KR20.txt

The Kuder-Richardson 20
 
     Suppose we have data from ten students, each of whom took a ten item
quiz on methods of determining reliability.  We code correct responses with
1 and incorrect with 0.  Below are the data and most of the calculations
needed to compute the KR20 using the formula in your textbook.
------------------------------------------------------------------------------
                       Test Item #
          -------------------------------------
Student   1   2   3   4   5   6   7   8   9  10    tot
-------   -------------------------------------    ---
   A      1   1   1   1   1   1   0   1   1   0     8
   B      1   0   1   1   0   1   1   1   0   1     7
   C      1   1   1   1   0   1   1   0   0   1     7
   D      0   0   1   0   0   0   1   0   0   0     2
   E      0   0   0   0   0   1   0   0   1   0     2
   F      1   1   1   0   1   1   1   1   1   1     9
   G      1   1   0   1   1   1   0   1   1   1     8
   H      1   1   1   1   1   1   1   1   0   1     9
   I      0   1   0   1   1   1   1   1   0   1     7
   J      1   1   0   1   1   0   1   1   1   0     7
------------------------------------------------
    p    .7  .7  .6  .7  .6  .8  .7  .7  .5  .6
    q    .3  .3  .4  .3  .4  .2  .3  .3  .5  .4
p * q    .21 .21 .24 .21 .24 .16 .21 .21 .25 .24
variance .21 .21 .24 .21 .24 .16 .21 .21 .25 .24  5.84
-----------------------------------------------------------------------------
     Look in your text and compare the formula for the KR20 with that for
the Cronbach alpha.  You should notice that the only difference is the
substitution of "pq" for the item variances.  Now look at the values of pq
for the data above and compare them to the item variances.  They are identical.
That is, the KR20 is simply Cronbach's alpha where the scores are all 0's and
1's.  Using the formula with pq might save you some time if you are computing
the KR20 by hand, but the easiest way to do it is to have a computer do it
for you, and for that you can use any program that is designed to compute
Cronbach's alpha.  See the file KR20 SAS on Karl's 192 D-disk, which will
do the KR20 on these data (go ahead, jobsub it and verify that it works OK).