Python - P-Value

The p-value is about the strength of a hypothesis. We build hypothesis based on some statistical model and compare the model's validity using p-value. One way to get the p-value is by using T-test.

This is a two-sided test for the null hypothesis that the expected value (mean) of a sample of independent observations a is equal to the given population mean, popmean. Let us consider the following example.

from scipy import stats
rvs = stats.norm.rvs(loc = 5, scale = 10, size = (50,2))
print stats.ttest_1samp(rvs,5.0)

The above program will generate the following output.

Ttest_1sampResult(statistic = array([-1.40184894, 2.70158009]),
pvalue = array([ 0.16726344, 0.00945234]))

Comparing two samples

In the following examples, there are two samples, which can come either from the same or from different distribution, and we want to test whether these samples have the same statistical properties.

ttest_ind − Calculates the T-test for the means of two independent samples of scores. This is a two-sided test for the null hypothesis that two independent samples have identical average (expected) values. This test assumes that the populations have identical variances by default.

We can use this test, if we observe two independent samples from the same or different population. Let us consider the following example.

from scipy import stats
rvs1 = stats.norm.rvs(loc = 5,scale = 10,size = 500)
rvs2 = stats.norm.rvs(loc = 5,scale = 10,size = 500)
print stats.ttest_ind(rvs1,rvs2)

The above program will generate the following output.

Ttest_indResult(statistic = -0.67406312233650278, pvalue = 0.50042727502272966)

You can test the same with a new array of the same length, but with a varied mean. Use a different value in loc and test the same.