Used
to compare frequencies (counts) among multiple categories of nominal or ordinal level data
for onesample (univariate analysis).
Problem:
You wish to evaluate variations in the proportion of defects produced from five assembly
lines. A random sample of 100 defective parts from the five assembly lines produced the
following contingency table.
Line
A 
Line
B 
Line
C 
Line
D 
Line
E 
24 
15 
22 
20 
19 
Assumptions
Independent
random sampling
Nominal
or Ordinal
level data
State
the Hypothesis
Ho:
There is no significant difference among the assembly lines in the observed frequencies of
defective parts.
Ha:
There is a significant difference among the assembly lines in the observed frequencies of
defective parts.
Set
the Rejection Criteria
Determine
degrees of freedom (df) = k – 1 where
k equals the number of categories
df=51 or df=4
Establish
the confidence level (.05, .01, etc.)
Use
the chisquare distribution table to establish the critical value
At
alpha
.05 and 4 degrees of freedom, the critical value from the chisquare distribution is 9.488
Compute
the Test Statistic
where
and
. . .
n
= sample size
k
= number of categories or cells
Fo
= observed frequency

Line
A 
Line
B 
Line
C 
Line
D 
Line
E 

Fo 
24 
15 
22 
20 
19 

Fe
(100/5=20) 
20 
20 
20 
20 
20 


.8 
1.25 
.2 
0 
.05 
2.30 
Decide
Results of Null Hypothesis
Since
the chisquare test statistic 2.30 does not meet or exceed the critical value of 9.488,
you cannot conclude there is a statistically significant difference among the assembly
lines in the observed frequencies of defective parts.
