R for Statistical Computing (Chapter 7)
R7.1 Distribution functions of the Z, Student’s t,  2 and F distributions:
computation of the p-values
To compute the cumulative distribution function of the above distributions at a value x,
use the following functions in R.
Z: pnorm(x)
t : pt(x,df =)
2 : pchisq(x,df =)
F1 ,  2 : pf(x,df1=1,df2=2)
For example, to evaluate the following probabilities
1. P(Z < 2.05)
2. P(t43 < 1.25)
3. P( 152  23.44 )
4. P( F4, 12  2.33 )
we use the following R commands:
> pnorm(2.05)
[1] 0.9798
> pt(1.25,df=43)
[1] 0.1090
> 1pchisq(23.44,df=15)
[1] 0.0752
> pf(2.33,df1=4,df2=12)
[1] 0.8848
R7.2
C7_mes data: the matched and unmatched sample t test
The data file C7_mes contains 20 observations of results in Mathematics, English and
Sciences, with variable names M, E and S, respectively. The path of the file is
c:/Stat/C7_mes.txt. We first load the data file into a data frame and call it “ms”. The
procedure is:
> ms = read.table(“c:/Stat/C7_mes.txt”,header=T)
> attach(ms)
Now the data frame contains the data of the three variables M, E and S. To compute the
mean and the standard deviation of these variables, we do the following:
> mean(ms)
M
E
81.45 74.95
S
81.10
> sd(ms)
M
E
S
7.997 6.065 9.279
For the matched sample t test, we compute the difference and then calculate its mean as
standard deviation as follows:
>D=SE
> mean(D)
[1] 6.15
> sd(D)
[1] 8.412