Herzog M.H., Francis G., Clarke A. Understanding Statistics And Experimental Design: How To Not Lie With Statistics

New York: Springer, 2019. — 146 p.This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III provides insight into meta-statistics (statistics of statistics) and demonstrates why experiments often do not replicate. Finally, the textbook shows how complex statistics can be avoided by using clever experimental design. Both non-scientists and students in Biology, Biomedicine and Engineering will benefit from the book by learning the statistical basis of scientific claims and by discovering ways to evaluate the quality of scientific reports in academic journals and news outlets.Science, Society, and StatisticsAbout This BookThe Essentials of StatisticsThe Basic Scenario
A Second Test
One More Example: Guillain-Barré Syndrome
Basics About Odds Ratios (OR)
Partial Information and the World of DiseaseThe Classic Scenario of SDT
SDT and the Percentage of Correct Responses
The Empirical dAnother Way to Estimate the Signal-to-Noise Ratio
Undersampling
Sampling Distribution of a Mean
Comparing Means
The Type I and II Error
Type I Error: The p-Value is Related to a Criterion
Type II Error: Hits, MissesAn Example
Implications, Comments and ParadoxesA Bit of Terminology
One-Sample t-Test
Dependent Samples t-Test
The Data Need to be Independent and Identically Distributed
Ratio Scale Dependent Variable
Fixed Sample Size
The Essentials of Statistical Tests
What Comes Next?The Multiple Testing ProblemIndependent Tests
How Many Scientific Results Are Wrong?
One-Way Independent Measures ANOVA
Logic of the ANOVA
What the ANOVA Does and Does Not Tell You: Post-Hoc Tests
Computation of the ANOVA
Post-Hoc Tests
Effect Size
Two-Way Independent Measures ANOVA
Repeated Measures ANOVA
Model Fits
Optimizing the Design
Computing Power
Power Challenges for Complex Designs
Covariance and Correlations
Hypothesis Testing with Correlations
Interpreting Correlations
Comparison to Model Fitting, ANOVA and t-Test
RegressionMeta-analysis and the Science CrisisStandardized Effect Sizes
Meta-analysis
Standardized Effect Sizes Beyond the Simple Case
Extended Example of the Meta-analysis
The Replication Crisis
Test for Excess Success (TES)
Excess Success from Publication Bias
Excess Success from Optional Stopping
Excess Success and Theoretical ClaimsYou Probably Have Trouble Detecting Bias
How Extensive Are These Problems?
Misunderstanding Replication
Hypothesizing After the Results Are Known (HARKing)
Misunderstanding Prediction
Sloppiness and Selective Double CheckingPreregistration
Alternative Statistical Analyses
The Role of Replication
A Focus on Mechanisms