Interpretting Scipy function's meaning and usage t.interval()

Question

I need some help using the scipy.stats.t.interval() function

http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.t.html?highlight=stats.t#scipy.stats.t

I am looking at the documentation, and it doesn't make sense. What are loc and scale? I'm used to student T intervals requiring a mean, sd, df, and confidence interval.

If you know the answer and can help, please post. Also if you could tell me how you learned it, that would be great. I've been having no luck with this documentation.

Answer 1

The docs page you linked has a link to the source code. Which even has a nicely formatted formula for the distribution in the comments (search for class t_gen).

loc and scale are a way all the continuous distributions in scipy.stats are parametrized: Basically, for a distribution f(x), specifying loc and scale means you get f(loc + x*scale) (line 1208 in the source linked above).

>>> import scipy.stats as stats
>>> stats.t.pdf(2, 2) 
0.06804138174397717
>>> stats.t.pdf(2, 2, loc=0, scale=1) 
0.06804138174397717
>>> stats.t.pdf(2+42, 2, loc=42, scale=1) 
0.06804138174397717

>>> stats.t.stats(9, moments='mvsk')
(array(0.0), array(1.2857142857142858), array(0.0), array(1.2))
>>> stats.t.stats(8, loc=1, moments='mvsk')
(array(1.0), array(1.3333333333333333), array(0.0), array(1.5))

>>> stats.t.interval(0.95, 4, loc=0)
(-2.7764451051977987, 2.7764451051977987)
>>> stats.t.interval(0.95, 4, loc=3)
(0.22355489480220125, 5.7764451051977987)

Yes, this is a little baffling at first sight :-).

Answer 2

Since the previous answer is not explicit, I made some research and just verified that:

loc is the mean.

scale is the standard error of the mean.

Such that: μ = M ± t(sM)

where μ is the t-interval, M is the mean, t is the t statistic, and sM = √(std^2/n) is the standard error of the mean.