# R example of Friedman's Test on the soybean data

# The response is yield 
# The treatments are the different varieties 
# The blocks are 3 different regions 

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##
# Reading the data into R:

my.datafile <- tempfile()
cat(file=my.datafile, "  
A 1 45
A 2 49
A 3 38
B 1 48
B 2 45
B 3 39
C 1 43
C 2 42
C 3 35
D 1 41
D 2 39
D 3 36
E 1 44
E 2 41
E 3 40
", sep=" ")

soy <- read.table(my.datafile, header=FALSE, col.names=c("variety", "region", "yield")) 
  
# Note we could also save the data columns into a file and use a command such as:
# soy <- read.table(file = "z:/stat_705/filename.txt", header=FALSE, col.names = c("variety", "region", "yield"))

attach(soy)


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#########
####################################################################

variety <- factor(variety)
region <- factor(region)

# In R, the Friedman test can be done with the friedman.test() function.  

friedman.test(yield, groups = variety, blocks = region)

# Or, equivalently:

friedman.test(yield ~ variety | region)


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# To calculate the ranks within blocks (regions):

tapply(yield, region, rank)