How To Calculate P-value For Two Lists Of Floats?

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 calcul

Solution 1:

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

>>>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:

>>>from itertools import combinations>>>from scipy.stats import ttest_ind>>>for list1, list2 in combinations(data.keys(), 2):...    t, p = ttest_ind(data[list1], data[list2])...print list1, list2, p...
a c 9.45895002589e-09
a b 0.315333596201
c b 8.15963804843e-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.

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

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

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