Creating an R function using randomization test of differences - r

Question

Write a function that will allow the user
to input a vector of numerical values,
with no missing values "the data", and
a vector of 1's and 2's, representing
two different groups that you want to compare.
"the treatments". The number of 1's and 2's does not need to be equal. You may assume
for now, that treatment 2 has a higher mean
than treatment 1.
The function will create the randomization
distribution of differences, and plot them
in a histogram. It will use the distribution
to calculate the p-value -- the chance that
the observed difference (or higher) could have
occurred by chance. It will print the observed
difference and the p-value, both
rounded to 4 digits, using text:
"The observed difference is xxxx and the
p-value is xxxx"
Using these two vectors I have determined how to get the differences but do not know how to put it into a function and implement a randomization test.
dat<- c(1,4,2,5,2,4,8,6,9,7)
trt <- c(1,1,1,1,1,2,2,2,2,2)
How to find the observed difference:
obsdiff <- mean(dat[trt == 2]) - mean(dat[trt == 1])
How to 'shuffle the treatments':
trtsh <- sample(trt, size = length(trt))
How to find a difference simulated
under the null hypothesis,
i.e., difference in means for shuffled
treatment 2 minus treatment 1:
simdiff <- mean(dat[trtsh == 2]) - mean(dat[trtsh == 1])
The p-value using these vectors should be .011

Answer 1

dat<- c(1,4,2,5,2,4,8,6,9,7)
trt <- c(1,1,1,1,1,2,2,2,2,2)
In general, it is a good idea to coerce all of your data into a data frame, a la
data.frame(dat, trt) -> mydata
Now you can calculate your obsdiff as
obsdiff <- mean(mydata$dat[mydata$trt == 2]) - mean(mydata$dat[mydata$trt == 1])
Here's one way you can shuffle your treatment values using a for-loop:
simdiff <- vector(length=10000)
for(j in 1:10000){
cat(paste(j, '\n') )
trtsh <- sample(trt)
mydatash <- data.frame(dat, trtsh)
simdiff[j] <- mean(mydatash$dat[mydatash$trt == 2]) - mean(mydatash$dat[mydatash$trt == 1])
}
For help with plotting, see ?hist (e.g. hist(simdiff)).
Now, you just need to wrap the pieces above into a function that calculates the quantile of simdiff where obsdiff >= simdiff and outputs the text.