# z score with nan values in matlab (vectorized)

I am trying to calculate the zscore for a vector of 5000 rows which has many nan values. I have to calculate this many times so I dont want to use a loop, I was hoping to find a vectorized solution.

the loop solution:

for i = 1:end vec(i,1) = (val(i,1) - nanmean(:,1))/nanstd(:,1) end

a partial vectorized solution:

zscore(vec(find(isnan(vec(1:end) == 0))))

but this returns a vector the length of the original vector minus the nan values. Thus it isn't the same as the original size.

I want to calculated the zscore for the vector and then interpolate missing data after words. I have to do this 100s of times thus I am looking for a fast vectorized approach.

## Answers

This is a vectorized solution:

% generate some example data with NaNs.

val = reshape(magic(4), 16, 1); val(10) = NaN; val(17) = NaN;

Here's the code:

valWithoutNaNs = val(~isnan(val)); valMean = mean(valWithoutNaNs); valSD = std(valWithoutNaNs); valZscore = (val-valMean)/valSD;

Then column vector valZscore contains deviations (Z scores), and has NaN values for NaN values in val, the original measurement data.

Sorry this answer is 6 months late, but for anyone else who comes across this thread:

The accepted answer isn't fully vectorised in that it doesn't do what the real zscore does so beautifully: That is, do zscores along a particular dimension of a matrix.

If you want to calculate zscores of a large number of vectors at once, as the OP says he is doing, the best solution is this:

Z = bsxfun(@divide, bsxfun(@minus, X, nanmean(X)) , nanstd(X) );

To do it on an arbitrary dimension, just put the dimension inside the nanmean and nanstd, and bsxfun takes care of the rest.

nanzscore = @(X,DIM) bsxfun(@divide, bsxfun(@minus, X, nanmean(X,DIM)), ... nanstd(X,DIM));

anonymous function:

nanZ = @(xIn)(xIn-nanmean(xIn))/nanstd(xIn);

nanZ(vectorWithNans)

vectorized version of below anonymous function (assumes observations are in rows, variables in columns):

nanZ = @(xIn)(xIn-repmat(nanmean(xIn),size(xIn,1),1))./repmat(nanstd(xIn),size(xIn,1),1); nanZ(matrixWithNans)