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Unit 10: Correlation: Scatter Diagram Method, Karl Pearson's Coefficient of Correlation

3. The value of the coefficient is unduly affected by the extreme items. Notes
4. As compared with some other methods this method is more time consuming.
Interpreting the Coefficient of Correlation

The coefficient of correlation measures the degree of relationship between two sets of figures. As the
reliability estimate depends upon the closeness of the relationship, it is imperative that utmost care is
taken while interpreting the value of coefficient of correlation, otherwise fallacious conclusion may
be drawn.
Unfortunately, the interpretation of the coefficient of correlation depends very much on experience.
The full significance of r will only be grasped after working out a number of correlation problems
and seeing the kinds of data that give rise to various values of r. The investigator must know his data
thoroughly in order to avoid errors of interpretation and emphasis. He must be familiar, or become
familiar, with all the relationships and theory which bear upon the data and should reach a conclusion
based on logical reasoning and intelligent investigation on significantly related matters. However,
the following general rules are given which would help in interpreting the value of r.
1. When r = + 1 it means there is perfect positive relationship between the variables.
2. When r = – 1 it means there is perfect negative relationship between the variables.
3. When r = 0 it means that there is no relationship between the variables, i.e., the variables are
uncorrelated.
4. The closer r is to + 1 or – 1, the closer the relationship between the variables and the closer r is
to 0, the less close the relationship. Beyond this it is not safe to go. The full interpretation of r
depends upon circumstances one of which is the size of the sample. All that can really be said
is that when estimating the value of one variable from the value of another, the higher the value
of r the better the estimate.
5. The closeness of the relationship is not proportional to r. If the value of r is 0.8 it does not
indicate a relationship twice as close as one of 0.4. It is in fact very much closer.
Coefficient of Correlation and Probable Error

The probable error of the coefficient of correlation helps in interpreting its value. With the help of
probable error it is possible to determine the reliability of the value of the coefficient in so far as it
depends on the conditions of random sampling. The probable error of the coefficient of correlation is
obtained as follows:

1– r 2
P.E. = 0.6745
N
where r is the coefficient of correlation and N the number of pairs of items.
1. If the value of r is less than the probable error there is no evidence of correlation, i.e., the value
of r is not at all significant.
2. If the value of r is more than six times the probable error, the existence of correlation is practically
certain, i.e., the value of r is significant.
3. By adding and subtracting the value of probable error from the coefficient of correlation we get
respectively the upper and lower limits within which coefficient of correlation in the population
can be expected to lie. Symbolically,

ρ = ± P.E.r
ρ (rho) denotes correlation in the population.
Carrying out the computation of the probable error, assuming a coefficient of correlation of 0.80
computed from a sample of 16 pairs of items, we have

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