Python numpy percentile vs scipy percentileofscore

Question

I am confused as to what I am doing incorrectly.

I have the following code:

import numpy as np
from scipy import stats

df
Out[29]: array([66., 69., 67., 75., 69., 69.])

val = 73.94
z1 = stats.percentileofscore(df, val)
print(z1)
Out[33]: 83.33333333333334

np.percentile(df, z1)
Out[34]: 69.999999999

I was expecting that np.percentile(df, z1) would give me back val = 73.94

Answer 1

I think you're not quite understanding what percentileofscore and percentile actually do. They are not inverses of each other.

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From the docs for scipy.stats.percentileofscore:

The percentile rank of a score relative to a list of scores.

A percentileofscore of, for example, 80% means that 80% of the scores in a are below the given score. In the case of gaps or ties, the exact definition depends on the optional keyword, kind.

So when you supply the value 73.94, there are 5 elements of df that fall below that score, and 5/6 gives you your 83.3333% result.

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Now in the Notes for numpy.percentile:

Given a vector V of length N, the q-th percentile of V is the value q/100 of the way from the minimum to the maximum in a sorted copy of V.

The default interpolation parameter is 'linear' so:

'linear': i + (j - i) * fraction, where fraction is the fractional part of the index surrounded by i and j.

Since you have provided 83 as your input parameter, you're looking at a value 83/100 of the way from minimum to the maximum in your array.

If you're interested in digging through the source, you can find it here, but here is a simplified look at the calculation being done here:

ap = np.asarray(sorted(df))
Nx = df.shape[0]

indices = z1 / 100 * (Nx - 1)
indices_below = np.floor(indices).astype(int)
indices_above = indices_below + 1

weight_above = indices - indices_below
weight_below = 1 - weight_above

x1 = ap[b] * weight_below   # 57.50000000000004
x2 = ap[a] * weight_above   # 12.499999999999956

x1 + x2

70.0