Hey everyone,
I have a set of data what is the best test to do to see if they are normally distributed or not?? I used norm plot is that enough or other ways are better?
MATLAB: Test for Normally distributed data
statistics
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n=300;%number of cases
minval=0;%lowest allowed integer
maxval=1000;%highest allowed integer
mu=50;%median value of distribution
sd=50;%standard deviation of distribution
data=floor(mu+sd*randn(n,1));%round down to integers
invalid= data<minval | data>maxval;while any(invalid) %replace invalid values with newly generated values
%this will bias the distribution
data(invalid)=floor(mu+sd*randn(sum(invalid),1)); invalid= data<minval | data>maxval;endI need to be careful to not start any discussion about how one actually define a normal distribution, but starting from the point that you don't want a exact perfect definition of normal distributed data you can use the Anderson-Darling test. The idea is to randomly sample 51 points from your array and them check if they are normal or not. To get it more robust, you can simply save the value with the highest p-value:
rng(33)ArraySize = 80000;A = rand(ArraySize,1); % not normal
A(500:1000) = randn(501,1); % normal
Founded = 0;MaxIter = 1000;Maxp = 0;Ite = 1;while ~Founded && Ite<MaxIter SampledIndex = randperm(ArraySize,51); % Sample from your array
Asampled = A(SampledIndex);[h,p] = adtest(Asampled); % Check if normal
% You can theoretically umcomment this, I however belive that looking at the max p
% is more robust
%Founded = ~h; % 0 if normal (can't reject the null hypotesis it is not normal)
if p>Maxp % Save the one that got the closest
BestAsoFar = Asampled;Maxp = p;endIte = Ite+1;endhistogram(BestAsoFar)
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