After  a  group  of  tests  has  been  given  and  each  test  has  been
rated,  the  result  is  a  collection  of  ratings  which  is  often  very
confusing.  It  is  quite  necessary,  from  every  point  of  view,  to
be  able  to  express  all  these  ratings  in  terms  of  a  single  rating
for  the  entire  group.  This  is  sometimes  done  by  adding  together ­
  the  results  in  each  test,  a  procedure  which  is  obviously
fallacious,  because  each  test  may  have  a  different  value.
The  value  of  each  test  is  determined  by  its  index  of  correlation. ­
  The  tests  for  inspectors,  for  instance,  were  found  to  have
correlations  of  plus  .56  for  2,  plus  .63  for  6,  and  plus  .72  for  8.
Therefore,  test  8  should  be  given  more  weight  in  the  final  result
than  6,  etc.  The  proportional  value  of  each  test  may  be  approximately ­
  found  by  dividing  each  correlation  by  the  sum  of  all  the
correlations.  In  the  above  instance  this  gives  .30  for  2,  .32  for
6,  and  .38  for  8.  That  is,  test  2  is  to  count  30%  of  the  total,
test  6,  32%,  and  test  8,  38%,  no  matter  what  the  record  in
each  test  is.
Pro-rating  is  the  process  of  applying  a  formula  by  which  the
rating  in  a  group  of  tests  can  be  combined  in  such  a  way  as  to
give  each  rating  its  proportional  value  in  the  final  result.  If
we  use  the  results  of  the  above  analysis,  and  apply  it  to  the
inspectors’  test,  we  shall  have  the  following  formula:
.30  X  2r  +  .32  X  6r  +  .38  X  8r  =  R,  in  which  R  is  the  final
group  rating,  and  2r,  6r,  and  8r  the  rating  in  each  of  the  three
tests.  If  our  deduction  has  been  correct,  R  should  be  1.00
when  each  test  has  been  done  in  reference  time.  E.  g.,  .30  X  1.00
+  .32  X  1.00  +  .38  X  1.00  =  1.00.
It  is  impossible  to  apply  this  formula  to  any  ratings  which
are  not  computed  on  a  standard  basis  similar  to  that  described
under  the  section  on  rating.
It  is  also  desirable  to  pro-rate  tests  in  accordance  with  changing ­
  and  special  conditions.  For  instance,  in  the  case  of  clerical
tests,  it  may  be  necessary  to  place  considerable  emphasis  on
the  arithmetical  test,  especially  for  ledger,  statistical,  and  ac ­