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Tetrachoric
Correlation
Coefficient
-

Appropriate if the two variables (both
artificial nominal dichotomous) are
correlated.

-

Denoted by rt.

Tetrachoric Correlation Coefficient
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
The Tetrachoric Correlation
Coefficient is given by the
following equation:

rt
=
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
Solution:
Hence, there is a weak positive
correlation between the performances of
the examinees on the test of the review
center and the board exam.


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
X

0

1

0

14

9

1

8

16

Y

Ex. Number of Students Who Got
Items x and y Right and Wrong
Compute for
, then look for
the corresponding value of rt .
=

= 0.321
Since there are no corresponding
table values for
, then the
reciprocal has to be computed.
Thus,
=

= 3.111
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.
rt =

=
= -0.42
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?
"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)

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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
  • 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.
  • 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)