This accessible introductory textbook provides a straightforward, practical explanation of how statistical analysis and error measurements should be applied in biological research.

Table of Contents

• Introduction
• Why do we need to evaluate errors?
• Probability distributions
• Random variables
• What is a probability distribution?
• Mean, median, variance and standard deviation
• Gaussian distribution
• Central limit theorem
• Log-normal distribution
• Binomial distribution
• Poisson distribution
• Student's t-distribution
• Measurement errors
• Where do errors come from?
• Simple model of random measurement errors
• Intrinsic variability
• Sampling error
• Simple measurement errors
• Statistical estimators
• Population and sample
• What is a statistical estimator?
• Estimator bias
• Commonly used statistical estimators
• Standard error
• Standard error of the weighted mean
• Error in the error
• Degrees of freedom
• Confidence intervals
• Sampling distribution
• Confidence interval: what does it really mean?
• Why 95%?
• Confidence interval of the mean
• Standard error versus confidence interval
• Confidence interval of the median
• Confidence interval of the correlation coefficient
• Confidence interval of a proportion
• Confidence interval for count data
• Bootstrapping
• Replicates
• Error bars
• Designing a good plot
• Error bars in plots
• When can you get away without error bars?
• Quoting numbers and errors
• Summary
• Propagation of errors
• What is propagation of errors?
• Single variable
• Multiple variables
• Correlated variables
• To use error propagation or not?
• Example: distance between two dots
• Derivation of the error propagation formula for one variable
• Derivation of the error propagation formula for multiple variables
• Errors in simple linear regression
• Linear relation between two variables
• Straight line fit
• Confidence intervals of linear fit parameters
• Linear fit prediction errors
• Regression through the origin
• General curve fitting
• Derivation of errors on fit parameters
• Worked example
• The experiment
• Results
• Discussion
• The final paragraph
• Solutions to exercises
• Appendix A
• Bibliography