Page 318 - DMTH404_STATISTICS

Statistics

Notes  Each pair of values (X , Y ) is denoted by a point on the graph. The set of such points (also
i i
known as dots of the diagram) may cluster around a straight line or a curve or may not
show any tendency of association.
 It can be used to specify the limits of population correlation coefficient  (rho) which are
defined as r – P.E.(r)  r  r + P.E.(r), where  denotes correlation coefficient in population
and r denotes correlation coefficient in sample.
 It can be used to test the significance of an observed value of r without the knowledge of
test of hypothesis. By convention, the rules are:

 If |r| < 6 P.E.(r), then correlation is not significant and this may be treated as a
situation of no correlation between the two variables.

 If |r|> 6 P.E.(r), then correlation is significant and this implies presence of a strong
correlation between the two variables.
 If correlation coefficient is greater than 0.3 and probable error is relatively small,
the correlation coefficient should be considered as significant.

22.11 Keywords

Correlation: It is an analysis of covariation between two or more variables.
Correlation Coefficient: It is a numerical measure of the degree of association between two or
more variables.
Scatter diagram: A scatter diagram of the data helps in having a visual idea about the nature of
association between two variables. If the points cluster along a straight line, the association
between variables is linear.

22.12 Self Assessment

1. Fill in the blanks :

(i) Coefficient of correlation is a measure of the strength of the ........ relationship between
two variables.
(ii) Coefficient of correlation is ........ of the change of origin and scale.

(iii) Coefficient of correlation between sale of woolen garments and the day temperature
is likely to be ........
(iv) Coefficient of correlation lies between ........ and ........ .

(v) Correlation between number of accidents and number of babies born in different
years is termed as ........ correlation.
(vi) If two variables X and Y are such that their difference (X – Y) is always equal to 25.
The correlation between X and Y is ........ and positive.
2. Examine the validity of the following statements giving necessary proofs and reasons for
your answer:
(i) If r = 0, then X and Y are always independent.
XY
(ii) If the sum of squares of the difference in ranks of 8 pairs of observations is 126, then
the rank correlation coefficient is 0.5.

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