1 Descriptive Statistics I: Univariate Statistics
1.1 Introduction
1.2 Types of Statistical Data
1.3 Univariate Data Visualisation
1.3.1 Dotplot
1.3.2 Histogram
1.3.3 Bar Chart
1.4 Measures of Central Tendency
1.4.1 Mean
1.4.2 Median
1.4.3 Mode
1.4.4 Calculating Measures of Central Tendency in MATLAB
1.4.5 Which Measure to Use?
1.5 Measures of Variation
1.5.1 Standard Deviation
1.5.2 Inter-Quartile Range
1.5.3 Calculating Measures of Variation in MATLAB
1.5.4 Which Measure of Variation to Use?
1.6 Visualising Measures of Variation
1.6.1 Visualising Mean and Standard Deviation
1.6.2 Visualising Median and IQR: the Box Plot
1.7 Summary
1.8 Further Resources
1.9 Exercises
2 Descriptive Statistics II: Bivariate Statistics
2.1 Introduction
2.2 Visualising Bivariate Statistics
2.2.1 Two Categorical Variables
2.2.2 Combining Categorical and Continuous Variables
2.2.3 Two Continuous Variables
2.2.4 General Comments on Choice of Visualisation
2.3 Pearson’s Correlation Coefficient
2.3.1 Example Use of Pearson’s Correlation Coefficient
2.3.2 p-values and Correlation Coefficient Values
2.4 Spearman’s Rank Correlation Coefficient
2.4.1 Example Use of Spearman’s Rank Correlation Coefficient
2.5 Which Measure of Correlation to Use?
2.6 Regression Analysis
2.6.1 Calculating the Equation of Best Fit Line Using MATLAB
2.6.2 Plotting the Best Fit Line
2.6.3 Using the Best Fit Line to Make Predictions
2.6.4 Fitting Non-linear Models
2.6.5 Fitting Higher Order Polynomials
2.7 Summary
2.8 Further Resources
2.9 Exercises
3 Descriptive Statistics III: ROC Analysis
3.1 Introduction
3.2 Notation
3.2.1 Sensitivity and Specificity
3.2.2 Positive and Negative Predictive Values
3.2.3 Example Calculation of Se, Sp, PPV and NPV
3.3 ROC Curves
3.4 Exercise
3.5 Recap on Scripts and Functions
3.6 Case Study: ROC Analysis
3.7 Summary
3.8 Further Resources
4 Inferential Statistics I: Basic Concepts
4.1 Introduction
4.2 Probability
4.2.1 Probabilities of Single Events
4.2.2 Probabilities of Multiple Events
4.3 Probability Distributions
4.3.1 Why the Normal Distribution is so Important: The
Central Limit Theorem
4.4 Standard Error of Mean
4.5 Confidence Intervals of Mean
4.6 Summary
4.7 Further Resources
4.8 Exercises
5 Inferential Statistics II: Parametric Hypothesis Testing
5.1 Introduction
5.2 Hypothesis Testing
5.2.1 Types of Data for Hypothesis Tests
5.3 The t-distribution and Student's t-test
5.4 One Sample Student’s t-test
5.5 Confidence Intervals for Small Samples
5.6 Two Sample Student’s t-test
5.6.1 Paired Data
5.6.2 Unpaired Data
5.6.3 Paired vs. Unpaired t-test
5.7 1-tailed vs. 2-tailed Tests
5.8 Summary
5.9 Further Resources
5.10 Exercises
6 Inferential Statistics III: Nonparametric Hypothesis Testing
6.1 Introduction
6.2 Sign Test
6.3 Wilcoxon Signed Rank Test
6.4 Mann-Whitney U test
6.5 Chi Square Hypothesis Test for Categorical Variables
6.6 Summary
6.7 Further Resources
6.8 Exercises
7 Inferential Statistics IV: Choosing a Hypothesis Test
7.1 Introduction
7.2 Visual Methods to Investigate Whether Sample Fits a Normal
Distribution
7.3 Numerical Methods to Investigate Whether Sample Fits a Normal Distribution
7.3.1 Probability Plot Correlation Coefficient
7.3.2 Comparing the Skews
7.3.3 Z-values
7.3.4 Shapiro-Wilk Test
7.3.5 Chi Square Test for Normality
7.4 So Should We Use a Parametric or Nonparametric Test?
7.5 Does it Matter if We Use the Wrong Test?
7.6 Summary
7.7 Further Resources
7.8 Exercises
8 Inferential Statistics V: Multiple Hypothesis Testing
8.1 Introduction
8.2 Bonferroni’s Correction
8.3 Analysis of Variance (ANOVA)
8.3.1 One Way ANOVA
8.3.2 Two Way ANOVA
8.4 Summary
8.5 Further Resources
8.6 Exercises
9 Experimental Design and Sample Size Calculations
9.1 Introduction
9.2 Experimental and Observational Studies
9.3 Random and Systematic Error (Bias)
9.4 Methods to Reduce Random and Systematic Errors
9.4.1 Blocking (Matching) Test and Control Subjects
9.4.2 Blinding
9.4.3 Multiple Measurement
9.4.4 Randomisation
9.5 Sample Size and Power Calculations
9.5.1 Illustration Power Calculation for Single Sample t-test
9.5.2 Illustration of a Sample Size Calculation
9.5.3 Power and Sample Size Calculations in MATLAB
9.6 Summary
9.7 Further Resources
9.8 Exercises
9.9 Experimental Design Case Studies
10 Statistical Shape Models
10.1 Introduction
10.2 SSMs and Dimensionality Reduction
10.3 Forming an SSM
10.3.1 Parameterise the Shape
10.3.2 Align the Centroids
10.3.3 Compute the Mean Shape Vector
10.3.4 Compute the Covariance Matrix
10.3.5 Compute the Eigenvectors and Eigenvalues
10.4 Producing New Shapes from an SSM
10.5 Biomedical Applications of SSMs
10.6 Summary
10.7 Further Resources
10.8 Exercises
11 Case Study on Descriptive and Inferential Statistics
11.1 Introduction
11.2 Data
11.3 Part A: Measuring Myocardium Thickness
11.4 Part B: Intra-observer Variability
11.5 Part C: Sample Analysis
11.6 Summary
11.7 Further Exercises
