,Part 1 – Describing Data.............................................................................................................3
Chapter 1 – STATS ON THE BEACH: Variables and Distributions............................................3
Chapter 2 – A NIGHT IN NEON: Comparing Groups...............................................................9
Chapter 3 – BIG TOP BONANZA: Quantitative Relationships...............................................15
Part 2 – Methodology and Psychometrics...............................................................................20
Chapter 4 – DREAMS OF THE ANCIENTS: Research Methods..............................................20
Chapter 5 – A FLUFFY FAREWELL: Inter-Rater Agreement...................................................28
Part 3 – Probabilities and Generalising....................................................................................31
Chapter 6 – DAYS DOWN UNDER: Probability Theory..........................................................31
Chapter 7 – HONOUR AMONG THIEVES: Discrete Distributions..........................................35
Chapter 8 – THE SILENT SHADOW: Continuous Distributions..............................................40
Chapter 9 – MAROONED WITH THE MONKEYS: Populations and Samples.........................43
Chapter 10 – UP TO THE STARS: Statistical Inference...........................................................47
Part 4 – Comparing Means.......................................................................................................52
Chapter 11 – TOWEL DAY: The One-Sample t-Test...............................................................52
Chapter 12 – FUR AND FURY: The Paired-Samples t-Test.....................................................55
Chapter 13 – A BRUSH WITH DATA: The Independent-Samples t-Test................................58
Chapter 14 – THE HERO’S CALLING: Tests for Frequency Tables..........................................63
Chapter 15 – SLAYING THE BEAST: Tests for Contingency Tables.........................................67
Part 6 – Regression...................................................................................................................69
Chapter 16 – THE SILVER HAVEN: Simple Regression...........................................................69
Part 7 – Building Bridges...........................................................................................................74
Chapter 17 – ZEALOTRY SQUARED: z-Tests for Proportions and χ²-Tests.............................74
Chapter 18 – TOOTHPASTE ON A SLOPE: t-Tests and Regression.........................................76
Chapter 19 – NUTS AND BOLTS: Advanced Data Analysis....................................................78
Chapter 20 – AGE OF THE SAVIOUR: ANOVA.......................................................................82
,Part 1 – Describing Data
Chapter 1 – STATS ON THE BEACH: Variables and Distributions
1.1 Types of Data – A Hot Topic
Statistical analysis begins with identifying the type of variable being measured. The measurement level
determines which summaries, graphs and statistical procedures are mathematically appropriate.
1.1.1 Categorical Variables
Categorical variables classify observations into groups rather than measuring numerical magnitude.
Nominal variables have categories without an intrinsic order, such as:
Gender category
Study programme
Blood type
Country of residence
Ordinal variables have an ordered structure, but the distances between categories cannot necessarily be
interpreted as equal.
Examples include:
Low, moderate, high
Strongly disagree to strongly agree
Educational attainment levels
For categorical data, frequencies and proportions are usually more informative than means.
1.1.2 Quantitative Variables
Quantitative variables represent numerical quantities for which arithmetic operations have substantive
meaning.
Two important forms are:
1. Discrete variables – values arise from counting, such as number of visits or number of errors.
2. Continuous variables – values arise from measurement and can theoretically take any value within an
interval, such as height, reaction time or temperature.
The distinction matters because continuous measurements can contain decimal values and are commonly
summarized using distributions, means and measures of variability.
1.1.3 Measurement Levels
A useful classification distinguishes four measurement levels:
Nominal: categories only
Ordinal: ordered categories
Interval: equal numerical intervals but no meaningful absolute zero
, Ratio: equal intervals plus a meaningful zero
Ratio-scale variables support meaningful statements about ratios. For example, 20 kg represents twice the
mass of 10 kg.
1.1.4 Variables in Statistical Research
A variable may represent an outcome, predictor or descriptive characteristic.
In an observational study, for example:
Outcome variable: examination score
Predictor variable: study hours
Categorical variable: programme type
Control variable: age
Correctly identifying the variable structure is essential before choosing an analytical method.
1.2 Tables and Graphs – Crystal-Clear Water
Tables and graphs transform raw observations into a form that makes patterns, differences and unusual
observations easier to identify.
1.2.1 Frequency Tables
A frequency table summarizes how often each value or category occurs.
For a category with frequency f iin a sample of size n , the relative frequency is:
fi
pi =
n
and the percentage is:
100 p i
For continuous variables, values are often grouped into intervals rather than displaying every individual
observation.
1.2.2 Graphical Displays
The graph should correspond to the structure of the variable.
Bar chart: categorical variables
Histogram: quantitative distributions
Boxplot: centre, spread and potential outliers
Scatterplot: relationship between two quantitative variables
A histogram differs fundamentally from a bar chart: histogram bars represent adjacent numerical intervals,
whereas bar-chart categories are distinct groups.
1.2.3 Histograms
A histogram divides quantitative observations into bins. The resulting shape depends partly on bin width.
