# Generating Random Values

A series of 20 fair (equal probability of head=1 or tail=0) coin flips can be generated by the random binomial generator

`rbinom(n=20, size=1, prob=0.5)  # size indicates the number of flips in each of the 20 trials`

Samples from a set of numbers or names can be drawn.

`sample(20)  # this arranges 1:20 in random ordersample(20,5)  # this draws 5 samples from 1:20sample(20, replace=T)`

The last example draws 20 samples from 1:20 with replacement, while the default is to sample without replacement. Use the `help` command to find more information about `sample` and `paste`.

`x24 <- paste('trt',1:10,sep='')sample(x24,5)`

### Example: Generating Randomized Treatment Maps

You can use random numbers and sampling in R to generate maps of treatments for experiments. For example, a completely randomized design assigns a set of treatments to experimental units at random throughout the set of experimental units. This is in contrast to a randomized complete block design, where each treatment is assigned to one experimental unit within a block. The easiest ways to conceptualize such experimental designs may be in the context of a field study in which a unit of land or a plot is an experimental unit or in terms of a greenhouse study in which a pot on a bench is an experimental unit.

For a completely randomized design, suppose there are `ntrt` treatments labeled 1 through `ntrt`, and `nrepl` replicates. The set of random treatment assignments can be generated by the following code, where arbitrary values of `ntrt` and `nrepl` are supplied as an example:

`ntrt <- 8nrepl <- 2sample(rep(x=1:ntrt,times=nrepl))# These treatments can be assigned to a map with#   particular dimensions by putting the values#   in a matrix of desired dimensiontemp <- sample(rep(x=1:ntrt,times=nrepl))# note that the function ‘rep’ already exists in R# and is not to be confused with our new variable ‘nrepl’# try ‘help(rep)’ for more informationmatrix(temp,nrow=nrepl,ncol=ntrt)`

For a randomized complete block design, each treatment has to be assigned once within each block before the same treatment can be assigned again. If `nrepl` = 1 (an unrealistic case), then the order of treatments can be randomized by:

`ntrt <- 8nrepl <- 1sample(1:ntrt)# Suppose nrepl is greater than 1nrepl <- 5randout <- sample(1:ntrt)for (j in 2:nrepl){randout <- c(randout,sample(1:ntrt))}# If the blocks should appear in the map as columnsmatrix(randout,nrow=ntrt,ncol=nrepl)`

Next: Statistical Distributions