correlation

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

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