[ Python 常見問題 ] How to calculate p-value for two lists of floats?

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Question
So I have lists of floats. Like [1.33,2.555,3.2134,4.123123] etc. Those lists are mean frequencies of something. How do I proof that two lists are different? I thought about calculating p-value. Is there a function to do that? I looked through scipy documentation, but couldn't figure out what to use.

HowTo
Let's say you have a list of floats like this:

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1. data = {'a': [0.9, 1.0, 1.1, 1.2],'b': [0.8, 0.9, 1.0, 1.1],'c': [4.9, 5.0, 5.1, 5.2],}  

Clearly, a is very similar to b, but both are different from c. There are two kinds of comparisons you may want to do:

1. Pairwise: Is a similar to b? Is a similar to c? Is b similar to c?
2. Combined: Are a, b and c drawn from the same group? (This is generally a better question)

The former can be achieved using independent t-tests as follows:

>>> data = {'a': [0.9, 1.0, 1.1, 1.2], 'b': [0.8, 0.9, 1.0, 1.1], 'c': [4.9, 5.0, 5.1, 5.2]}
>>> from itertools import combinations
>>> from scipy.stats import ttest_ind
>>> for k1, k2 in combinations(data.keys(), 2):
... t, p = ttest_ind(data[k1], data[k2])
... print(f"{k1} with {k2} has p={p}")
...
a with b has p=0.3153335962012298
a with c has p=9.458950025885854e-09
b with c has p=8.159638048425986e-09

This provides the relevant p-values, and implies that that a and c are different, b and c are different, but a and b may be similar. (Check "What a p-value tells you about statistical significance". A p-value less than 0.05 is statistically significant in difference.)

The latter can be achieved using the one-way ANOVA as follows:

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1. >>> from scipy.stats import f_oneway  
2. >>> t, p =  f_oneway(*data.values())  
3. >>> p  
4. 7.959305946160327e-12  

The p-value indicates that a, b, and c are unlikely to be from the same population.