Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Theory of Tests, p-Values, and Confidence Intervals
- 3 From Scientific Theory to Statistical Hypothesis Test
- 4 One-Sample Studies with Binary Responses
- 5 One-Sample Studies with Ordinal or Numeric Responses
- 6 Paired Data
- 7 Two-Sample Studies with Binary Responses
- 8 Assumptions and Hypothesis Tests
- 9 Two-Sample Studies with Ordinal or Numeric Responses
- 10 General Methods for Frequentist Inferences
- 11 k-Sample Studies and Trend Tests
- 12 Clustering and Stratification
- 13 Multiplicity in Testing
- 14 Testing from Models
- 15 Causality
- 16 Censoring
- 17 Missing Data
- 18 Group Sequential and Related Adaptive Methods
- 19 Testing Fit, Equivalence, and Noninferiority
- 20 Power and Sample Size
- 21 Bayesian Hypothesis Testing
- References
- Notation Index
- Concept Index
8 - Assumptions and Hypothesis Tests
Published online by Cambridge University Press: 17 April 2022
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Theory of Tests, p-Values, and Confidence Intervals
- 3 From Scientific Theory to Statistical Hypothesis Test
- 4 One-Sample Studies with Binary Responses
- 5 One-Sample Studies with Ordinal or Numeric Responses
- 6 Paired Data
- 7 Two-Sample Studies with Binary Responses
- 8 Assumptions and Hypothesis Tests
- 9 Two-Sample Studies with Ordinal or Numeric Responses
- 10 General Methods for Frequentist Inferences
- 11 k-Sample Studies and Trend Tests
- 12 Clustering and Stratification
- 13 Multiplicity in Testing
- 14 Testing from Models
- 15 Causality
- 16 Censoring
- 17 Missing Data
- 18 Group Sequential and Related Adaptive Methods
- 19 Testing Fit, Equivalence, and Noninferiority
- 20 Power and Sample Size
- 21 Bayesian Hypothesis Testing
- References
- Notation Index
- Concept Index
Summary
This short chapter formally defines hypothesis tests in terms of decision rules paired with assumptions. It defines when one set of assumptions is more restrictive than another set. It further defines a multiple perspective decision rule, where one decision rule (and hence its p-value function) can be applied under different sets of assumptions, called perspectives.For example, the one sample t-test p-value may be interpreted as testing a mean restricted to the class of normal distributions, but that same p-value is asymptotically valid under an expanded class of distributions that does not require the normality assumption. This multiple perspective decision rule formulation may allow an appropriate interpretation the t-test p-value even when the data are clearly not normally distributed. Another example is presented, giving the Wilcoxon–Mann–Whitney decision rule under two different perspectives.
- Type
- Chapter
- Information
- Statistical Hypothesis Testing in ContextReproducibility, Inference, and Science, pp. 124 - 128Publisher: Cambridge University PressPrint publication year: 2022