CODEWITHSUNDEEP
pythonarraysnumpyscikit-learnstandard-deviation
user706838
user706838

Reputation: 5380

How to calculate how many standard deviations a number is from the mean?

I have a matrix of size (61964, 25). Here is a sample:

array([[  1.,   0.,   0.,   4.,   0.,   1.,   0.,   0.,   0.,   0.,   3.,
          0.,   2.,   1.,   0.,   0.,   3.,   0.,   3.,   0.,  14.,   0.,
          2.,   0.,   4.],
       [  0.,   0.,   0.,   1.,   2.,   0.,   0.,   0.,   0.,   0.,   1.,
          0.,   2.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   5.,   0.,
          0.,   0.,   1.]])

Scikit-learn provides a useful function provided that our data are normally distributed:

from sklearn import preprocessing

X_2 = preprocessing.scale(X[:, :3])

My problem, however, is that I have to work on a row basis - which does not consist of 25 observations only - and so the normal distribution is not applicable here. The solution is to use t-distribution but how can I do that in Python?

Normally, values go from 0 to, say, 20. When I see unusually high numbers, I filter out the whole row. The following histogram shows what my actual distribution looks like:

enter image description here

Upvotes: 4

Views: 5134

Answers (1)

Alex Riley
Alex Riley

Reputation: 176810

scipy.stats has the function zscore which allows you to calculate how many standard deviations a value is above the mean (often refered to as the standard score or Z score).

If arr is the example array from your question, then you can compute the Z score across each row of 25 as follows:

>>> import scipy.stats as stats
>>> stats.zscore(arr, axis=1)
array([[-0.18017365, -0.52666143, -0.52666143,  0.8592897 , -0.52666143,
        -0.18017365, -0.52666143, -0.52666143, -0.52666143, -0.52666143,
         0.51280192, -0.52666143,  0.16631414, -0.18017365, -0.52666143,
        -0.52666143,  0.51280192, -0.52666143,  0.51280192, -0.52666143,
         4.32416754, -0.52666143,  0.16631414, -0.52666143,  0.8592897 ],
       [-0.43643578, -0.43643578, -0.43643578,  0.47280543,  1.38204664,
        -0.43643578, -0.43643578, -0.43643578, -0.43643578, -0.43643578,
         0.47280543, -0.43643578,  1.38204664, -0.43643578, -0.43643578,
        -0.43643578, -0.43643578, -0.43643578, -0.43643578, -0.43643578,
         4.10977027, -0.43643578, -0.43643578, -0.43643578,  0.47280543]])

This calculation uses the population mean and standard deviation for each row. To use the sample variance instead (as with the t-statistic), additionally specify ddof=1:

stats.zscore(arr, axis=1, ddof=1)

Upvotes: 5

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