Phi Coefficient Example
• A researcher wishes to determine if a significant
relationship exists between the gender of the
worker and if they experience pain while
performing an electronics assembly task.
• One question asks “Do you experience pain
while performing the assembly task? Yes No”
• The second question asks “What is your
gender? ___ Male ___ Female”
Step 1: Null and Alternative
Hypotheses
• Ho: There is no relationship
between the gender of the worker
and if they feel pain while
performing the task.
• H1: There is a significant
relationship between the gender of
the worker and if they feel pain
while performing the task.
Step 1A: Determine dependent and
independent variables and their
formats.
• Gender is dichotomous,
independent
• Feeling pain is dichotomous,
dependent
Step 2: Choose test statistic
• Phi Coefficient
Step 3: Choose Alpha Level
• Use Alpha Level = .05
• Interpreted as “There is a 5% chance
that a significant relationship really
does not exist although the results
indicate one does (5% chance of
committing a Type I error or stated as
5% chance of rejecting the Null
hypothesis when in reality it is false).
Step 4: Determine the Critical Score
• For the Phi Coefficient, the critical score is
determined using a Chi Square Table.
• The first column is the Degrees of Freedom
and the other columns are the Alpha levels.
• The degrees of freedom for the Phi
Coefficient is equal to 1.00
• (Rows-1)(Columns-1)= (2-1)*(2-1)=1.00
• At .05 and DF = 1.00, the critical score is
3.84
Chi Square Table
Step 5: Run the Test
• The Phi Coefficient should be set
up as follows:
–Box A contains the number of
Males that said Yes to the pain
item
–Box B contains the number of
Females that said Yes to the pain
item
Table Cells
Males
Females
Total
Yes
A
B
E
No
C
D
F
Total
G
H
Example Data
Males
Females
Total
Yes
4
6
10
No
11
8
19
Total
15
14
29
Phi Coefficient Test Formula
(bc  ad )

(efgh)
Phi Coefficient Test Formula
(bc  ad ) (6*11)  (4*8)
34



 .17
(efgh)
10*19*15*14 199.75
Step 6: Compare your score to the
critical score
• To interpret the .17, you need to convert it
to a Chi Square value.
• To do this, multiply N X (Phi Coeff)2
• If the obtained score is greater than the
critical score, reject the Null and accept the
alternative.
• In this example, 29 X .172 = .84
• Since .84 is less than 3.84, do not reject the
Null Hypothesis.
Step 7: Conclusions
• There is no significant
relationship between the genders
of the workers and if they feel
pain while they perform the task.
• Both males and females have
pain (or no pain) at equal
frequencies.