The document explains tetrachoric correlation, a statistical method used to measure the relationship between two dichotomous variables. It distinguishes between natural dichotomies, like gender, and artificial dichotomies, created by threshold comparisons of interval-scaled variables. The tetrachoric correlation coefficient estimates the strength of association between these ratings, providing insight into variable relationships such as adjustment and success in a job setting.

1. Tetrachoric
Correlation
rt.
K.THIYAGU,
Assistant Professor,
Department of Education,
Central University of Kerala, Kasaragod

2. Number Multiplier
1 mono-
2 di-
3 tri-
4 tetra-
5 penta-
6 hexa-
7 hepta-
8 octa-
9 nona-
10 deca-

3. Tetrachoric
Correlation
Estimating the relationship between two
variables when both variables are
dichotomous.
Variable 1:
Dichotomous Variable 2:
Dichotomous
rt.
Artificial Dichotomy

4. Artificial Dichotomy
Socially adjusted Socially maladjusted
Athletic non-athletic
Radical Conservative
Poor Not poor
Social minded Mechanical minded
Drop outs Stay-ins
Successful Unsuccessful
Moral Immoral
Pass Fail
Natural Dichotomy
Male Female
Living Dead
Owning a home Not owing a home
Being a farmer Not being a farmer
Being a Ph.D Not being a Ph.D
Living in Delhi Not living in Delhi
Yes No
While Natural Dichotomy occurs with
variables which "naturally" may assume
only two possible states (e.g. gender or
pregnancy)
Artificial dichotomy can be created
simply by comparing an interval scaled
variable to a threshold (for example,
Intelligence : Above Average & Below
Average)

5. Tetrachoric correlation is used to
measure rater agreement for
binary data; Binary data is data
with two possible answers —
usually right or wrong.
The tetrachoric correlation
estimates what the correlation
would be if measured on a
continuous scale.
The Tetrachoric Correlation Coefficient rtet
(sometimes written as r* or rt) tells us
how strong (or weak) the association is
between ratings for two raters.

6. Eg:
To study the relationship
between intelligence and
emotional maturity,
The first variable, ‘Intelligence’
may be dichotomised as above
average and below average
and the other variable
‘emotional maturity’, as
emotionally mature and
emotionally immature.
Tetrachoric Correlation
is suitable for situations in
which neither of the
two variables
Can be Measured
in terms of scores
But
both the variables
Can be Separated
in terms of
Two Categories.
Above Average
&
Below Average
Emotionally Mature
&
Emotionally immature

7. Example:
If we want to study the
relationship between
‘adjustment’ and ‘success’
in a job, we can
dichotomize the variables
as adjusted-maladjusted
and success-failure.
Adjusted Maladjusted
Success (A) (B)
Failure (C) (D)

8. The underlying variables come from a
Normal Distribution.
There is a latent Continuous Scale
underneath your binary data. In other
words, the trait you are measuring
should be continuous and not discrete.
Assumptions for the Test
Artificial
Dichotomy

9. Pass Fail
Trained (A) (B)
Untrained (C) (D)
Formula for Tetrachoric Correlation is
If AD is greater than BC, then the correlation is Positive
If BC is greater than AD, then the correlation is negative.
Artificial
Dichotomy
Success Failure
Adjusted (A) (B)
Maladjusted (C) (D)

10. Two binary variables
are considered
positively associated
if most of the data falls
along the diagonal cells
i.e.,
a and d
are larger than
b and c.
In contrast,
two binary variables
are considered
negatively associated
if most of the data
falls off the diagonal.
i.e.,
a and d
are lesser than
b and c.
Artificial Dichotomy

13. Types of Correlation Coefficients
Correlation Coefficient Types of Scales
Pearson product-moment Both Scales - Interval (or) Ratio
Spearman rank-order Both Scales - Ordinal
Phi Both scales are Naturally Dichotomous (nominal)
Tetrachoric Both scales are Artificially Dichotomous (nominal)
Point-biserial
One scale Naturally Dichotomous (nominal),
one scale interval (or ratio)
Biserial
One scale Artificially Dichotomous (nominal),
one scale interval (or ratio)
Gamma One scale nominal, one scale ordinal

14. Thank You
K.THIYAGU, Assistant
Professor, Department of Education,
Central University of Kerala, Kasaragod