> > > where are the values in array critical_runs come from ?
> > > for example, when there are total 50 sample points, if the total runs
> > > value is larger than 19, then the value of a and b is reliable.
> > >
> > > the comment is "Critical value for number of runs of residuals with
> > > same sign. 5% critical region for now."
> > > what is the formula or method to get the runs value of 19 for 50
> > > samples?
> >
> > It's the Wald-Wolfowitz runs test with the assumption that n1==n2.
> >
> > The table is calculated like this:
> > - for i < 8 it's 0
> > - for i >= 8 it's mu - sqrt(var) * z where:
> > mu = 2.0 * (i / 2.0) * (i / 2.0) / i + 1.0
> > var = (mu - 1.0) * (mu - 2.0) / (i - 1)
> > z = 1.65
>
> I examed this formula with i up to 129, and the result is same with
> critical_runs array !
> thanks very much!
I found a formula on the web:
Z = [ r - E(r) ] / sigma
E(r) = ( 2 * n1 * n2 ) / ( n1 + n2 ) + 1,
sigma = sqrt{ [ 2 * n1 * n2 * ( 2 * n1 * n2 - n1 - n2 ) ] / [ ( n1 + n2
) * ( n1 + n2 ) * ( n1 + n2 -1 ) ] }
if Z is z , r is runs , E(r) is mu , sigma is sqrt(var), then r = Z * sigma
+ E(r).
should runs be "mu + sqrt(var)" or "mu -sqrt(var)" ?
