## Section 2: Tools for Formal Statistical Inference

### Instructor: Tatsuki Koyama

The statistical inferences needed to answer many of the scientific questions addressed in biomedical research take the form of formal hypothesis tests and estimation of effects. For example, a clinical trial can address the question of whether a new therapy is superior to a standard treatment and can provide an assessment of the magnitude of the benefit of the new therapy. This section describes the concepts involved in formal hypothesis testing and estimation, including the interpretation of P-values and confidence intervals.

### Learning Objectives

1. To illustrate the basic logic behind hypothesis testing using a simple example.
2. To discuss the notion of a null and alternative hypothesis.
3. To discuss the notion of a P-value and statistical power.
4. To demonstrate how sample size can influence statistical power.
5. To illustrate the use of a confidence interval.

### Required Reading

• K&S Chapters 5-9, Sections 30.2, 33.1, 33.2, 35.1-35.4, 35.6, 35.7

### Topics and Key Words

1. normal distribution
2. central limit theorem
3. large sample / small sample
4. confidence interval
5. hypothesis test
• type I error, type II error, power, value
6. paired test
7. z test, t test, ANOVA
8. fixed effects / random effects
9. nonparametric methods
10. Bayesian statistics
11. sample size calculation

### Case Studies and Additional Required Reading

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Topic revision: r11 - 15 Sep 2005, TatsukiKoyama

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