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Unit 6 : Validity – Types , Methods and Usability



            4.  Tetrachoric correlation method.                                                      Notes
            5.  Expectancy table method.
            6.  Cut-off score method.
            7.  Differential predictors method.
            8.  Factor-analysis method.
            1.  Simple Correlation Method : This method is the most prevalent method to calculate validity
                coefficient. This is a very simple method. In this, students’ scores are compared with the
                correlation efficient scores obtained on criterion. In calculating correlation coefficient, the product
                moment method is used. Sometimes, the scatter diagram method is also used if the number of
                students is large, whose formula is as follows :

                                     N∑  fd d −  xy  ∑  fd ∑  x  fd y

                          r =  ⎡  N∑  y 2  ( fd −  fd x )∑  2 ⎡  ⎦  ⎢ ⎢  ⎣  N∑  2 y  ( fd −  fd y ) ∑  2 ⎤ ⎤  ⎥ ⎥ ⎣  ⎦

                If the amount of correlation efficient is positive and of high level, then the level of a test’s
                validity too is considred high. On the basis of correlation coefficient, some important conclusions
                can be drawn :

                (a)  What is the correlation coefficient of the test ?
                                                                       2
                (b)  From the change occurring in a variable from the calculation of r , the effect of change on
                     another variable can be estimated; for example, supposing correlation coefficient is .50,
                     then r  = (.50)  = .25, or the difference of 25% which has occurred from Y-variable, has
                                2
                         2
                     occurred due to the difference of scores in X-variable.
                (c)  Just in this way, we can use the regression equation in order to predict the scores of an
                     individual in one subject (X) on the basis of his scores in another subject (Y). The concerned
                     formula is :
                                      σ y
                                 Y =   r  (  −  X  )XM  +  M Y
                                      σ x
                     Besides, standard error of estimate in this prediction can be calculated with the help of
                     the following formula :
                                      σ y
                                 Y =   r σ x (  −  X  )XM  +  M Y

                (d)  On the basis of correlation coefficient too, the forecasting efficiency of a test can be
                     estimated, for which the following formula is used :

                               (estyσ  ) = σ y  1 r 2
                                         −
                     For example, supposing correlation efficient between test and criterion is .80, then
                     prediction efficiency of the test will be .40 or 40%.

                          E =  1 −  (1 −  ).80  2

                             =  1 −  1 .64
                                  −
                             =  1 −  .36
                             = 1 – .60 = .40




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