Python p-value from t-statistic

Question

I have some t-values and degrees of freedom and want to find the p-values from them (it's two-tailed). In the real world I would use a t-test table in the back of a Statistics textbook; how do I do the equivalent in Python?

e.g.

t-lookup(5, 7) = 0.00245 or something like that.

I know in SciPy if I had arrays I could do scipy.stats.ttest_ind, but I don't. I just have t-statistics and degrees of freedom.

Presumably stats tables exist for convenience instead of having to calculating those values from an equation. Given this is a computer program, why not use that equation directly instead? — dilbert, Jul 10 '13 at 00:01
It's quite complicated. I would hope there was some method somewhere in some library that could do it for me. — Andrew Latham, Jul 11 '13 at 21:47

score 49 · Accepted Answer · answered Jul 11 '13 at 21:57

49

From http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html

As an exercise, we can calculate our ttest also directly without using the provided function, which should give us the same answer, and so it does:

tt = (sm-m)/np.sqrt(sv/float(n))  # t-statistic for mean
pval = stats.t.sf(np.abs(tt), n-1)*2  # two-sided pvalue = Prob(abs(t)>tt)
print 't-statistic = %6.3f pvalue = %6.4f' % (tt, pval)
t-statistic =  0.391 pvalue = 0.6955

answered Jul 11 '13 at 21:57

Andrew Latham

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Why do they call it (stats.t.sf) a survival function? Is it actually the same as https://en.wikipedia.org/wiki/Survival_function – wordsforthewise Aug 11 '16 at 10:58
What if it were a one-sided test? – zthomas.nc Mar 07 '19 at 06:07
Follow-up to the accepted answer: The p-value of one-sided t-test is the p-value of the two-sided t-test divided by 2: ``` pval_one_sided = stats.t.sf(np.abs(tt), n-1) ``` – PavelLes May 17 '19 at 14:00

Sandipan Dey · Answer 2 · 2021-09-11T22:06:50.617

We can compute using the t.cdf() function too:

from scipy.stats import t
t_stat = 2.25
dof = 15
# p-value for 2-sided test
2*(1 - t.cdf(abs(t_stat), dof))
# 0.03988800677091664
2*(t.cdf(-abs(t_stat), dof))
# 0.03988800677091648

The below figure shows how the critical region for 5% level of significance looks like for a 2-sided t-test. For the above example, we can see that the null hypothesis can be rejected.

Python p-value from t-statistic

2 Answers2

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