point biserial correlation example categorical variable: yes-no, f-m ratio or interval variable: no....
TRANSCRIPT
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.