Statistics at Square One

Cover
Title Page
Copyright Page
Contents
Preface
About the companion website
Chapter 1 Understanding basic numbers
	When is a number large?
	Ratios
	Using ratios to adjust for other variables
	Proportions, percentages and odds
	Percentage difference and percentage change: importance of baseline
	Rounding proportions and percentages
	Probabilities and risks
	Prevalence and incidence rate
	Trusting numbers
	Conclusions
	Further reading
	Exercises
	References
Chapter 2 Data display and summary
	Types of data
	Stem-and-leaf plots and dot plots
	Box-whisker plots
		Median
		Measures of variation
	Frequency tables and histograms
	Bar charts
	Further reading
	Common questions
		What is the distinction between a histogram and a bar chart?
		What are poor methods of displaying data?
	Displaying data in papers
	Exercises
	References
Chapter 3 Summary statistics for quantitative data
	Mean
	Variance and standard deviation
		Standard deviation from ungrouped data
		Standard deviation from grouped data
	Normal distribution
	Skewness
	Between-subjects and within-subjects standard deviation
	Common questions
		When should I quote the mean and when should I quote the median to describe my data?
		When should I use a standard deviation to summarise variability?
		How can I tell if data are skewed from a table?
		When should I use the mode?
	Formula appreciation
	Reading and Displaying Summary Statistics
		Exercises
	References
Chapter 4 Summary statistics for binary data
	Summarising one binary variable
	Summarising the relationship between two binary variables
		Relative Risks versus Odds Ratios
	Odds ratios and cross-sectional studies
	Odds ratios and case–control studies
		Example of a case–control study
		Estimating relative risk from case–control studies
	Common questions
		When should I quote an odds ratio and when should I quote a relative risk?
		How does one choose the numerator and denominator for a relative risk?
		How should one quote relative risks?
		Should one ever quote a number needed to treat?
	Reading and displaying summary statistics
	Exercises
	References
Chapter 5 Diagnostic and screening tests
	Diagnostic and screening tests
	Examples
		Example 1: Test for COVID-19
		Example 2: Test for generalised anxiety disorder
	Sensitivity and Specificity
	Positive predictive value in relation to prevalence
	Likelihood ratio
	Receiver operating characteristics curves
	Further discussion on diagnostic and screening tests
	Limitations of the conventional diagnostic testing paradigm
	Reading and reporting diagnostic/screening tests
	Exercises
	References
Chapter 6 Populations and samples
	Populations
	Samples
	Unbiasedness and precision
	Problems of bias in non-randomised samples (especially Big Data)
	Randomisation
	Variation between samples
	Standard error of the mean
	Example of standard error
	Standard error of a proportion or a percentage
	Problems with non-random samples
	Common questions
		What is an acceptable response rate from a survey?
		Given measurements on a sample, what is the difference between a standard deviation and a standard error?
		When should I use a standard deviation to describe data and when should I use a standard error?
	Important points
	Reading and reporting populations and samples
	Exercises
	References
Chapter 7 Statements of probability and confidence intervals
	Reference ranges
	Confidence intervals
	Large sample standard error of difference between means
	Large sample confidence interval for the difference in two means
	Standard error of difference between percentages or proportions
	Confidence interval for a difference in proportions or percentages
	Confidence interval for an odds ratio
	Confidence interval for a relative risk
	Confidence Intervals for other estimates
	Common Questions
		What is the difference between a reference range and a confidence interval?
		If I repeated a study with the same sample size, would the new results fall in the confidence interval 95% of the time?
	Reading and reporting confidence intervals
	Formula appreciation
	Exercises
	References
Chapter 8 P values, power, type I and type II errors
	Null hypothesis and type I error
	Testing for differences of two means
	Testing for a difference in two proportions
	P value
	P values, confidence intervals and clinically important results
	Alternative hypothesis and type II error
	Other types of statistical inference
	Issues with P values
	One-sided and two-sided tests
	Tests for superiority, tests for non-inferiority and tests for equivalence
	Links with diagnostic tests
	Common questions
		Why is the P value not the probability that the null hypothesis is true?
		Why is 5% usually used as the level at which results are deemed ‘significant’?
	Reading and reporting significance tests
	Exercises
	References
Chapter 9 Tests for differences between two groups of a quantitative outcome with small samples
	Student’s t test
	Confidence interval for the mean from a small sample
	Difference of sample mean from population mean (one-sample t test)
	Difference between means of two samples
	Unequal standard deviations
	Difference between means of paired samples (paired t test)
	Non-parametric or distribution-free tests
	Tests for differences in unpaired samples of non-Normally distributed data (Mann–Whitney U test)
	Tests for differences in paired samples of non-Normally distributed data (Wilcoxon test)
	Computer-intensive methods
		Permutation tests: unpaired tests
		Permutation tests: paired tests
		The bootstrap
	Discussion
	Reading and reporting t tests and non-parametric tests
	Common questions
		Should I test my data for Normality before using the t test?
