Lectures
STATISTICS 2
Lamker, Patricia
NWI- BB020C
Radboud University, 2022
,Table of Content
1. Lecture - Introduction ......................................................................................................................... 4
1.1 Example I ....................................................................................................................................... 5
1.1.1 Pregnancy outcomes in a study group exposed to cetirizine and a control group ............... 5
1.1.2 How do you look at the data? ................................................................................................ 5
1.1.3 How would you analyse the data? ......................................................................................... 5
1.2 Recapitulation: .............................................................................................................................. 6
1.2.1 Variables: Independent vs. dependent, qualitative vs. quantitative and choice of
statistical tests ................................................................................................................................ 6
1.2.2 Which tests? Analysing differences between sample with one independent variable. ....... 6
1.3 Back to the Example I .................................................................................................................... 6
1.3.1 Analysis of the cetirizine data using a 2 -test of Independence in JASP 0.16 ..................... 6
1.3.2 Analysis and interpretation of the cetirizine data ................................................................. 7
1.4 Example II ...................................................................................................................................... 8
1.4.1 Analysis of the amygdala data using linear regression in JASP 0.16 ...................................... 8
1.5 Why all this stuff about different choices in statistical analysis? ................................................. 9
1.6 Additional Notes ......................................................................................................................... 10
2. Lecture .............................................................................................................................................. 11
2.1 Sex/ Gender Bias ......................................................................................................................... 11
2.2 Factorial Experimental Designs ................................................................................................... 11
2.2.1 Looking for interactions between factors ............................................................................ 11
2.2.2. Analysing factorial experimental designs using contrasts .................................................. 18
2.3 Bottom lines ................................................................................................................................ 21
3. Lecture – Multiple Linear Regression (Spurious relationships, model selection) ............................. 22
3.1 Example “How to win a Nobel Prize” .......................................................................................... 22
3.1.1 Flavonols .............................................................................................................................. 22
3.1.2 Eat chocolate! ...................................................................................................................... 22
...................................................................................................................................................... 22
...................................................................................................................................................... 22
3.1.3 Eat chocolate? ...................................................................................................................... 22
3.1.4 Some context: Nobel laureates by country. ........................................................................ 22
3.1.5 A matter of national development? .................................................................................... 23
3.2 Recap Statistics 1 ........................................................................................................................ 23
3.2.1 A straight line: ...................................................................................................................... 23
3.2.2 Overview of linear regression calculations on a calibration curve: ..................................... 23
1
, 3.2.3 In multiple regression we will try to fit a best fitting hyperplane in more than two
dimensions (1DV, ≥ 2 IVs)............................................................................................................. 24
3.3 Why multiple linear regression? ................................................................................................. 24
3.4 Watch out for: ............................................................................................................................. 24
3.4.1 Simplification by dichotomization ....................................................................................... 24
3.4.2 Model abuse and spurious correlations & correlation =/ causation ................................... 27
3.4.3 The Simpson Paradox – an extreme example of a confounding variable............................ 32
3.5 Bottom lines: ............................................................................................................................... 34
4. Lecture – Power Analysis and Sample Size Calculation .................................................................... 35
4.1 Power Analysis ............................................................................................................................ 35
4.1.1 Biomedical research’s replication crisis ............................................................................... 35
4.2 Sample Size (n) determination .................................................................................................... 37
4.2.1 Example ................................................................................................................................ 37
4.2.2 The power of a statistical test indicates the sensitivity of a test to detect an effect when
there is one. .................................................................................................................................. 39
4.2.3 B – E – A – N – S (more on this later) ................................................................................... 39
4.2.4 How sample size, variability, and significance level affect power of a statistical analysis. 40
4.2.5 How many times will your test give a significant outcome when there is no difference
between groups? .......................................................................................................................... 40
4.2.6 Example – Biological Variation ............................................................................................. 41
4.2 ..................................................................................................................................................... 44
4.2.1 B – E – A – N – S.................................................................................................................... 44
4.2.2 Randomization and Stratification ........................................................................................ 48
4.3 Sample size calculations and power analyses using G*Power ................................................... 48
4.3.1 The bottom line when it comes to sample size: .................................................................. 49
4.3.2 Size does matter! ................................................................................................................. 49
4.3.3 Rule of thumb assuming a normal distribution ................................................................... 49
4.3.4 Formal calculation using the t-distribution .......................................................................... 50
4.3.5 Six approaches to justify sample sizes ................................................................................. 50
4.3.6 Six possible ways to think about effect size ......................................................................... 51
1. Guest Lecture – Dokter Media .......................................................................................................... 52
2. Guest Lecture – Syrcle....................................................................................................................... 54
2.1 Introduction to systematic reviews on animal studies ............................................................... 54
