Point Biserial Correlation Example

• Categorical variable: Yes-No, F-M• Ratio or interval variable: No. of

incidents, lost days, or grade

Formula

Example

Hypothesis Setup

• Ho: There is no relationship between respondent gender and earned score

• H1: There is a relationship between respondent gender and earned score

• Use an Alpha Level=.05• n = 20

Is the Correlation Significant?

• Now we need to determine if the correlation coefficient of -0.23 is significant.

• This is done by performing a t-test.

T-test for Correlations

df = 20-2 = 18r = 0.23To interpret the , compare the 1.00 to the critical score. If the obtained score is greater than the critical score, reject the Null and accept the alternative. The critical score from the t-table at .05 and DF = 18 is 2.1 (NOTE: On a T-table, use the .025 column since .025 at one end and .025 at the other end gives you .05).

T-Table

The critical score from the t-table at .05 and DF = 18 is 2.1. (NOTE: On a T-table, use the .025 column since .025 at one end and .025 at the other end gives you .05).

Conclusions

• Since 1.0 is less than 2.1, We fail to Reject the Null Hypothesis and conclude the relationship between the variables is not significant.

Rank Biserial Correlation

• Variable 1: Nominal• Variable 2: Ordinal

Rank Biserial Correlation Example

• A researcher wishes to determine if a significant relationship exists between ratings on job satisfaction and gender

Question 1: Your gender Question 2 asks “How satisfied are you with your job” • 1 2 3 4 5 6 7 8 9 10• Very dissatisfied Neutral Very satisfied

Step 1: Data Setup

X Y

Case Question 1 Question 2

1 F 2

2 F 7

3 F 4

4 F 6

5 F 1

6 M 10

7 M 6

8 M 9

9 M 2

10 M 8

Step 1: Data Setup

Case Female (Yo) Male (Y1)

1 2 10

2 7 6

3 4 9

4 6 2

5 1 8

Average 20/5 = 4 35/5 = 7

Formula

rrb = 2(Y0 – Y1)/n

Yo: average in group “o”Y1: average in group “1”n: total cases or subjects

Calculations:

• Yo = 4• Y1 = 7• N = 10

r = 2(4-7)/10 = -0.6

t-test Calculations:

t = 0.6/sqrt((1-0.62)/8) t = 2.12

Critical t from tables:t = 2.3 at α = 0.05/2 df = 8Since t calculated is less than t critical, then we fail to reject H0 and we conclude that the relationship is not significant.

PHI Correlation

• Both variables are dichotomous nominal

• As an example, consider the following data organized by gender and employee classification (faculty/staff). Check for correlation between gender and employee classifications

Contingency table 2x2

phi = (25-100)/sqrt(15•15•15•15) = -75/225 =

-0.33, indicating a slight correlation

t-test Calculations:

t = 0.33/sqrt((1-0.332)/28) t = 1.85

Critical t from tables:t = 2.05 at α = 0.05/2 df = 30-2=28Since t calculated is less than t critical, then we fail to reject H0 and we conclude that the relationship is not significant.