Descriptive STATISTICS: Chi Square

Introduction: chi square: There are two different chi-square tests: one in which we have different levels of a single categorical variable and one in which we have different levels of two categorical variables. A chi-square test on a single categorical variable is called a chi-square goodness-of-fit test.

Formula
	Chi Square

Restrictions:
1. Chi square can only be used with frequency data.
2. the individual events or observations that constitute the data must be independent of each other.
3. we must have in the data both the frequency of occurrence and the frequency of nonoccurrence if we are recording whether or not an event occurs.
4. no expected frequencies should be less than 5.
Note: an alternative to chi square is the Fisher exact probability test.

 

prgmX2GOF

Line	Command or Statement	Comments
1.	ClrHome	Clear Screen
2.	Disp "OBS LIST"	Observed
3.	Input "L1=",Str1
4.	expr("{"+Str1->L1
5.	0->A
6.	For(I,1,dim(L1
7.	A+L1(I)->A
8.	End
9.	L1->ιθO
10.	Disp "EXP LIST	Expected
11.	Input "L2=",Str2
12.	expr("{"+Str2->L2
13.	0->B
14.	For(J,1,dim(L2
15.	B+L2(J)->B
16.	End
17.	L2->ιθE
18.	ClrHome
19.	dim(ιθO)-1->K	df
20.	Fix 4
21.	Disp "X2 ="
22.	(ιθO-ιθE)²/ιθE->ιCOMP	X2GOF formula
23.	sum(ιCOMP)->T
24.	Output(1,4,T)
25.	Disp"P ="
26.	Output(2.3.1-X²cdf(0,T,K))
27.	Float
28.	Disp "df ="
29.	Output(3,4,K)
30.	Pause
31.	ClrHome

 

Example:

List: Observed: 39, 15, 28, 18

List: Expected: 25, 25, 25, 25

Answers: X ² = 14.16