2.1.1 Steps of a systematic review ................................................................................................ 54
2.1.2 Benefits of preclinical SRs .................................................................................................... 54
2.1.3 Study Quality ........................................................................................................................ 55
2
, 2.1.4 Forest Plot ............................................................................................................................ 55
2.1.5 Subgroup Analysis ................................................................................................................ 56
2.1.6 Tools per phase .................................................................................................................... 56
2.2 Practical Data Extraction ............................................................................................................. 57
2.2.1 Types of outcome measures ................................................................................................ 57
2.2.2 Assignment – extracting outcome data ............................................................................... 57
2.2.3 Take Home Message ............................................................................................................ 59
2.3 Data-analysis and Meta-analysis................................................................................................. 60
2.3.1 Data-analysis or meta-analysis ............................................................................................ 60
2.3.2 Meta-analysis ........................................................................................................................... 60
2.3.3 From study data to forest plot ............................................................................................. 60
2.3.4 Choosing your effect size measure. continuous data .......................................................... 60
2.3.5 Continuous Data: MD vs. SD ................................................................................................ 61
2.3.6 Combining data – fixed vs. random effects ......................................................................... 61
2.3.7 Calculating the summary effect size .................................................................................... 62
2.3.8 Heterogeneity ...................................................................................................................... 62
2.3.9 Take Home Message ............................................................................................................ 63
2.4 Meta-analysis .............................................................................................................................. 64
2.4.1 Assessing publication bias: funnel plot ................................................................................ 64
5. Lecture – Bayesian inference ............................................................................................................ 66
5.1 Differences between classical frequentists and Bayesian statistical reasoning ......................... 66
5.1.2 Analysis of the cetirizine data. ............................................................................................. 66
5.1.2 Thomas Bayes (1701? – 1761) ............................................................................................. 68
5.2 Example ....................................................................................................................................... 68
5.2.1 Bayesian logic in interpreting laboratory tests. ................................................................... 68
5.2.2 Probability: sets and Venn diagrams. .................................................................................. 71
5.2.3 What is the probability that patient A carries the disease? Bayes’ theorem. .................... 72
5.3 p (A|B) ≠ p (B|A) ......................................................................................................................... 73
5.3.1 An example data set: Data from students in a statistics course, 2010-2011 ...................... 73
5.4 Bottom Lines ............................................................................................................................... 79
Additional: Summary online e-learning module Systematic Reviews of Animal Studies 80
3
STATISTICS 2
Lamker, Patricia
NWI- BB020C
Radboud University, 2022
,Table of Content
1. Lecture - Introduction ......................................................................................................................... 4
1.1 Example I ....................................................................................................................................... 5
1.1.1 Pregnancy outcomes in a study group exposed to cetirizine and a control group ............... 5
1.1.2 How do you look at the data? ................................................................................................ 5
1.1.3 How would you analyse the data? ......................................................................................... 5
1.2 Recapitulation: .............................................................................................................................. 6
1.2.1 Variables: Independent vs. dependent, qualitative vs. quantitative and choice of
statistical tests ................................................................................................................................ 6
1.2.2 Which tests? Analysing differences between sample with one independent variable. ....... 6
1.3 Back to the Example I .................................................................................................................... 6
1.3.1 Analysis of the cetirizine data using a 2 -test of Independence in JASP 0.16 ..................... 6
1.3.2 Analysis and interpretation of the cetirizine data ................................................................. 7
1.4 Example II ...................................................................................................................................... 8
1.4.1 Analysis of the amygdala data using linear regression in JASP 0.16 ...................................... 8
1.5 Why all this stuff about different choices in statistical analysis? ................................................. 9
1.6 Additional Notes ......................................................................................................................... 10
2. Lecture .............................................................................................................................................. 11
2.1 Sex/ Gender Bias ......................................................................................................................... 11
2.2 Factorial Experimental Designs ................................................................................................... 11
2.2.1 Looking for interactions between factors ............................................................................ 11
2.2.2. Analysing factorial experimental designs using contrasts .................................................. 18
2.3 Bottom lines ................................................................................................................................ 21
3. Lecture – Multiple Linear Regression (Spurious relationships, model selection) ............................. 22
3.1 Example “How to win a Nobel Prize” .......................................................................................... 22
3.1.1 Flavonols .............................................................................................................................. 22
3.1.2 Eat chocolate! ...................................................................................................................... 22
...................................................................................................................................................... 22
...................................................................................................................................................... 22
3.1.3 Eat chocolate? ...................................................................................................................... 22
3.1.4 Some context: Nobel laureates by country. ........................................................................ 22
3.1.5 A matter of national development? .................................................................................... 23
3.2 Recap Statistics 1 ........................................................................................................................ 23
3.2.1 A straight line: ...................................................................................................................... 23
