Welch's t-test for two samples, not assuming equal sample size or variance. Requires Python, NumPy, and SciPy.

t_welch.py

from collections import namedtuple

import numpy as np
import scipy.stats as st

TtestResults = namedtuple("Ttest", "T p")

def t_welch(x, y, tails=2):
    """
    Welch's t-test for two unequal-size samples, not assuming equal variances
    """
    assert tails in (1,2), "invalid: tails must be 1 or 2, found %s"%str(tails)
    x, y = np.asarray(x), np.asarray(y)
    nx, ny = x.size, y.size
    vx, vy = x.var(ddof=1), y.var(ddof=1)
    df = ((vx/nx + vy/ny)**2 / # Welch-Satterthwaite equation
            ((vx/nx)**2 / (nx - 1) + (vy/ny)**2 / (ny - 1)))
    t_obs = (x.mean() - y.mean()) / np.sqrt(vx/nx + vy/ny)
    p_value = tails * st.t.sf(abs(t_obs), df)
    return TtestResults(t_obs, p_value)

Hi @jdmonaco! I was using this function of yours and noticed that the results are very close to being spot on.

After doing some digging around, I believe the sample-specific variance calculations should be adjusted slightly to account for a single degree of freedom because NumPy's var() method defaults to zero. That is:
vx, vy = x.var(ddof=1), y.var(ddof=1)

Further, the degrees of freedom for calculating the p-value could optionally be executed with greater precision by dropping the int() in the Welch-Satterthwaite equation.

Thanks @jonkrohn! It's annoying because I pulled this from a larger stats module I wrote that had ddof=1 in every other std/var call. I somehow neglected these instances. And I was apparently under the impression in 2013 that dof's could only be integers, which is obviously not right (but at least the int cast produced a conservative bias).

Anyway, I've updated this gist (and the corresponding module, which I do still use). Thanks again.

Nice, looks perfect now :)

I checked out your website, btw -- very cool! I did a neuroscience PhD and so naturally get jealous when I see fascinating work like yours by people who stayed on the academic course.