Runstest: a good interpretation

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Damiano Capocci 2018-3-31

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https://ww2.mathworks.cn/matlabcentral/answers/391888-runstest-a-good-interpretation

评论： Damiano Capocci 2018-4-1

I've found this thing:

I generate 100000 random numb through rand but sometimes the null hypotesis is rejected. For see this thing here is the code:

tr = 300;
hyp = nan(1,tr);
for n = 1:tr
      a=rand(1,100000);
      [h,p]=runstest(a,median(a));
      hyp(n) = h;
end
perc_one=size(find(hyp),2)/300;

where in my case:

perc_one=0.04

How could we interpret runstest? ok it tests the randomness of the order but in each step of the previous generation the coeff of correlation (corrcoef) is near zero so i dont understand how these two tests are related.

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dpb 2018-4-1

They're not all that directly related; one is the overall test of the whole sample as an aggregate; the other tests whether there are sub-sequences within the series that may appear non-random.

Also, remember that on occasion a truly random sample may just "appear" nonrandom. You can toss 5 heads in a row with a fair coin.

Damiano Capocci 2018-4-1