Hypothesis testing with Scipy Cheat Sheet

A Programming › Python cheat sheet in English by sasha2411

Python Programming Coding Scipy Data Science Hypothesis Dataanalysis

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1 Sample T-Testing

For numerical data.

Compares a sample mean to a hypothetical population mean.

from scipy.stats import ttest_1samp

ttest_1samp requires two inputs, a distribution of values and an expected mean.

tstat, pval = ttest_1samp(example_distribution, expected_mean)

2 Sample T-Test

For numerical data.

Compares two sets of data, which are both approximately normally distributed.

The null hypothesis, in this case, is that the two distributions have the same mean.

from scipy.stats import ttest_ind

It takes the two distributions as inputs and returns the t-statistic and a p-value.

t, pval = ttest_ind(dataset1, dataset2)

ANOVA

For numerical data.

Compares more than two numerical datasets.
ANOVA (Analysis of Variance) tests the null hypothesis that all of the datasets have the same mean.

from scipy.stats import f_oneway

It takes in each dataset as a different input and returns the t-statistic and the p-value.

t, pval = f_oneway(a, b, c)

Tukey's Range Test

For numerical data.

We can perform a Tukey's Range Test to determine the difference between datasets.

from statsmodels.stats.multicomp import pairwise_tukeyhsd

We have to provide the function with one list of all of the data and a list of labels that tell the function which elements of the list are from which set. We also provide the significance level we want, which is usually 0.05.

values = np.concatenate([a, b, c])
labels = ['a'] * len(a) + ['b'] * len(b) + ['c'] * len(c)
tukey_results = pairwise_tukeyhsd(values, labels, 0.05)

Binomial Test

For categorical data.

To analyze a dataset with two different possibilities for entries.

The null hypothesis, in this case, would be that there is no difference between the observed behavior and the expected behavior.

from scipy.stats import binom_test

binom_test requires three inputs, the number of observed successes, the number of total trials, and an expected probability of success.

pval = binom_test(525, n=1000, p=0.5)

Chi Square Test

For categorical data.

To compare two or more categorical datasets.

from scipy.stats import chi2_contingency

The input to chi2_contingency is a contingency table where:

- The columns represent different outcomes, like "Survey Response A" vs. "Survey Response B" or "Clicked a Link" vs. "Didn't Click"
- The rows are each a different condition, such as men vs. women or Interface A vs. Interface B

X = [[30, 10],
[35, 5],
[28, 12],
[20, 20]]
_, pval, _, _ = chi2_contingency(X)

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