Preface
How to use this book
Packages used
Example data
Acknowledgements
1 - Eight steps to successful data analysis
2 - The basics
Observations
Hypothesis testing
P-values
Sampling
Experiments
Statistics:
Descriptive statistics
Tests of difference
Tests of relationships
Tests for data investigation
3 - Choosing a test: a key
Remember - eight steps to successful data analysis
The art of choosing a test
A key to assist in your choice of statistical test
4 - Hypothesis testing, sampling and experimental design
Hypothesis testing
Acceptable errors
P-values
Sampling
Choice of sample unit
Number of sample units
Positioning of sample units to achieve a random sample
Timing of sampling
Experimental design
Control
Procedural controls
Temporal control
Experimental control
Statistical control
Some standard experimental designs
5 - Statistics, variables and distributions
What are statistics?
Types of statistics
Descriptive statistics
Parametric statistics
Non-parametric statistics
What is a variable?
Types of variables or scales of measurement
Measurement variables
Continuous variables
Discrete variables
How accurate do I need to be?
Ranked variables
Attributes
Derived variables
Types of Distributions
Why do you need to know about distributions?
Discrete distributions
Poisson distribution
Binomial distribution
Negative binomial distribution
Hypergeometric distribution
Continuous distributions
Rectangular distribution
Normal distribution
Standardised normal distribution
Convergence of a Poisson distribution to a normal distribution
Sampling distributions and the âcentral limit theoremâ
Describing the normal distribution further
Skewness
Kurtosis
Is a distribution normal?
Transformations
Angular transformation
Logit transformation
t-distribution
Confidence intervals
Chi-square distribution
Exponential distribution
Non-parametric âdistributionsâ
Ranking, quartiles and the inter-quartile range
Box and whisker Plots
6 - Descriptive and presentational techniques
General advice
Displaying data: summarising a single variable
Box and whisker (Box plot)
Displaying data: showing the distribution of a single variable
Bar chart
Histogram
Number of classes to display in a histogram
Pie chart
Descriptive statistics
Statistics of location
Arithmetic mean
Geometric mean
Harmonic mean
Median
Mode
Statistics of distribution, dispersion or spread
Range
Interquartile range
Variance
Standard deviation
Standard error
Confidence intervals
Coefficient of variation
Other summary statistics
Skewness
Kurtosis
Using the computer packages
Displaying data: summarising two or more variables
Box and whisker (box plots)
Error bars and confidence intervals
Displaying data: comparing two variables
Associations
Scatterplots
Multiple scatterplots
Trends, predictions and time series
Lines
Fitted lines
Confidence intervals
Displaying data: comparing more than two variables
Associations
Three-dimensional scatterplots
Multiple trends, time series and predictions
Multiple fitted lines
Surfaces
7 - The tests 1: tests to look at differences
Do frequency distributions differ?
Questions
G-test
Chi-square test (ï£2)
Kolmogorov-Smirnov test
Anderson-Darling test
Shapiro-Wilk test
Do the observations from two groups differ?
Paired data
Paired t-test
Wilcoxonâs signed ranks test
Sign test
Unpaired data
T-test
One-way ANOVA
Mann-Whitney U
Do the observations from more than two groups differ?
Repeated measures
Friedman test (for repeated measures)
Repeated measures ANOVA
Independent samples
One-way ANOVA
Post hoc testing: after one-way ANOVA
Kruskal-Wallis test
Post hoc testing: after the Kruskal-Wallis test
There are two independent ways of classifying the data
One observation for each factor combination (no replication)
Friedman test
Two-way ANOVA (without replication)
More than one observation for each factor combination (with replication)
Interaction
Two-way ANOVA (with replication)
Scheirer-Ray-Hare test
There are more than two independent ways to classify the data
Multi-factorial testing
Three-way ANOVA (without replication)
Three-way ANOVA (with replication)
Multi-way ANOVA
Not all classifications are independent
Non-independent factors
Nested factors
Random or fixed factors
Nested / hierarchical designs
Two-level nested design ANOVA
8 â" The tests 2: tests to look at relationships
Is there a correlation or association between two variables?
Observations assigned to categories
Chi-square test of association
Cram©r coefficient of association
Phi coefficient of association
Observations assigned a value
âStandardâ correlation (Pearsonâs product-moment correlation)
Spearmanâs rank-order correlation
Kendallâs rank-order correlation
Is there a âcause and effectâ relationship between two variables?
Questions
âStandardâ linear regression
Prediction
Interpreting r2
Comparison of regression and correlation
Residuals
Confidence intervals
Prediction intervals
Kendallâs robust line-fit method
Jonckheer-Terpstra test
Logistic regression
Model II regression
Polynomial, cubic and quadratic regression
Tests for more than two variables
Tests of association
Questions
Correlation
Partial correlation
Kendallâs partial rank-order correlation
Cause(s) and effect(s)
Questions.
Regression
ANCOVA (analysis of covariance)
Multiple regression
Stepwise regression
Path analysis
9 - The tests 3: tests for data exploration
Types of data
Observation, inspection and plotting
Principal component and factor analysis (PCA)
Canonical variate analysis (CVA)
Discriminant function analysis
Multivariate analysis of variance (MANOVA)
Multivariate analysis of covariance (MANCOVA)
Cluster analysis
10 - Symbols and letters used in statistics
Greek letters
Symbols
Upper case letters
Lower case letters
11 - Glossary
12 - Assumptions of the tests
Test by test list of assumptions
What if the assumptions are violated?
13 - Hints and tips
Using a computer
Sampling
Statistics
Displaying the data
14 - A table of statistical tests
