object giving the group for the corresponding elements of `x`.
* `...`: Further arguments to be passed to or from methods.
```

--------------------------------

### ChaAllPairsNashimotoTest with Default and H-distribution

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Compares ChaAllPairsNashimotoTest with default standard normal distribution and with h-distribution for post-hoc testing.

```R
## post-hoc test, default is standard normal distribution (NPT'-test)
summary(chaAllPairsNashimotoTest(x, g, p.adjust.method = "none"))

## same but h-distribution (NPY'-test)
chaAllPairsNashimotoTest(x, g, dist = "h")
```

--------------------------------

### Nemenyi's All-Pairs Rank Comparison Test - Default Method

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

The default S3 method for kwAllPairsNemenyiTest takes a numeric vector and a grouping vector. The 'dist' argument specifies the distribution for p-value calculation.

```R
## Default S3 method:
kwAllPairsNemenyiTest(x, g, dist = c("Tukey", "Chisquare"), ...)
```

--------------------------------

### Perform Median Test with asymptotic distribution

Source: https://cran.r-project.org/web/packages/PMCMRplus/refman/PMCMRplus.html

Conducts a Median Test using asymptotic distribution. This is suitable for general use when sample sizes are adequate.

```R
medianTest(x ~ g, dat)
```