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Educational Measurement and Evaluation
Notes 2. Bi-serial Correlation Method : Under certain situations when the individuals of a group fall
under a variable, then we can measure in the score form, but under the second variable, we can
divide into categories only those individuals, and the correlation calculated between these two
variables is called bi-serial correlation, and the variable which is divided into two categories is
called dictotomous variable.
For example, if we want to know correlation between mental age and social adjustment, then
we can measure mental age of students under the first variable, but under the second variable,
we will have to divide students into two categories. One category will be socially adjusted and
the second will be socially maladjusted.
Some examples of dichotomous variables can be as follows :
(a) Likes and dislikes.
(b) Radical and conservative.
(c) Socially-minded and mechanically-minded.
(d) Pass and fail.
(e) Athletic and non-athletic.
(f) Drops-outs and stay-ins.
This correlation is calculated by the following formula :
m − m q pq
p
r bias = σ ⋅ y
Where, m = mean of the group in the first category in which the group shows higher ability
p
m = mean of the group of the second category
q
σ = SD of the entire group
p = proportion of the entire group in category one
q = proportion of the entire group in category second, i.e.
q = l – p
and y = the ordinate of the normal curve at the point of division of p and q.
Bi-serial correlation has its own certain limitations too, which are as follows :
(a) Bi-serial correlation is less reliable than product moment correlation. The standard error
of r obtained from the same sample is more than Pearson correlation efficient (r). From
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this standpoint, Pearson (r) is better than r .
bias
(b) Though r is correlation between two variables, yet it cannot be applied in the regression
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equation, nor can its error of estimate by predicted.
(c) Though r is an estimate of product moment (r), yet its value is not limited within plus-
bias
minus 1, but it can exceed 1. therefore, this coefficient cannot be compared with the other
coefficient. Finally, r is still suitable for finding out validity in achievement tests.
bias
3. Point bi-serial Correlation Method : The chief difference between bi-serial correlation method
and point bi-serial correlation method is that in the point bi-serial correlation method, the
dichotomous variable is in fact discrete. Therefore, when some such situation arises, then the
point bi-serial correlation method should be used. It has been seen that some variables are such
which are not dichotomous in fact, and their distribution from the standpoint of population is
also homogeneous. In such a situation from the viewpoint of convenience, these variables itself
are taken as dichotomous. Supposing, an item has been scored correctly and incorrectly. Now
the truth remains that the students who have solved this question correctly, their abilities within
the group is not similar. If the ability of these students is measured fully, it can be seen that it is
continuously distributed, but in practice, we divide these students into two groups, and thus
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