In [1]:

    

alpha <- 0.05


    

In [2]:

    

data <- data.frame(I=c(15, 25, 32, 17, 11), II=c(9, 18, 29, 28, 16))
data


    

    
Out[2]:





I
II

	
1
15
9
	
2
25
18
	
3
32
29
	
4
17
28
	
5
11
16

In [3]:

    

J <- length(data)
nj <- colSums(data)
n <- sum(nj)
k <- nrow(data)
c(J=J, nj=nj, n=n, k=k)


    

    
Out[3]:





	
J
		
2
	
nj.I
		
100
	
nj.II
		
100
	
n
		
200
	
k
		
5

In [4]:

    

pi <- 1/n * rowSums(data)
pi


    

    
Out[4]:





	
0.12
	
0.215
	
0.305
	
0.225
	
0.135

In [5]:

    

QI <- sum((data$I - nj[1]*pi)^2/(nj[1]*pi))
QI


    

    
Out[5]:




3.20094534107115

In [6]:

    

QII <- sum((data$II - nj[2]*pi)^2/(nj[2]*pi))
QII


    

    
Out[6]:




3.20094534107115

In [7]:

    

Q <- QI + QII
Q


    

    
Out[7]:




6.4018906821423

In [8]:

    

qchisq(1-alpha, (J-1)*(k-1))


    

    
Out[8]:




9.48772903678115