# Statistical Analysis: an Introduction using R/R/Random sampling

#### Random sampling

From the help page, we have seen that the sample function can take a number of different arguments. x must be a vector of items, size must be a number. Since 1:6 gives a vector of the numbers from 1 to 6, we can set x=1:6 and size=5. Here are 5 examples (note that the first 4 are equivalent, although the actual result will differ due to chance effects when sampling[1]).
```###The next 4 lines are equivalent, 5 numbers are selected from a list of 1..6
sample(x=1:6, size=5, replace=FALSE) #when sampling WITHOUT replacement, each number only appears once
sample(replace=FALSE, size=5, x=1:6) #you can change the order of the arguments
sample(x=1:6, size=5)                #the same, because replace=FALSE by default
sample(1:6, 5)        #we don't need x= and size= if arguments are in the same order as in the help file
### The next line is a different model
sample(1:6, 5, TRUE)                 #sampling WITH replacement (the same number can appear twice)
###The next 4 lines are equivalent, 5 numbers are selected from a list of 1..6
sample(x=1:6, size=5, replace=FALSE) #when sampling WITHOUT replacement, each number only appears once
[1] 1 5 4 3 6
sample(replace=FALSE, size=5, x=1:6) #you can change the order of the arguments
[1] 5 6 4 2 1
sample(x=1:6, size=5)                #the same, because replace=FALSE by default
[1] 2 3 4 6 5
sample(1:6, 5)        #we don't need x= and size= if arguments are in the same order as in the help file
[1] 1 6 3 5 4
### Now simulate a different model
sample(1:6, 5, TRUE)                 #sampling WITH replacement (the same number can appear twice)
[1] 3 6 2 1 3```
As noted, our "fair die" model is one of sampling with replacement: the same number can appear twice (and indeed does in our data). So our simulation model in R is simply
`sample(1:6, 5, TRUE) `

## References

1. call set.seed(1) before each chapter to get exactly the same results