The document discusses biserial correlation, which estimates the relationship between a continuous variable and a dichotomous variable. It distinguishes between true/discrete dichotomies (e.g., male vs female) and artificial dichotomies (e.g., pass vs fail). The formula for calculating biserial correlation is also provided, emphasizing the importance of understanding these types of correlations in educational research.

1. Biserial
Correlation
rbis
K.THIYAGU,
Assistant Professor,
Department of Education,
Central University of Kerala, Kasaragod

2. • Artificial
Dichotomy
• Continuous
One
Variable
Other
Variable
Biserial Correlation
Estimate of the relationship between a
continuous variable and a dichotomous
variable.
The Term ‘Dichotomous’ means cut into
two parts or divided into two categories
rbis

3. Continuous or Artificial Dichotomies are those which we assume
there to be an underlying continuum but we assign individuals to a
category based on some arbitrary criterion. Examples of this
artificial dichotomy are pass vs fail (based on some cutoff score on a
test) or short vs tall (based on some arbitrary height).
Dichotomous variables can be either
a discrete/true/Natural dichotomy
or
a continuous/artificial one.
Natural / Discrete Dichotomies are male vs female, dead vs alive.
There is no underlying continuum between the groups.

4. A point-biserial and biserial correlation is
used to correlate a dichotomy with an
interval scaled variable.
Point-biserial correlation is used when the dichotomous
variable is a true or discrete dichotomy.
The biserial correlation is used with an
artificial dichotomy.

5. 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
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, all
folks being older than 40
years will get assigned a
value of 1, all other people a
value of 0).

6. Formula for Biserial Correlation is
rbis biserial r
Mp & Mq Mean test scores
respectively for those who
pass and fail the item
p & q Proportions who pass and
fail the item
y height of the ordinate of the
normal curve at the point of
division between p and q
proportions of cases
 SD of the entire group

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