Statistical Methods

STATISTICAL METHODS USED IN

RESEARCH

contents

Correlation analysis

Time series analysis

Regression analysis

CORRELATION

Correlation analysis refers to

the techniques used in

measuring the closeness of

relation ship between the

variables.

According to A .M. Turltle,

“ correlation is an analysis of

co variation between two or

more variables”.

UTILITY IN RESEARCH

Used to estimate and predict on

the basis of some other variable,

how it is related with each other.

Used in reducing uncertainty in

matter of prediction.

Types of correlation

Simple.

multiple.

Partial.

Positive.

Negative.

Linier .

Non linier.

MEASURES OF CORRELATIONScatter diagram.

Karl Pearson's coefficient of

correlation.

Spearman's rank correlation.

Concurrent deviation.

Least square method.

Graphic method.

KARL PEARSON'S COEFFICIENT

OF CORRELATION

It measures the nature of correlation

and the extent of correlation in

numerical form.

The value of coefficient should be

between

(+ 1)or(-1).

The degree of relation ship between

two variables is represented by “r”.

When r=+1, it is perfect positive

correlation.

When r=-1, it is perfect negative

correlation.

When r=>0, it is imperfect positive

correlation.

When r=<0, it is imperfect negative

correlation.

W hen r=0, it is absence of

correlation.

The measure extends strength and direction of linier

correlation and is measured by, formula,

Where,

r= coefficient of correlation.

N= no of pairs of observation.

X= given value of first variable.

Y= given value of second variable.

STEPS

Arrange table in tabular manner

representing first variable as x and second

as y.

Multiply each pair of value of x and y and

get it totaled as xy.

Square up the value of x y and get totaled

as x2 and y2.

Get total no of pairs as n.

Substititute the different value in formula to

find value of r.

Requirements of “r”

The distributons of x and y should be linier

relation.

Samples must be drawn on random basis.

It cannot be used for curvilinear variables.

The distributions should be normal,

especially for small samples.

EVALUATIONCorrelation analysis can determine the degree of

association between variables.

But for research purpose it is essential to determine

the existence of casual relationship.

To determine casual relationship we need to use

researchers conceptual knowledge and reasoning

ability.

TIME SERIES ANALYSIS

A time series analysis may be

defined as “A set of observations of

a variable recorded at successive

intervals or point of time.

Time series is influenced by variety of forces. Which operate at regular intervals of it or at a random.

The data of series are decomposed to study each of these influence known as time series analysis.

Factors are,

. Secular trend- shows the direction of series in long period of time.

Eg cost of living index.

. Cyclical fluctuation- it refers to the wave like rise and decline in an activity.

Eg business cycle.

. Seasonal variation- it refers to the recurring changes in

an year and it is caused by changes in climatic condition

and social customs in a year.

Eg fall in agriculture prices in harvest season.

. Irregular variation- it is a non recurring unpredictable

variation taking place at random .

Eg natural calamity strike lock out etc and the

occurrences of these factors cause irregular variation.

MEASUREMENT OF TREND

LEAST SQURES.

MOVING AVERAGE.

SEMI AVERAGE.

FREE HAND CURVE.

LEAST SQURE

Most suitable method of computing secular trend.

Formula for least square,

y= a+bx.

Where ,

y- is the calculated value of trend.

a- the intercept of y. or height of line at the origin that is, a=y.

b- the amount by which the slope of trend line raise or falls.

x- the number of units of time in each given year lies away from the middle year.

The value of a and b for a least square straight line can be

found by solving following equation.

a = ∑ Y / N.

b = ∑ XY / ∑X 2.Where,

y= actual value of series for the period

X= value assigned to each period.

N= no of values included.

steps

Find‘ x’ x= deviation from the

origin.

Find ‘y’ y= given variable .

Find a = ∑ Y / N.

b = ∑ XY / ∑X 2.

After finding the variables the

value of a and b can be

substituted in the formula, y= a

+bx

REGRESSION ANALYSIS

The term regression analysis refers

to “the methods by which estimates

are made of the values of the

variables from a knowledge of value

of one or more variable and to the

measurement of the errors involved in

the estimation process”.

Utility in research

It is used to describe the nature of

association of variables.

It is a valuable tool for solving many

problems of economic and business

research.

It is a useful measure in research for

estimating an unknown value of one

variable for a given value of another

variable.

The ultimate goal is to construct an

equation that the error of prediction will be

In social science most relationship are linier in nature and

can be fitted into linier function

A function is said to be linier when pairs of x and y falls

into a straight line.

Y= a +bx.

Where ,

a = y intercept or the value of y when x=o.

b = slope of the line across the group , expressing the

number of units in y accompanying one unit of change in x.

According to this equation ‘a’ and ‘b’ in regression

equation can be computed by the formula.

LINE Y ON X

y= a+bx.

∑ xy = a∑x +b∑ x2.

conclusionIn researchers point of view statistical techniques like

correlation, regression and time series analysis are havingan important role.

.Correlation helps the researcher to analyze the relation

ship of variables under study.

.Time series analysis helps to identify the trend and there

by it can be used to forecast future.

.Regression analysis helps to predict an unknown value

from there known variable.

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