Testing of Hypotheses: Parametric & Non-Parametric
Null vs. Alternative Hypotheses, Type I/II Errors, Z-test, t-test & Chi-Square
The definitive mathematical and conceptual guide to statistical decision theory: defining significance levels, critical values, p-values, degrees of freedom, and choosing appropriate tests.
1. Foundational Concepts & Core Principles
Formulation of Null (H0) and Alternative (Ha) hypotheses
Rigorous academic inquiry requires precise delimitation of this principle to ensure internal consistency, falsifiability, and methodological replicability.
Type I (alpha) and Type II (beta) errors; Power of a statistical test (1 - beta)
Rigorous academic inquiry requires precise delimitation of this principle to ensure internal consistency, falsifiability, and methodological replicability.
Parametric tests: Z-test (large samples), Student's t-test (two-sample independent and paired)
Rigorous academic inquiry requires precise delimitation of this principle to ensure internal consistency, falsifiability, and methodological replicability.
Analysis of Variance (ANOVA): One-way and Two-way F-tests
Rigorous academic inquiry requires precise delimitation of this principle to ensure internal consistency, falsifiability, and methodological replicability.
Non-parametric tests: Chi-Square (chi^2) test of goodness-of-fit and independence, Mann-Whitney U
Rigorous academic inquiry requires precise delimitation of this principle to ensure internal consistency, falsifiability, and methodological replicability.
2. Methodological Comparison & Trade-offs
Used when population variance is known and sample size n >= 30.
Used when population variance is unknown and sample size n < 30.
Non-parametric test comparing observed vs expected categorical frequencies.
3. Practical Guidelines & Common Methodological Pitfalls
- Explicitly state operational definitions before measurement.
- Acknowledge potential confounders and data limitations in the methodology section.
- Pre-register hypothesis and statistical tests when conducting quantitative trials.
- Provide full provenance for historical, epigraphical, and archival texts.
- Confusing statistical correlation with causal determination.
- Using non-probability convenience samples to claim population generalizations.
- Failing to report negative results or unexpected anomalies.
- Relying on unverified secondary citations without reading the primary source.