Pearson Product Moment Correlation - Thiyagu

The coefficient of correlation computed by product moment coefficient of correlation or Pearson's correlation coefficient and symbolically represented by r. This presentation explains the concept, computation, merits and demerits of Pearson Product Moment Correlation.

1. K.THIYAGU,Assistant Professor,Department of Education,
Central University of Kerala,Kasaragod
Pearson Product Moment Correlation

2. Linear means Straight Line.
Correlation means co-relation,
or the degree that two variables "go together".
Linear correlation means to go together in a straight line.

3. Thecorrelation coefficientis a number that summarizes
the direction and degree (closeness)of linear relations
between two variables.
The correlation coefficient is also known as thePearson Product-
Moment Correlation Coefficient.

4. The sample value is calledr,
and
the population value is called (rho).

5. For example,
on average, as height
in people increases, so
does weight.
The correlation
coefficient can take
values between
-1 through 0 to +1.
The sign (+ or -) of the
correlation affects its
interpretation.
When the correlation
is positive (r> 0), as
the value of one
variable increases, so
does the other.

6. Pearson Product Moment Correlation
•PPMCCorPCCorPearson’sr
•Itisameasureofthestrengthofa
linearassociationbetweentwo
variablesandisdenotedbyr.
•Itisameasure ofthe
linearcorrelationbetweentwo
variablesXandY
It was developed byKarl Pearsonfrom a related idea introduced byFrancis Galtonin the 1880s.
Early work on the distribution of the sample correlation coefficient was carried out byAnil Kumar Gain
andR. A. Fisherfrom theUniversity of Cambridge.

7. Born 27 March 1857, Islington, London, England
Died 27 April 1936(aged79), Surrey, England
ResidenceEngland
NationalityBritish
KnownforPrincipal Component Analysis
Pearson distribution
Pearson's r
Pearson's chi-squared test
Phi coefficient
Academic
advisors
Francis Galton
Pearson with
Sir Francis Galton
Karl Pearson

8. Statistics is the grammer of science.
(Karl Pearson)

9. Pearson's correlation
coefficient is
thecovarianceof the
two variables divided
by the product of
theirstandard
deviations.
Pearson Product Moment Correlation InterpretationCorrelation
Perfect Positive +1.0
Very high positive+0.90 to +0.99
High positive+0.70 to +0.90
Moderate positive+0.50 to +0.70
Low positive+0.30 to +0.50
Very low positive+0.10 to +0.30
Negligible positive+0.01 to +0.10
No correlation 0.0
Negligible negative-0.01 to -0.10
Very low negative-0.10 to -0.30
Low negative-0.30 to -0.50
Moderate negative-0.50 to -0.70
High negative-0.70 to -0.90
Very high negative-0.90 to -0.99
Perfect negative -1.0
Interpretation Table2222
)()(
))((
YYNXXN
YXXYN
r




11. •Correlationisusedtodescribethedegreeofrelationshipbetween
twovariables.
•ThereliabilityoftestiscalculatedintermsofPearson(r)
•Thevalidityisestimatedbytheco-efficientofcorrelation(r)
•ItemdiscriminationpoweriscalculatedbyusingPearson’s(r)
•MultiplecorrelationbasedonPearson’sr
•Partialcorrelationemploystheco-efficientofcorrelation(r)
•Factor-analysistechniqueistheextensionofPearson’sr
•Itpredictsthedependedvariablesonthebasisofindependent
variable
•Mostofthepersonalitytheoriesarealsodevelopedbyusingthis
correlation.
uses
of PPMCC

12. •Itisalinearcorrelation.Whenthe
twovariableshavethelinear
distributionwouldyieldaccurate
co-efficientofcorrelation,butthe
twovariablesarecurvelinearly
distributed,thenthecorrelationof
co-efficientoftwovariablesisnot
dependable.Thisassumptionis
takenintoconsiderationwhile
usingthistechnique.
•Thedistributionofscoresofthe
twovariablesshouldbenormal.It
thedistributionsareskewed,it
wouldnotyielddependable
correlation.Theassumptionisnot
usuallyobserved.
Disadvantages of PPMCC

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