1. Tetrachoric
Correlation
Coefficient

2. -
Appropriate if the two variables (both
artificial nominal dichotomous) are
correlated.
-
Denoted by rt.
Tetrachoric Correlation Coefficient

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. The Tetrachoric Correlation
Coefficient is given by the
following equation:
rt
=

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. Solution:

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. 
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. X
0
1
0
14
9
1
8
16
Y
Ex. Number of Students Who Got
Items x and y Right and Wrong

10. Compute for
, then look for
the corresponding value of rt .
=
= 0.321

11. Since there are no corresponding
table values for
, then the
reciprocal has to be computed.
Thus,
=
= 3.111

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. rt =
=
= -0.42

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. "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)