# [Python-ideas] NAN handling in the statistics module

Steven D'Aprano steve at pearwood.info
Sun Jan 6 19:27:22 EST 2019

```Bug #33084 reports that the statistics library calculates median and
other stats wrongly if the data contains NANs. Worse, the result depends
on the initial placement of the NAN:

py> from statistics import median
py> NAN = float('nan')
py> median([NAN, 1, 2, 3, 4])
2
py> median([1, 2, 3, 4, NAN])
3

See the bug report for more detail:

https://bugs.python.org/issue33084

The caller can always filter NANs out of their own data, but following
the lead of some other stats packages, I propose a standard way for the
statistics module to do so. I hope this will be uncontroversial (he
says, optimistically...) but just in case, here is some prior art:

(1) Nearly all R stats functions take a "na.rm" argument which defaults
to False; if True, NA and NAN values will be stripped.

(2) The scipy.stats.ttest_ind function takes a "nan_policy" argument
which specifies what to do if a NAN is seen in the data.

https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html

(3) At least some Matlab functions, such as mean(), take an optional
flag that determines whether to ignore NANs or include them.

https://au.mathworks.com/help/matlab/ref/mean.html#bt5b82t-1-nanflag

I propose adding a "nan_policy" keyword-only parameter to the relevant
statistics functions (mean, median, variance etc), and defining the
following policies:

IGNORE:  quietly ignore all NANs
FAIL:  raise an exception if any NAN is seen in the data
PASS:  pass NANs through unchanged (the default)
RETURN:  return a NAN if any NAN is seen in the data
WARN:  ignore all NANs but raise a warning if one is seen

PASS is equivalent to saying that you, the caller, have taken full
responsibility for filtering out NANs and there's no need for the
function to slow down processing by doing so again. Either that, or you
want the current implementation-dependent behaviour.

FAIL is equivalent to treating all NANs as "signalling NANs". The
presence of a NAN is an error.

RETURN is equivalent to "NAN poisoning" -- the presence of a NAN in a
calculation causes it to return a NAN, allowing NANs to propogate
through multiple calculations.

IGNORE and WARN are the same, except IGNORE is silent and WARN raises a
warning.

Questions:

- does anyone have an serious objections to this?

- what do you think of the names for the policies?

- are there any additional policies that you would like to see?

- are you happy with the default?

Bike-shed away!

--
Steve
```