{smcl}
{* 9sept2006/5nov2006}{...}
{hline}
help for {hi:nruns}{right:(SJ6-4: st0044_1)}
{hline}

{title:Number of runs compared with random shuffles}

{p 8 17 2}
{cmd:nruns}
{varname}
{ifin} 
[{cmd:, nreps(}{it:#}{cmd:)}
{bind:{cmd:saving(}{it:filename} [{cmd:, replace}]{cmd:)}}]


{title:Description}

{p 4 4 2}{cmd:nruns} counts runs in a sequence of values given by
{it:varname}, which may be either numeric or string, showing the
successive occurrence of categories, such as {cmd:1 2 2 2 3 3 3 1 1 1}
or {cmd:A A A A B B A A}.  A run ends when values change from one
category to another or at the end of the sequence. Thus, in these
examples, there are four and three runs, respectively.  

{p 4 4 2}{cmd:nruns} shuffles the sequence randomly a given number of
times. It displays the simulated frequency and probability distributions
under randomness of the number of runs possible with the same values and
the probabilities of fewer than, the same number as, or more than that
observed. 
    
{p 4 4 2}To ensure reproducible results, {helpb set seed}
beforehand.


{title:Options} 

{p 4 8 2}{opt nreps(#)} indicates the number of shuffles to be simulated. 
The default is {cmd:nreps(10000)}.

{p 4 8 2}{cmd:saving(}{it:filename} [{cmd:, replace}])} indicates that
results, meaning variables containing values, number of runs, frequencies, and
probabilities, should be saved to the specified file. 


{title:Example}

{p 4 8 2}{cmd:. nruns sequence}


{title:Saved results}

{pstd}{cmd:nruns} saves the following in {hi:r()}:

{col 5}r(pless)   {col 18}probability of fewer runs than observed 
{col 5}r(psame)   {col 18}probability of same number of runs as observed 
{col 5}r(pmore)   {col 18}probability of more runs than observed 


{title:Authors}

{p 4 4 2}Nicholas J. Cox, Durham University, UK{break} 
n.j.cox@durham.ac.uk

{p 4 4 2}Nigel C. Smeeton, King's College London, UK{break} 
nigel.smeeton@kcl.ac.uk 


{title:Acknowledgments} 

{p 4 4 2}Kit Baum and William Gould made valuable suggestions on speeding up
the Mata code. 


{title:Also see} 

{p 4 13 2}Online: {helpb nrunsi} 
{p_end}