DATA ANAYLSIS for manager DATA ANAYLSIS for manager CORRELATION CORRELATION Prepare by: Nurul Faezah Binti Mohd Talib 811839
Oct 23, 2015
DATA ANAYLSIS for managerDATA ANAYLSIS for manager
CORRELATIONCORRELATION
Prepare by:Nurul Faezah Binti Mohd Talib811839
Correlation CoefficientCorrelation CoefficientA statistical measure that indicates the extent
to which two or more variables fluctuate together
Example : relation between price and demand, weight and height
The absolute value divide to:◦Magnitude◦Direction
MagnitudeMagnitudeThe strength of the relationship
Strong Weak
DirectionDirectionSign of the relationship:
Positive Negativ
e
Range of correlation Range of correlation
Magnitude Direction
• Greater absolute value : stronger
of relationship
• Stronger relationship is the
correlation of -1 to 1
•Weakest absolute value :
correlation is zero
•Sign of correlation describes the
direction
•Positive sign : variables move in
the same direction
•Negative sign : variables move in
opposite direction
Scatter Diagram and Scatter Diagram and RelationshipRelationshipThe data is displayed as a
collection of points, each having the value of one variable determining the position on the vertical axis and horizontal axis.
The kind of plot also called as scatter diagram, scatter chart and scatter graph.
Scatter Diagram and Scatter Diagram and RelationshipRelationship
Maximum positive correlation
(r = 1.0)
Scatter Diagram and Scatter Diagram and RelationshipRelationship
Strong positive correlation
(r = 0.8)
Scatter Diagram and Scatter Diagram and RelationshipRelationship
Zero Correlation
(r = 0)
Scatter Diagram and Scatter Diagram and RelationshipRelationship
Negative positive correlation
(r = -1.0)
Scatter Diagram and Scatter Diagram and RelationshipRelationship
Moderate negative correlation
(r = -0.43)
Scatter Diagram and Scatter Diagram and RelationshipRelationship
Strong correlation and outlier
(r = 0.71)
Linear correlation coefficient Linear correlation coefficient Pearson Pearson rr
The measure of the strength of linear dependence between two variable was develop by Karl Pearson.
Which correlation coefficient and denoted by r.
The value always lies between or equal to 1.00 and -1.00
-1.00 ≤ r ≤ 1.00
Linear correlation coefficient Linear correlation coefficient Pearson Pearson rrDividing the covariance of the two
variable by the product of their standard deviation.
Spearman’s Correlation CoefficientSpearman’s Correlation Coefficient
The Spearman rank-order correlation coefficient
is a non-parametric measure of the strength and
direction of association that exists between two
variables measured on at least an ordinal scale.
It is denoted by the symbol rs
Spearman’s Correlation CoefficientSpearman’s Correlation Coefficient
The test is used for either ordinal variables or
for interval data that has failed the assumptions
necessary for conducting the Pearson's product-
moment correlation.
For example, Spearman’s correlation to
understand whether there is an association
between exam performance and time spent
revising.
Point-Biserial
Point-biserial : rpb , is a special case of
Pearson in which one variable is quantitative and the other variable is dichotomous and nominal
Formula : rpb = (Y1 - Y0) • sqrt(pq) / Y
Phi CoefficientPhi Coefficient
If both variables instead are nominal and dichotomous,
introduce contingency tablesFormula :
phi=(BC- AD)/sqrt((A+B)(C+D)(A+C)(B+D)).
Biserial Correlation CoefficientBiserial Correlation Coefficient
Termed : rb , is similar to the point biserial
but pits quantitative data against ordinal data, but
ordinal data with an underlying continuity but
measured discretely as two values (dichotomous)
Formula: rb = (Y1 - Y0) • (pq/Y) / Y,
Tetrachoric Correlation CoefficientTetrachoric Correlation Coefficient
Termed : rtet , is used when both variables
are dichotomous
Applied to ordinal vs. ordinal data
The formula involves a trigonometric
function called cosine
Formula : rtet = cos(180/(1 + sqrt(BC/AD)).
Rank-Biserial Correlation CoefficientRank-Biserial Correlation Coefficient
Termed : rrb , is used for dichotomous
nominal data vs rankings (ordinal)
The formula assumes no tied ranks are
present
Formula : rrb = 2 •(Y1 - Y0)/n,
Correlation using SPSSCorrelation using SPSS
•From the Options dialog box, click on "Means and standard deviations" to get
some common descriptive statistics.
•Click on the Continue button in the Options dialog box.
•Click on OK in the Bivariate Correlations dialog box.
•The SPSS Output Viewer will appear.
In this example, we can see that the Pearson correlation coefficient, r, is 0.777, and that this is statistically significant (p < 0.0005). For interpreting multiple correlations
There was a strong, positive correlation between height and distance jumped
Thank You