1. Point Biserial Correlation Example Categorical variable: Yes-No, F-M Ratio or interval variable: No. of incidents, lost days, or grade

2. Formula

3. Example

4. 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

6. 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.

7. T-test for Correlations df = 20-2 = 18 r = 0.23 To 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).

8. 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).

9. 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.

10. Rank Biserial Correlation Variable 1: Nominal Variable 2: Ordinal

11. 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” 12 3 45678910 Very dissatisfiedNeutralVery satisfied

12. Step 1: Data Setup XY CaseQuestion 1Question 2 1 F2 2 F7 3 F4 4 F6 5 F1 6 M10 7 M6 8 M9 9 M2 M8

13. Step 1: Data Setup CaseFemale (Yo)Male (Y1) 1 210 2 7 6 3 49 4 62 5 18 Average 20/5 = 435/5 = 7

14. Formula r rb = 2(Y0 – Y1)/n Yo: average in group “o” Y1: average in group “1” n: total cases or subjects

15. Calculations: Yo = 4 Y1 = 7 N = 10 r = 2(4-7)/10 = -0.6

16. t-test Calculations: t = 0.6/sqrt((1-0.6 2 )/8) t = 2.12 Critical t from tables: t = 2.3 at α = 0.05/2 df = 8 Since t calculated is less than t critical, then we fail to reject H0 and we conclude that the relationship is not significant.

17. 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

18. Contingency table 2x2

19. phi = (25-100)/sqrt(15151515) = -75/225 = -0.33, indicating a slight correlation

20. t-test Calculations: t = 0.33/sqrt((1-0.33 2 )/28) t = 1.85 Critical t from tables: t = 2.05 at α = 0.05/2 df = 30-2=28 Since t calculated is less than t critical, then we fail to reject H0 and we conclude that the relationship is not significant.