ONE SAMPLE  RUNS  TEST

A number of  methods have been  developed fro  judging the randomness of samples on the basis of  the order in which  teh observations  are taken. It is possible  to determine whether the samples  that look  suspiciously non random may be attributed to chance. The technique discussed below is based on the theory of runs. A run is  a  succession of identical letters ( or  other kinds  of symbols) which is followed  or preceded by different letter or no  letters at all. To illustrate consider the following  arrangement of letters.

AAA     BBBB     CCCC      DDDDDD         KKK      NNN

Using  underlines to combine the letters which  constitute the runs  we find that first  share is  a run of three a then a run  of four

B then a run  four C  then a run  of six D then a run of two K s and  lastly a run of three N s. In  all there  are six  runs  of varying lengths.

It may  be pointed  to that the total  number of runs  appearing  in an agreement is often a good  indication of a possible lack of randomness. If  there are  too few runs a definite grouping clustering  or trend may be suspected. On  the other hand if there are too many runs some sort of repeated alternating pattern may be suspected. Thus  it may  be possible  to prove that too  many  or too  few  runs  in a sample  indicate something  other than chance when the items  were  selected.

The  number of runs of r is a statistic with  its own  special  sampling  distribution  and its own  test. To  derive the mean  of the  sampling  distribution  of  r statistic  the following  formula  is used.