Biserial Correlation - Thiyagu

Biserial correlation is computed between two variables when one of them is in continuous measure and the other is reduced to artificial dichotomy (forced division into two categories). This Presentation slides explains the condition and assumption to use biserial correlation with appropriate illustrations.

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

2. •Artificial
Dichotomy
•Continuous
One
Variable
Other
Variable
Biserial Correlation
Estimateoftherelationshipbetweena
continuousvariableandadichotomous
variable.
TheTerm‘Dichotomous’meanscutinto
twopartsordividedintotwocategories
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3. ContinuousorArtificialDichotomiesarethosewhichweassume
theretobeanunderlyingcontinuumbutweassignindividualstoa
categorybasedonsomearbitrarycriterion.Examplesofthis
artificialdichotomyarepassvsfail(basedonsomecutoffscoreona
test)orshortvstall(basedonsomearbitraryheight).
Dichotomous variables can be either
a discrete/true/Natural dichotomy
or
a continuous/artificial one.
Natural/DiscreteDichotomiesaremalevsfemale,deadvsalive.
Thereisnounderlyingcontinuumbetweenthegroups.

4. A point-biserial and biserial correlation is
used to correlate a dichotomy with an
interval scaled variable.
Point-biserialcorrelation 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)
Artificialdichotomycanbe
createdsimplybycomparing
anintervalscaledvariableto
athreshold(forexample,all
folksbeingolderthan40
yearswillgetassigneda
valueof1,allotherpeoplea
valueof0).

6. Formula for Biserial Correlation is
r
bis biserialr
M
p& M
qMean test scores
respectivelyforthosewho
passandfailtheitem
p & q Proportionswhopassand
failtheitem
y heightoftheordinateofthe
normalcurveatthepointof
divisionbetweenpandq
proportionsofcases
 SDoftheentiregroup

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