		Should I test for equality of the standard deviations before using the usual t test?
		Why should I use a paired test if my data are paired? What happens if I don’t?
		Do non-parametric tests compare medians?
		How is the Mann–Whitney U test related to the t test?
		How is the Mann–Whitney U test related to the area under the receiver operating characteristics curve of Chapter 5?
	References
Chapter 10 Tests for association in binary and categorical data
	General chi-squared test
	2 × 2 tables
		Small numbers: Yates’ correction, Fisher’s Exact Test and the permutation test
	2 test for trend
	Comparison of an observed and a theoretical distribution
	Tests for paired binary data
	Examples of a paired comparison
	Extensions of the 2 test
	Common questions
		There are a number of tests of association for a 2 × 2 table. Which should I choose?
		I have matched data, but the matching criteria were very weak. Should I use McNemar’s test?
		Do chi-squared tests apply to large contingency tables?
		Is the chi-squared test a non-parametric test?
	Formula appreciation
	Reading and reporting chi-squared tests
	Exercises
	References
Chapter 11 Correlation and regression
	The correlation coefficient
	Looking at data: scatter diagrams
	Calculation of the correlation coefficient
	Significance test for a correlation coefficient
	Spearman rank correlation
	The regression equation
	Simple checks of the model
	Using regression in t tests
	More advanced methods
	Common questions
		If two variables are correlated, are they causally related?
		How do I test the assumptions underlying linear regression?
		When should I use correlation and when should I use regression?
		Which are the important assumptions for linear regression?
	Formula appreciation
	Reading and reporting correlation and regression
	Exercises
	References
Chapter 12 Survival analysis
	Why survival analysis is different
	Kaplan–Meier survival curve
	Example of calculation of survival curve
	The log rank test
	Further methods
	Common questions
		Do I need to test for a constant relative risk before doing the log rank test?
		If I don’t have any censored observations, do I need to use survival analysis?
		How does the hazard calculated under the log rank compare with the usual estimate of risk?
	Reading and reporting survival analysis
	Exercises
	References
Chapter 13 Modelling data
	Basics
	Models
	Model fitting and analysis: exploratory and confirmatory analyses
	Bayesian methods
	Models generally
		X1 binary and X2 binary
		X1 continuous and X2 continuous
		X1 binary and X2 continuous
	Multiple linear regression
	Example linear regression
		Paper critique
	Logistic regression
		Logistic regression instead of a chi-squared test
		Example of logistic regression from the literature
		Paper critique
	Survival analysis
		Proportional hazards models
		Proportional hazards model instead of log rank
		Example of proportional hazards model
		Paper critique
	Other things to consider in modelling
	References
Chapter 14 Study design and choosing a statistical test
	Design
	Sample size
	Choice of test
	Reading and reporting on the design of a study
	Further reading
	Exercises
	References
Chapter 15 Use of computer software
	Chapter 2: Data display and summary
		Figure 2.2
		Figure 2.3
		Medians and five number summary
		Figure 2.4
		Figure 2.5
		Figure 2.6
		Figure 2.7
		Exercise 2.2
	Chapter 3: Summary statistics for quantitative data
		Table 3.1
		Table 3.2
		Exercise 3.1
		Exercise 3.2
	Chapter 4: Summary statistics for binary data
		Table 4.2
		Table 4.4
		Table 4.8
	Chapter 5: Diagnostic and screening tests
		Table 5.2
		Table 5.3
		Figure 5.3
	Chapter 6: Populations and samples
	Chapter 7: Statements of probability and confidence intervals
		Figure 7.1
		Exercise 7.3
	Chapter 8: P values, power, type I and type II errors
		Figure 8.2
	Chapter 9: Tests for differences between two groups of a quantitative outcome with small samples
		Tables 9.1 and 9.6
		Table 9.2
		Table 9.3
		Table 9.5
		Table 9.7
		Exercise 9.7
	Chapter 10: Tests for association in binary and categorical data
		Tables 10.1, 10.3 and 10.4
	Table 10.8
	Chapter 11: Correlation and regression
		Exercise 11.2
	Chapter 12: Survival analysis
		Figure 12.2
	Chapter 13: Modelling data
		Figure 13.1
	Appendix
		Table A
	Software packages
	References
Answers to exercises
Glossary of statistical terms
Appendix
Index
EULA