1. Measures of relationships
•Cross tabulation and percentage difference
•Gamma
•Spearman’s rank order correlation co-efficient(Rho)

2.  This section examines the relationship
between variables.
E.g.
 Children grow, their weight increases
 Demand increases if price decreases
 Application of fertilizers increases crop yield
There may be,
 Direct-indirect relationship
 Positive-negative relationship

3. In examining the relationship between variables, we
have to consider certain questions:
 Is there relationship between variables?
 What is the degree and direction of their
relationship?
 Is the relationship a casual one?
 Is the relationship statistically significant?

4. Cross tabulation and percentage
difference
 It is used for Nominal variables which are
purely qualitative and can be categorized
only.
 E.g.Age, income, brand, religion, language
etc..

5. Procedure,
 Two way table is prepared.
 The value of one variable are put along one side
of the table.
 And the values of the other variable along the
other side of the table
 Each variable is categorized into two or more
categories; and the variables are cross-tabulated
for those sub categories.
 The percentages are computed for them.
 On the basis of the percentages, conclusions are
drawn.

6. Preference for brand X and Age
(Hypothetical)

8.  The strength of relationship is determined
by the pattern of differences between the
values of variables.

9. Gamma
 The ordinal level variables have rank
order differences .
 The most common ordinal variables are
Gamma & Spearman’s rank order
correlation coefficient.
 Gamma or G or ϒ
G= (ns – nd )/ (ns + nd )
 ns the number of similar pairs
 Nd the number of dissimilar pairs

10.  It is based on pair by pair comparison
 It uses information about one variable to
tell us something about a second one.
 E.g. suppose two respondents X andY are
asked to rank the product characteristics
that they would consider while buying a
scooter.

11.  After counting the number of similar and
dissimilar pairs, the level of association
between the two sets of ranks is
compared by the ratio of the
preponderant type of pairs.
 This value is ϒ

12.  .Characteristics Respondent X Respondent Y
Fuel efficiency -F 1 1
Price - P 2 2
Mechanical Efficiency - M 3 3
Riding comfort - R 4 4
Style- S 5 5
F 1 5
P 2 4
M 3 3
R 4 2
S 5 1
F 1 1
P 2 2
M 3 3
R 4 5
S 5 4

14.  ns= 10; nd= 0
 ns= 0; nd= 10
 ns= 08; nd= 02
 G= (10 - 0) / (10 + 0) = +1
 G= (0- 10) / (0 + 10) = -1
 G= (8 – 2) / (8 + 2 ) = +.60

15.  A coefficient of +1 indicates the perfect
positive association between the variables
in terms of pair by pair comparison.
 G= -1 indicates the perfect inverse
association.
 G= + 0.60 combination of similar &
dissimilar ones.

16. Spearman’s rank order correlation
co-efficient Rho or e
 This is the oldest of the frequently used
measures of ordinal associations.
 It is a measure of the extent of agreement
or disagreement between two sets of ranks.
 It is nonparametric measures and so it dose
not require the assumption of a bivariate
normal distribution.
 Its value ranges between -1 (perfect negative
association) and +1 (perfect positive
association)

17.  Rho or e = 1- [ (6∑D2 ) / n(n2 – 1) ]
 D= difference between X,Y ranks
assigned to the object.
 n= number of observation

19.  e= 1- [ (6∑D2 ) / n(n2 – 1) ]
=1-[(6*40)/ 5(52- 1) ]
= -1.0
This value – 1 indicates that there is perfect
negative association between the two sets
of ranks.

20. Correlation analysis
It involves three main aspects:
1. Measuring the degree of association
between two variables
2. Testing whether the relationship is
significant
3. Establishing the cause and effect
relationship if any.

21.  When two variables move in same
direction, their association is termed as
positive correlation.
 When they move in opposite direction,
their association is termed as negative
correlation.

22. Karl pearson product moment
correlation coefficient r
 Most common measure
 This measure expresses both strength and
direction of linear correlation.
 This measure expresses both strength and
direction of linear correlation.

24. •Examine the relationship between
period of education (X) and religious
prejudice (Y) for a sample of six
respondents.
X Y
3 1
6 7
8 3
9 5
10 4
2 2
38 22

25. X Y X2 Y2 XY
3 1 9 1 3
6 7 36 49 42
8 3 64 9 24
9 5 81 25 45
10 4 100 16 40
2 2 4 4 4
38 22 294 104 158

26.  r= 0.53
 The correlation coefficient ranges from -
1.0 to +1.0.
 -1.0 indicates perfect negative correlation
& +1 indicated perfect positive
correlation.
 + or - 0.5 moderate positive or negative
correlation.