##############################################################
> # Contingency tables 

> coursegrade
 [1] 4 4 1 3 4 4 3 4 4 3 3 3 2 1 0 4 1 2 3 4 3 2 3 2 3 4 2 3 3 3 4 3 4 3 3 0 4 3
[39] 3 3 1 4 3 3 1 4 2 4 3

> table(coursegrade)
coursegrade
 0  1  2  3  4 
 2  5  6 21 15 

> table(coursegrade,Class)
           Class
coursegrade  2  3  4
          0  0  2  0
          1  0  3  2
          2  0  4  2
          3  2  8 11
          4  0  6  9
>
> # Read summary counts into a matrix for chi-square analysis
> 
> classdata<-matrix(c(0,2,0,0,3,2,0,4,2,2,8,11,0,6,9),nrow=5,byrow=T)
> classdata
     [,1] [,2] [,3]
[1,]    0    2    0
[2,]    0    3    2
[3,]    0    4    2
[4,]    2    8   11
[5,]    0    6    9
> dimnames(classdata)<-list(c("F","D","C","B","A"),c("Sophomore","Junior","Senior"))
> classdata
  Sophomore Junior Senior
F         0      2      0
D         0      3      2
C         0      4      2
B         2      8     11
A         0      6      9

*********************************************************************************
> # Chi-square test for independence
>
> chisq.test(classdata, correct=F)

	Pearson's Chi-squared test

data:  classdata 
X-squared = 6.8326, df = 8, p-value = 0.5548

Warning message:
In chisq.test(classdata, correct = F) :
  Chi-squared approximation may be incorrect

# Better to store output
>
> out<-chisq.test(classdata, correct=F)
Warning message:
In chisq.test(classdata, correct = F) :
  Chi-squared approximation may be incorrect

> attributes(out)
$names
[1] "statistic" "parameter" "p.value"   "method"    "data.name" "observed" 
[7] "expected"  "residuals"

$class
[1] "htest"

> out$expected
   Sophomore    Junior     Senior
F 0.08163265 0.9387755  0.9795918
D 0.20408163 2.3469388  2.4489796
C 0.24489796 2.8163265  2.9387755
B 0.85714286 9.8571429 10.2857143
A 0.61224490 7.0408163  7.3469388