Understanding Statistical Error: A Primer for Biologists

Editor/Author Gierlinski, Marek
Publication Year: 2016
Publisher: Wiley

ISBN: 978-1-119-10691-3
Category: Mathematics & Statistics - Statistics
Image Count: 68
Book Status: Pending
Predicted Release Month: March 2019
Table of Contents

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

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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