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by Michael H. Herzog (Author), Gregory Francis (Author), Aaron Clarke (Author)
About the Author
Michael Herzog is a professor at the EPFL in Switzerland. He studied Mathematics, Biology, and Philosophy at the Universities of Erlangen, Tübingen, and MIT. His primary area of research is the field of vision using all sorts of experimental designs including psychophysical methods, TMS, EEG, and mathematical modeling.
Greg Francis is a professor of Psychological Sciences at Purdue University. His primary area of research develops and tests computational neural network models of human visual perception. A secondary area of interest explores how to identify faulty uses of statistics, such as publication bias and questionable research practices. He also applies cognitive models to topics in human factors and develops on-line teaching tools.
Aaron Clarke is a professor at Bilkent University. He is a psychologist by training with a special emphasis on computational neuroscience and statistics.
About this book
This 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.
Brief contents
Part I The Essentials of Statistics
1 Basic Probability Theory 3
1.1 Confusions About Basic Probabilities: Conditional Probabilities 4
1.1.1 The Basic Scenario 4
1.1.2 A Second Test. 7
1.1.3 One More Example: Guillain-Barré Syndrome 8
1.2 Confusions About Basic Probabilities: The Odds Ratio. 9
1.2.1 Basics About Odds Ratios (OR) 9
1.2.2 Partial Information and the World of Disease 10
References 11
2 Experimental Design and the Basics of Statistics: Signal Detection Theory (SDT) 13
2.1 The Classic Scenario of SDT 13
2.2 SDT and the Percentage of Correct Responses 17
2.3 The Empirical d' 19
3 The Core Concept of Statistics 23
3.1 AnotherWay to Estimate the Signal-to-Noise Ratio 24
3.2 Undersampling 26
3.2.1 Sampling Distribution of a Mean 27
3.2.2 Comparing Means 30
3.2.3 The Type I and II Error. 33
3.2.4 Type I Error: The p-Value is Related to a Criterion 35
3.2.5 Type II Error: Hits, Misses 36
3.3 Summary. 38
3.4 An Example 40
3.5 Implications, Comments and Paradoxes 41
Reference 50
4 Variations on the t-Test 51
4.1 A Bit of Terminology 52
4.2 The Standard Approach: Null Hypothesis Testing. 53
4.3 Other t-Tests 53
4.3.1 One-Sample t-Test 53
4.3.2 Dependent Samples t-Test 54
4.3.3 One-Tailed and Two-Tailed Tests 55
4.4 Assumptions and Violations of the t-Test 55
4.4.1 The Data Need to be Independent and Identically Distributed 55
4.4.2 Population Distributions are Gaussian Distributed 56
4.4.3 Ratio Scale Dependent Variable 56
4.4.4 Equal Population Variances 57
4.4.5 Fixed Sample Size 57
4.5 The Non-parametric Approach 58
4.6 The Essentials of Statistical Tests 58
4.7 What Comes Next? 59
Part II The Multiple Testing Problem
5 The Multiple Testing Problem 63
5.1 Independent Tests 63
5.2 Dependent Tests 65
5.3 How Many Scientific Results Are Wrong? 65
6 ANOVA 67
6.1 One-Way Independent Measures ANOVA 67
6.2 Logic of the ANOVA. 68
6.3 What the ANOVA Does and Does Not Tell You: Post-Hoc Tests. 71
6.4 Assumptions 72
6.5 Example Calculations for a One-Way Independent Measures ANOVA 72
6.5.1 Computation of the ANOVA 72
6.5.2 Post-Hoc Tests 74
6.6 Effect Size 76
6.7 Two-Way Independent Measures ANOVA. 77
6.8 Repeated Measures ANOVA. 80
7 Experimental Design: Model Fits, Power, and Complex Designs 83
7.1 Model Fits 83
7.2 Power and Sample Size 86
7.2.1 Optimizing the Design 86
7.2.2 Computing Power 87
7.3 Power Challenges for Complex Designs 90
8 Correlation 95
8.1 Covariance and Correlations. 95
8.2 Hypothesis Testing with Correlations 96
8.3 Interpreting Correlations. 98
8.4 Effect Sizes 100
8.5 Comparison to Model Fitting, ANOVA and t-Test 100
8.6 Assumptions and Caveats 101
8.7 Regression 101
Part III Meta-analysis and the Science Crisis
9 Meta-analysis. 105
9.1 Standardized Effect Sizes 106
9.2 Meta-analysis 107
Appendix 108
Standardized Effect Sizes Beyond the Simple Case 108
Extended Example of the Meta-analysis 109
10 Understanding Replication 111
10.1 The Replication Crisis 111
10.2 Test for Excess Success (TES). 114
10.3 Excess Success from Publication Bias 116
10.4 Excess Success from Optional Stopping 117
10.5 Excess Success and Theoretical Claims. 120
Reference 121
11 Magnitude of Excess Success 123
11.1 You Probably Have Trouble Detecting Bias 123
11.2 How Extensive Are These Problems? 125
11.3 What Is Going On? 127
11.3.1 Misunderstanding Replication 127
11.3.2 Publication Bias 128
11.3.3 Optional Stopping 128
11.3.4 Hypothesizing After the Results Are Known (HARKing).. 128
11.3.5 Flexibility in Analyses 129
11.3.6 Misunderstanding Prediction. 129
11.3.7 Sloppiness and Selective Double Checking 130
12 Suggested Improvements and Challenges. 133
12.1 Should Every Experiment Be Published? 134
12.2 Preregistration 134
12.3 Alternative Statistical Analyses. 136
12.4 The Role of Replication.. 138
12.5 A Focus on Mechanisms. 139
Series: Learning Materials in Biosciences
Pages: 142 pages
Publisher: Springer; 1st ed. 2019 edition (August 14, 2019)
Language: English
ISBN-10: 3030034984
ISBN-13: 978-3030034986
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