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# Tetrachoric Correlation Coefficient

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### Tetrachoric Correlation Coefficient

1. 1. Tetrachoric Correlation Coefficient
2. 2. - Appropriate if the two variables (both artificial nominal dichotomous) are correlated. - Denoted by rt. Tetrachoric Correlation Coefficient
3. 3. Consider the 2x2 contingency table: X 0 1 TOTAL 1 a b a+b 0 c d c+d TOTAL a+c b+d n Y
4. 4. The Tetrachoric Correlation Coefficient is given by the following equation: rt =
5. 5. Example: Number of the Examinees Who Passed and Failed the Two Exams X 0 1 TOTAL 9 15 24 13 10 23 22 25 47 Y 1 0 TOTAL
6. 6. Solution:
7. 7. Hence, there is a weak positive correlation between the performances of the examinees on the test of the review center and the board exam.
8. 8.  Thomas O. Maguire prepared a table of values of rt corresponding to the ratio or .  These values of rt are given in Table H in Appendix A. Another way of solving rt w/o trigonometric values
9. 9. X 0 1 0 14 9 1 8 16 Y Ex. Number of Students Who Got Items x and y Right and Wrong
10. 10. Compute for , then look for the corresponding value of rt . = = 0.321
11. 11. Since there are no corresponding table values for , then the reciprocal has to be computed. Thus, = = 3.111
12. 12. Using Table H in Appendix A, 3.111 is found between 3.060 and 3.153 and the value of rt is -0.42. This means that item x is negatively correlated with item y. Hence, many of the students who are correct in item y are wrong in item x, and vice versa.
13. 13. rt = = = -0.42
14. 14. Among the following problems that can be answered using tetrachoric correlation coefficient include the ff.: 1. Is the personality (introvert/extrovert) related to success or failure in a job that requires contact with people? 2. Is motivation (high/low) related to the development of scientific literacy?
15. 15. "Mathematicians are like Frenchmen: Whatever you say to them, they translate it into their own language, and forthwith it means something entirely different." Johann Wolfgang von Goethe (1749 – 1832)