Statistical inference tests are formal procedures for evaluating claims about population parameters using sample data. They form the backbone of evidence-based decision-making in fields from medicine to machine learning, enabling researchers to distinguish genuine effects from random noise. Each test comes with specific assumptions about data distribution, sample size, and measurement scaleβchoosing the right test requires understanding both your research question and your data's characteristics. A critical insight: no test "proves" a hypothesis true; instead, tests quantify the probability that observed results could occur by chance alone under a null hypothesis, guiding decisions about what conclusions the data support.
What This Cheat Sheet Covers
This topic spans 21 focused tables and 132 indexed concepts. Below is a complete table-by-table outline of this topic, spanning foundational concepts through advanced details.
Table 1: Core Hypothesis Testing Concepts
| Concept | Example | Description |
|---|---|---|
Hβ: ΞΌ = 50 | β’ Statement of no effect or no difference β’ the default assumption tested against | |
Hβ: ΞΌ β 50 | β’ Statement that contradicts Hβ β’ what researcher seeks evidence for | |
p = 0.032 | β’ Probability of obtaining observed data (or more extreme) if Hβ is true β’ lower values indicate stronger evidence against Hβ | |
Ξ± = 0.05 | β’ Threshold for rejecting Hβ β’ typical values are 0.05, 0.01, or 0.001 | |
t = 2.45, z = 1.96 | β’ Numerical summary of sample data under Hβ β’ compared to a reference distribution to obtain p-value | |
Reject Hβ when true | β’ False positive β’ probability equals Ξ± | |
Fail to reject Hβ when false | β’ False negative β’ probability denoted Ξ² |