Page 76 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH
P. 76

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
                                             bias
                                           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
                                                  bias
                                           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



        70                                 LOVELY PROFESSIONAL UNIVERSITY
   71   72   73   74   75   76   77   78   79   80   81