Chi Square Example
• A researcher wants to determine if
there is a relationship between
gender and the type of training
received.
• The gender question is male/female
(categorical) and the training is
categorical.
Setting Up the Tables
To set up the Chi Square Test, set up the table with the frequencies of the
responses in the format below. These are the observed cases.
Hand-on
Classroom
Both Types
Total
Male
15
4
20
39
Female
5
12
11
28
Total
20
16
31
67
Expected Number of Cases
• The next step is to determine the expected
number of cases in the cells.
• To do this, take the row total multiplied by the
column total divided by the grad total.
• To determine the expected number of cases in
the Male and Yes cell, the math would be (39
X 20)/67 = 11.6. Do this for each of the inner
table cells.
Setting Up the Tables
To set up the Chi Square Test, set up the table with the frequencies of the
responses in the format below. These are the expected cases.
Hand-on
Classroom
Both Types
Total
Male
11.6
9.3
18
39
Female
8.4
6.7
13
28
Total
20
16
31
67
Chi Squared Formula
• Next, using the Chi Square Test, you will take
the (observed minus the expected)2 /
expected and sum the results from each of the
cells. In this example, there will be 4 parts
that will be added to get the Chi Square
answer.
Chi Squared Formula
X
2
X
2
 (15  11.6) 2   (4  9.3) 2   (20  18) 2   (5  8.4) 2   (12  6.7 ) 2   (11  13) 2 







11.6
9.3
18
8.4
6.7
13

 
 
 
 
 

 (1.00)  (3.02)  (.22)  (1.38)  (.31)  5.93
Determining the Critical Score
• With this answer, you will need to compare
your Chi Square answer to the “cutoff” score.
To find the cut off score, you need to calculate
the degrees of freedom. With tables, the
degrees of freedom are calculated by (#Rows
– 1)X(#columns – 1) or (2-1)*(3-1) = 2 d.f.
Chi Squared Table
With 2 degrees of freedom and the alpha level (.05), using the Chi Square
table, one can find the cutoff score of 5.99.
Making the Decision
• If the obtained Chi Square is greater than the cut
off score, then you reject the null hypothesis and
conclude there is a significant relationship
between being trained and the gender of the
person.
• In this example, the obtained X2 is 5.93 which is
less than 5.99. Therefore, the researcher does not
reject the null hypothesis. The conclusion
reached is that there is not a significant
relationship between gender of the worker and
the type of training they received.