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.