Phi Coefficient of Correlation - Thiyagu

The phi coefficient is that system of correlation which is computed between two variables, where neither of them is available in a continuous measures and both of them are expressed in the form of natural or genuine dichotomies. This presentation slides describes the concept and procedures to do the computation of phi coefficient of correlation.

1. Phi Coefficient of Correlation

K.THIYAGU,
Assistant Professor,
Department of Education,
Central University of Kerala,Kasaragod

2. Phicoefficientcorrelationis
suitableforsituationsin
whichneitherofthetwo
variablescanbemeasured
intermsofscoresbutboth
thevariablescanbe
separatedintermsoftwo
categories.Whenboththe
variablesaredichotomous
inthesameattributes,we
canusethephicoefficient
correlation
Phi Coefficient

Natural Dichotomy

3. The Phi Coefficient
is a measure of association between
two binary variables
(i.e. living/dead, black/white, success/failure).
It is also called
the Yule phi
or
Mean Square Contingency Coefficient
and is used for contingency tables when:
At least one variable is a nominal variable
&
Both variables are dichotomous variables.

4. The phi is a nonparametric statistic
used in cross-tabulated table data
where both variables are
dichotomous.
Dichotomous means that there are
only two possible values for a
variable.
Asanexample,thevariableaddressinglifehasonlytwolevels,“alive”and“notalive”(ordead).
Soifapublichealthdepartmentwasresearchingtheproportionofnewbornsbornaliveversus
borndead,eachbabycouldbebornaliveorborndead;therearenootherpossibilities.
Natural Dichotomy

5. Phi Coefficient
Computecorrelation/relationship
betweentwovariableswhichare
genuinelydichotomous
Genuine
Dichotomous
Same
attributes
Genuine
Dichotomous

Male Female
Married
(A) (B)
Single
(C) (D)
Natural Dichotomy

6. Yes No
Yes (A) (B)
No (C) (D)
No Yes
Yes (B) (A)
No (D) (C)
Favourable Unfavourable
Favourable (A) (B)
Unfavourable (C) (D)
If AD is greater than BC, then the correlation is Positive
If BC is greater than AD, then the correlation is negative.
Formula for Phi Coefficient ()
correlation is
Natural Dichotomy
Male Female
Alive
(A) (B)
Notalive
(C) (D)
Yes No
Male (A) (B)
Female (C) (D)

7. 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.
Yes No
Yes (A) (B)
No (C) (D)
Natural Dichotomy

9. Generalruleofthumbforcorrelation
coefficientsandyoucanusethesamerulefor
thePhicoefficient.
•-1.0 to -0.7 strong negative association.
•-0.7 to -0.3 weak negative association.
•-0.3 to +0.3 little or no association.
•+0.3 to +0.7 weak positive association.
•+0.7 to +1.0 strong positive association.
Interpretation of the
Phi coefficient.

10. 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)
TetrachoricBoth 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

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