Hypothesis quantification specifies the expected numerical magnitude of a difference or change, rather than only predicting its presence or direction. section 3.1.3
Quantify a hypothesis by:
- Estimating the expected difference between groups and stating that estimate as part of the hypothesis. section 3.1.3
- Grounding the estimate in peer-reviewed research, organizational data, or stakeholder domain knowledge rather than inventing a number. section 3.1.3
- Using the estimate as an early step toward probabilistic thinking, without requiring a full treatment of Bayesian statistics. section 3.1.3
Treatment and control distributions
A hypothetical treatment group can be modeled with a normal distribution shifted two standard deviations to the right of a control group. Overlapping histograms then represent a hypothesized, highly effective treatment difference. section 3.1.3
import numpy as np #1 import matplotlib.pyplot as plt c = np.random.normal(0, 1, size=500) #2 t = np.random.normal(2, 1, size=500) plt.hist(c, alpha=0.5, bins=25, color="black") #3 plt.hist(t, alpha=0.5, bins=25, color="lightgray") plt.legend(["Control", "Treatment"])
Generate normally distributed control and treatment samples in Python and compare them with overlapping histograms. section 3.1.3