Chapter 1 – STATS ON THE BEACH: Variables and Distributions............................................3
Chapter 2 – A NIGHT IN NEON: Comparing Groups...............................................................9
Chapter 3 – BIG TOP BONANZA: Quantitative Relationships...............................................15
Part 2 – Methodology and Psychometrics...............................................................................20
Chapter 4 – DREAMS OF THE ANCIENTS: Research Methods..............................................20
Chapter 5 – A FLUFFY FAREWELL: Inter-Rater Agreement...................................................28
Part 3 – Probabilities and Generalising....................................................................................31
Chapter 6 – DAYS DOWN UNDER: Probability Theory..........................................................31
Chapter 7 – HONOUR AMONG THIEVES: Discrete Distributions..........................................35
Chapter 8 – THE SILENT SHADOW: Continuous Distributions..............................................40
Chapter 9 – MAROONED WITH THE MONKEYS: Populations and Samples.........................43
Chapter 10 – UP TO THE STARS: Statistical Inference...........................................................47
Part 4 – Comparing Means.......................................................................................................52
Chapter 11 – TOWEL DAY: The One-Sample t-Test...............................................................52
Chapter 12 – FUR AND FURY: The Paired-Samples t-Test.....................................................55
Chapter 13 – A BRUSH WITH DATA: The Independent-Samples t-Test................................58
Chapter 14 – THE HERO’S CALLING: Tests for Frequency Tables..........................................63
Chapter 15 – SLAYING THE BEAST: Tests for Contingency Tables.........................................67
Part 6 – Regression...................................................................................................................69
Chapter 16 – THE SILVER HAVEN: Simple Regression...........................................................69
Part 7 – Building Bridges...........................................................................................................74
Chapter 17 – ZEALOTRY SQUARED: z-Tests for Proportions and χ²-Tests.............................74
Chapter 18 – TOOTHPASTE ON A SLOPE: t-Tests and Regression.........................................76
Chapter 19 – NUTS AND BOLTS: Advanced Data Analysis....................................................78
Chapter 20 – AGE OF THE SAVIOUR: ANOVA.......................................................................82
,Part 1 – Describing Data
Chapter 1 – STATS ON THE BEACH: Variables and Distributions
1.1 Types of Data – A Hot Topic
Statistical analysis begins with identifying the type of variable being measured. The measurement level
determines which summaries, graphs and statistical procedures are mathematically appropriate.
1.1.1 Categorical Variables
Categorical variables classify observations into groups rather than measuring numerical magnitude.
Nominal variables have categories without an intrinsic order, such as:
Gender category
Study programme
Blood type
Country of residence
Ordinal variables have an ordered structure, but the distances between categories cannot necessarily be
interpreted as equal.
Examples include:
Low, moderate, high
Strongly disagree to strongly agree
Educational attainment levels
For categorical data, frequencies and proportions are usually more informative than means.
1.1.2 Quantitative Variables
Quantitative variables represent numerical quantities for which arithmetic operations have substantive
meaning.
Two important forms are:
1. Discrete variables – values arise from counting, such as number of visits or number of errors.
2. Continuous variables – values arise from measurement and can theoretically take any value within an
interval, such as height, reaction time or temperature.
The distinction matters because continuous measurements can contain decimal values and are commonly
summarized using distributions, means and measures of variability.
1.1.3 Measurement Levels
A useful classification distinguishes four measurement levels:
Nominal: categories only
Ordinal: ordered categories
Interval: equal numerical intervals but no meaningful absolute zero
, Ratio: equal intervals plus a meaningful zero
Ratio-scale variables support meaningful statements about ratios. For example, 20 kg represents twice the
mass of 10 kg.
1.1.4 Variables in Statistical Research
A variable may represent an outcome, predictor or descriptive characteristic.
In an observational study, for example:
Outcome variable: examination score
Predictor variable: study hours
Categorical variable: programme type
Control variable: age
Correctly identifying the variable structure is essential before choosing an analytical method.
1.2 Tables and Graphs – Crystal-Clear Water
Tables and graphs transform raw observations into a form that makes patterns, differences and unusual
observations easier to identify.
1.2.1 Frequency Tables
A frequency table summarizes how often each value or category occurs.
For a category with frequency f iin a sample of size n , the relative frequency is:
fi
pi =
n
and the percentage is:
100 p i
For continuous variables, values are often grouped into intervals rather than displaying every individual
observation.
1.2.2 Graphical Displays
The graph should correspond to the structure of the variable.
Bar chart: categorical variables
Histogram: quantitative distributions
Boxplot: centre, spread and potential outliers
Scatterplot: relationship between two quantitative variables
A histogram differs fundamentally from a bar chart: histogram bars represent adjacent numerical intervals,
whereas bar-chart categories are distinct groups.
1.2.3 Histograms
A histogram divides quantitative observations into bins. The resulting shape depends partly on bin width.
