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

( )

( )

bc ad

efgh

Phi Coefficient Test Formula

( ) (6*11) (4*8) 34.17

199.75( ) 10*19*15*14

bc ad

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.