STATISTICS FOR MANAGEMENT – 05MBA13

Topic Of Discussion: Correlation

Faculty: Ms. Prathima Bhat K.

Department of Management Studies

Acharya Institute of Technology; B’lore

Contact: 9242187131

or mail me: prathimabhatk@gmail.com

CORRELATION

Correlation analysis is used as a

statistical tool to ascertain the

association between two variables.

The problem in analyzing the

association between two variables

can be broken down into three steps:

Try to know whether the two variables are related or independent of each other.

If there is a relationship between the two variables, then know its nature & strength. (i.e., positive/negative; how close is that relationship)

Know if there is a causal relationship between them. i.e., variation in one variable causes variation in another.

CORRELATION & CAUSATION Correlation may be due to chance particularly

when the data pertain to a small sample.

It is possible that both the variables are influenced by one or more other variables.

It may be that case, where both the variables may be influencing each other - we cannot say which is the cause and which is the effect.

TYPES OF CORRELATION

Positive and negative

Linear and non-linear

Simple, partial and multiple

DIFFERENT METHODS OF CORRELATION

METHODS OF CORRELATION

GRAPHIC ALGEBRAIC

SCATTER DIAGRAM RANK

METHODCOVARIANCE

METHOD CONCURRENT

DEVIATIONMETHOD

ALGEBRAIC METHOD (COVARIENCE METHOD)

r =б x.бy

Cov (x,y)

Cov (x,y) = 1 Σ(x-x) (y-y) n

PROCESS OF CALCULATION Calculate the means of the two series, X & Y. Take deviations - from their respective means,

indicated as x and y. The deviation should be taken in each case as the value of the individual item minus (–) the arithmetic mean.

Square the deviations in both the series and obtain the sum of the deviation. This would give Σ x2 and Σ y2.

PROCESS (Contd…..)

Take the product of the deviations, that is, Σxy. This means individual deviations are to be multiplied by the corresponding deviations in the other series and then their sum is obtained.

The values thus obtained in the preceding steps Σxy, Σx2 and Σy2 are to be used in the formula for correlation.

SHORT-CUT METHOD

Choose convenient values as assumed means of the two series, X and Y.

Deviations (now dx and dy instead of x and y) are obtained from the assumed means in the same manner as in the earlier.

Obtain the sum of the dx and dy columns, that is, Σ dx and Σ dy.

SHORT-CUT METHOD (Contd…)

Deviations dx and dy are squared up and their totals Σdx2 and Σ dy2 are obtained.

Finally, obtain Σ dxdy, which is the sum of the products of deviations taken from the assumed means in the two series.

IMPORTANT FORMULAS

r =Σ dx.dy

√Σdx2 . Σ dy2

r =nΣxy – (Σx)(Σy)

√[nΣx2 – (Σx)2] [nΣy2 – (Σy)2]

IMPORTANT FORMULAS

r =NΣfuv – (Σfu)(Σfv)

√[N Σfu2 – (Σfu)2] [NΣfv2 – (Σfv)2]

r =NΣfxy – (Σfx)(Σfy)

√[N Σfx2 – (Σfx)2] [NΣfy2 – (Σfy)2]

PROPERTIES Limits for Correlation Coefficient. Independent of the change of origin & scale. Two independent variables are uncorrelated but the

converse is not true. If variable x & y are connected by a linear equation:

ax+by+c=0, if the correlation coefficient between x & y is (+1) if signs of a, b are different & (-1) if signs of a, b are alike.

ALGEBRAIC METHOD (RANK CORRELATION METHOD)

ρ = 1- 6ΣD2

n(n2 – 1)

ρ = 1- 6[ΣD2 +{m(m2-1)/12}]

n(n2 – 1)

When ranks are not repeated:

When ranks

are repeated

ALGEBRAIC METHOD (CONCURRENT DEVIATIONS)

r = √+ + [(2c-n)/n]