3.2.2 Overview of linear regression calculations on a calibration curve: ..................................... 23
1
, 3.2.3 In multiple regression we will try to fit a best fitting hyperplane in more than two
dimensions (1DV, ≥ 2 IVs)............................................................................................................. 24
3.3 Why multiple linear regression? ................................................................................................. 24
3.4 Watch out for: ............................................................................................................................. 24
3.4.1 Simplification by dichotomization ....................................................................................... 24
3.4.2 Model abuse and spurious correlations & correlation =/ causation ................................... 27
3.4.3 The Simpson Paradox – an extreme example of a confounding variable............................ 32
3.5 Bottom lines: ............................................................................................................................... 34
4. Lecture – Power Analysis and Sample Size Calculation .................................................................... 35
4.1 Power Analysis ............................................................................................................................ 35
4.1.1 Biomedical research’s replication crisis ............................................................................... 35
4.2 Sample Size (n) determination .................................................................................................... 37
4.2.1 Example ................................................................................................................................ 37
4.2.2 The power of a statistical test indicates the sensitivity of a test to detect an effect when
there is one. .................................................................................................................................. 39
4.2.3 B – E – A – N – S (more on this later) ................................................................................... 39
4.2.4 How sample size, variability, and significance level affect power of a statistical analysis. 40
4.2.5 How many times will your test give a significant outcome when there is no difference
between groups? .......................................................................................................................... 40
4.2.6 Example – Biological Variation ............................................................................................. 41
4.2 ..................................................................................................................................................... 44
4.2.1 B – E – A – N – S.................................................................................................................... 44
4.2.2 Randomization and Stratification ........................................................................................ 48
4.3 Sample size calculations and power analyses using G*Power ................................................... 48
4.3.1 The bottom line when it comes to sample size: .................................................................. 49
4.3.2 Size does matter! ................................................................................................................. 49
4.3.3 Rule of thumb assuming a normal distribution ................................................................... 49
4.3.4 Formal calculation using the t-distribution .......................................................................... 50
4.3.5 Six approaches to justify sample sizes ................................................................................. 50
4.3.6 Six possible ways to think about effect size ......................................................................... 51
1. Guest Lecture – Dokter Media .......................................................................................................... 52
2. Guest Lecture – Syrcle....................................................................................................................... 54
2.1 Introduction to systematic reviews on animal studies ............................................................... 54
2.1.1 Steps of a systematic review ................................................................................................ 54
2.1.2 Benefits of preclinical SRs .................................................................................................... 54
2.1.3 Study Quality ........................................................................................................................ 55
2
, 2.1.4 Forest Plot ............................................................................................................................ 55
2.1.5 Subgroup Analysis ................................................................................................................ 56
2.1.6 Tools per phase .................................................................................................................... 56
2.2 Practical Data Extraction ............................................................................................................. 57
2.2.1 Types of outcome measures ................................................................................................ 57
2.2.2 Assignment – extracting outcome data ............................................................................... 57
2.2.3 Take Home Message ............................................................................................................ 59
2.3 Data-analysis and Meta-analysis................................................................................................. 60
2.3.1 Data-analysis or meta-analysis ............................................................................................ 60
2.3.2 Meta-analysis ........................................................................................................................... 60
2.3.3 From study data to forest plot ............................................................................................. 60
2.3.4 Choosing your effect size measure. continuous data .......................................................... 60
2.3.5 Continuous Data: MD vs. SD ................................................................................................ 61
2.3.6 Combining data – fixed vs. random effects ......................................................................... 61
2.3.7 Calculating the summary effect size .................................................................................... 62
2.3.8 Heterogeneity ...................................................................................................................... 62
2.3.9 Take Home Message ............................................................................................................ 63
2.4 Meta-analysis .............................................................................................................................. 64
2.4.1 Assessing publication bias: funnel plot ................................................................................ 64
5. Lecture – Bayesian inference ............................................................................................................ 66
5.1 Differences between classical frequentists and Bayesian statistical reasoning ......................... 66
5.1.2 Analysis of the cetirizine data. ............................................................................................. 66
5.1.2 Thomas Bayes (1701? – 1761) ............................................................................................. 68
5.2 Example ....................................................................................................................................... 68
5.2.1 Bayesian logic in interpreting laboratory tests. ................................................................... 68
5.2.2 Probability: sets and Venn diagrams. .................................................................................. 71
5.2.3 What is the probability that patient A carries the disease? Bayes’ theorem. .................... 72
5.3 p (A|B) ≠ p (B|A) ......................................................................................................................... 73
5.3.1 An example data set: Data from students in a statistics course, 2010-2011 ...................... 73
5.4 Bottom Lines ............................................................................................................................... 79
Additional: Summary online e-learning module Systematic Reviews of Animal Studies 80
3
