# R program for paired t-test with cement data

# There are two easy ways to run these commands in R.  One is to merely 'copy and paste' 
# these commands into R's 'Console window'.  They will be executed automatically, and 
# you can then go back and see which commands resulted in what output.

# A better way, in general, is to (within R) click on 'File -> New script', and then 
# copy and paste the commands into the script file that has opened up.  With that 
# window highlighted, click on 'Edit -> Run all'.  
# You can save this script file, and run it again later, perhaps after making changes to it.

# In doing assigned questions it is a good idea to put your commands into a script file, and
# just keep running/changing/running the script file, until you get things right.  That way, 
# once you get some of the commands right, you won't have to keep re-entering them.



mod <- c(16.85, 16.40, 17.21, 16.35, 16.52, 17.04, 16.96, 17.15, 16.59, 16.57)
unmod <- c(17.50, 17.63, 18.25, 18.00, 17.86, 17.75, 18.22, 17.90, 17.96, 18.15)

differences <- mod-unmod

differences
summary(differences)

# perform paired t-test
t.test(mod, unmod,paired=T)



#Compare with a one-sample t-test on the differences

t.test(differences)

 

qqnorm(differences)
qqline(differences)
cor(sort(differences), qnorm((.5:9.5)/10))