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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–Box C contains the number of Males that said No
to the pain item–Box D contains the number of Females that said
No to the pain item
Table CellsMales Females Total
Yes A B E
No C D F
Total G H
Example DataMales Females Total
Yes 4 6 10
No 11 8 19
Total 15 14 29
Phi Coefficient Test Formula
( )
( )
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efgh
Phi Coefficient Test Formula
( ) (6*11) (4*8) 34.17
199.75( ) 10*19*15*14
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efgh
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.