Types of Data:
Ratio
• Specific intervals between
consecutive numbers
• True zero value
Interval level:
• Specific intervals between
consecutive values
• Zero is just a number in the string
Ordinal level:
• numbers establish rank
order
• distance between
numbers is not any specific
interval
e.g., 1st , 2nd, 3rd...
Nominal level:
• Numbers only categorize data.
• Numbers have no mathematical
value.
e.g., 1 = male, 2 = female
Chi Square Goodness of fit
• for nominal level data
• identifies if a sample of
people conform to the
categories as expected.
 
2
f
e
 fo 
fe
Where:

2
Chi Square
fe
Frequency expected
fo
Frequency observed
2
Frequency expected:
The amount of subjects that
you would expect to find in
each category based on known
information.
Frequency observed:
The amount of subjects
you actually find to be in
each category in the
present data.
 
2
f
e
 fo 
fe
2
Let’s assume that:
h.s.
Some
college
MA
Ph.D
30%
15%
10%
college
20%
25%
First:
How many people do we expect to find in
each category, based on these percentages?
Assume that the sample that you test has
n=50.
f e   % n
The percentage needs to be written as a
fraction or decimal.
h.s.
Some
college
MA
Ph.D
30%
15%
10%
college
20%
f e   .20 50
f e  10
25%
h.s.
Some
college
MA
Ph.D
30%
15%
10%
college
20%
25%
f e   .25 50
f e  12.5
h.s.
Some
college
MA
Ph.D
30%
15%
10%
college
20%
25%
f e   .30 50
f e  15
h.s.
Some
college
MA
Ph.D
30%
15%
10%
college
20%
25%
f e   .15 50
f e  7.5
h.s.
Some
college
MA
Ph.D
30%
15%
10%
college
20%
25%
f e   .10 50
fe  5
h.s.
Some
college
MA
Ph.D
25%
30%
15%
10%
12.5
15
7.5
5
college
20%
f e 10
h.s.
Some
college
MA
Ph.D
college
20%
25%
30%
15%
10%
fe
10
12.5
15
7.5
5
fo
5
7
25
12
1
 
2
f
e
 fo 
fe
2
h.s.
Some
college
MA
Ph.D
college
fe
10
12.5
15
7.5
5
fo
5
7
25
12
1
H . S .
10  5
10
2
H. S. 
10  5
10
2
5
H. S 
10
25
H. S. 
10
H . S .  2.5
2
h.s.
Some
college
MA
Ph.D
college
fe
10
12.5
15
7.5
5
fo
5
7
25
12
1

12.5  7 2
12.5
Some college:
1)
2)

12.5  7
12.5
2
3)
30.25

12.5
4)
 2.42
2
55
.

12.5
h.s.
Some
college
MA
Ph.D
college
fe
10
12.5
15
7.5
5
fo
5
7
25
12
1

15  25
15
2
College:
1)
2)

15  25 2
3)
15
 102

15
4)
100

15
 6.67
h.s.
Some
college
MA
Ph.D
college
fe
10
12.5
15
7.5
5
fo
5
7
25
12
1

 7.5  12
7.5
2
M.A.
1)
2)

 7.5  12 2
3)
7.5
 4.52

7.5
4)
20.25

7.5
 2.70
h.s.
Some
college
MA
Ph.D
college
fe
10
12.5
15
7.5
5
fo
5
7
25
12
1

 5  1 2
5
Ph.D.
1)

2)
 5  1
2
3)
16

5
5
2
4

5
4)
 3.20
  2.50  2.42  6.67  2.70  3.20
2
  17.49
2
Critical Value:
Chi Square table
df = K-1
where k is # of groups
df=4
crit value = 9.488
17.49 > 9.48
Therefore there is a significant
difference between the expected
and observed frequencies.