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05.04A · Cours 4 — Tests statistiques I

Course 4 — Statistical tests I

Course and questions · 54 pages

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1Statistical Tests I2Review of Statistical Inference3Review of 95% Confidence Interval4Lecture Objectives
Observed vs Real Difference
5Small Sample — Overlapping CIs6Larger Sample — Non-overlapping CIs
Principle of a Statistical Test
7Coin Toss Intuition8Null Hypothesis and Rejection Logic9H0 and Ha in Clinical Research
Research Question and Hypotheses
10Anesthetic Risk Example — H0 and Ha11Acupuncture RCT — Study Design12Pain Scale Interpretation13Acupuncture Example — H0 and Ha14Smoking Cessation — Study Design15Smoking Cessation — H0 and Ha
Statistical Test Procedure
16Decision Matrix Overview17Sampling Distribution Under H018Rejection and Non-rejection Zones19Significant vs Non-significant Result20Deriving the z Test Statistic21z Distribution Under H022Decision Rule for z23Smoking Cessation — z = −4.0
Link Between Test and 95% CI
24Equivalence of z-test and CI25CI Contains vs Excludes H0 Value
Type I Error (α)
26Error Matrix — False Positive275% Rejection Under H028α = 5% by Construction
P-value
29Introduction to the P-value30Definition and Interpretation31Reference Distribution — Blue Area = 0.0532P-value When z in Rejection Region33P-value When z in Non-rejection Region34Interpretation Rules and Caveats35Smoking Cessation — p = 0.000136Smoking Cessation — Conclusion
37Test Procedure Summary
Type II Error and Power
38Type I vs Type II Error — Overview39Decision Table — α, β, Power40β and Power Definition41z Distribution Under H0 (Revisited)42z Distribution Under Ha — β and Power43Four Outcomes of a Test
Factors Affecting Power
44Larger Effect → Higher Power45Smaller σ → Higher Power46Larger n → Higher Power47Lower α → Lower Power48Summary of Power Determinants
Low Power and Sample Size Planning
49Low Power in Small Studies50Non-significance ≠ No Effect51Sample Size Calculation — When, Why, How
52Asymmetry of Hypothesis Testing53Lecture Summary54Next Session Preview