The Sampling Lab

Sources and simplifications

Every reference cited on this site, and every place a figure idealizes the real system.

References

  1. Pearson, K. (1894). Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society of London A 185, 71–110. doi:10.1098/rsta.1894.0003. primary Introduces the term “standard deviation”. (Standard deviation)
  2. NIST/SEMATECH (2012). NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.6 Measures of Scale. National Institute of Standards and Technology. standard (Standard deviation)
  3. Rice, J. A. (2007). Mathematical Statistics and Data Analysis, 3rd edition. Duxbury (Thomson Brooks/Cole). ISBN 978-0-534-39942-9. textbook Ch. 2–4 (distributions, moments), §5.3 (central limit theorem), ch. 7 (survey sampling, the n − 1 divisor), ch. 9 (testing). (Standard deviation)
  4. Chan, T. F., Golub, G. H. & LeVeque, R. J. (1983). Algorithms for computing the sample variance: analysis and recommendations. The American Statistician 37(3), 242–247. doi:10.1080/00031305.1983.10483115. primary (Standard deviation)
  5. Welford, B. P. (1962). Note on a method for calculating corrected sums of squares and products. Technometrics 4(3), 419–420. doi:10.1080/00401706.1962.10490022. primary (Standard deviation)
  6. Stigler, S. M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Belknap Press of Harvard University Press. ISBN 978-0-674-40341-3. scholarship Ch. 2 (de Moivre’s normal approximation, 1733), ch. 4 (Laplace and the central limit theorem), ch. 8 (Galton). (Standard deviation)
  7. Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh (ch. III, §12, p. 47). primary (Standard deviation)
  8. NIST/SEMATECH (2012). NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.6.6.1 Normal Distribution. National Institute of Standards and Technology. standard (Normal & z-scores)
  9. Olver, F. W. J. et al. (eds.) (2024). NIST Digital Library of Mathematical Functions, §7.9 Error functions: continued fractions. National Institute of Standards and Technology. standard (Normal & z-scores)
  10. Pukelsheim, F. (1994). The three sigma rule. The American Statistician 48(2), 88–91. doi:10.1080/00031305.1994.10476030. primary (Normal & z-scores)
  11. NIST/SEMATECH (2012). NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.6.7.1 Cumulative Distribution Function of the Standard Normal Distribution. National Institute of Standards and Technology. standard (Normal & z-scores)
  12. Pearson, K. (1920). Notes on the history of correlation. Biometrika 13(1), 25–45. doi:10.1093/biomet/13.1.25. primary p. 25: Pearson recalls naming the Laplace–Gaussian curve the “normal” curve and regrets that the name suggests other distributions are abnormal. Added by the verifier. (Normal & z-scores)
  13. Galton, F. (1889). Natural Inheritance. Macmillan, London (ch. V, the apparatus later called the Galton board). primary (Binomial & Poisson)
  14. NIST/SEMATECH (2012). NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.6.6.18 Binomial Distribution. National Institute of Standards and Technology. standard (Binomial & Poisson)
  15. NIST/SEMATECH (2012). NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.6.6.19 Poisson Distribution. National Institute of Standards and Technology. standard (Binomial & Poisson)
  16. Le Cam, L. (1960). An approximation theorem for the Poisson binomial distribution. Pacific Journal of Mathematics 10(4), 1181–1197. doi:10.2140/pjm.1960.10.1181. primary (Binomial & Poisson)
  17. Quine, M. P. & Seneta, E. (1987). Bortkiewicz’s data and the law of small numbers. International Statistical Review 55(2), 173–181. doi:10.2307/1403193. scholarship (Binomial & Poisson)
  18. Freedman, D., Pisani, R. & Purves, R. (2007). Statistics, 4th edition. W. W. Norton. ISBN 978-0-393-92972-0. textbook Ch. 4 (the standard deviation), ch. 5 (the normal approximation), ch. 16–18 (chance variability and the CLT), ch. 21 (accuracy of percentages). (Central limit theorem)
  19. Tversky, A. & Kahneman, D. (1974). Judgment under uncertainty: heuristics and biases. Science 185(4157), 1124–1131. doi:10.1126/science.185.4157.1124. primary (Central limit theorem)
  20. Wainer, H. (2007). The most dangerous equation. American Scientist 95(3), 249–256. doi:10.1511/2007.65.1026. review (Central limit theorem)
  21. Wasserman, L. (2004). All of Statistics: A Concise Course in Statistical Inference. Springer. doi:10.1007/978-0-387-21736-9. textbook §5.4 (central limit theorem), §6.3 (confidence sets), ch. 10 (hypothesis testing, p-values). (Central limit theorem)
  22. Fischer, H. (2011). A History of the Central Limit Theorem: From Classical to Modern Probability Theory. Springer. doi:10.1007/978-0-387-87857-7. scholarship (Central limit theorem)
  23. Hesterberg, T. C. (2015). What teachers should know about the bootstrap: resampling in the undergraduate statistics curriculum. The American Statistician 69(4), 371–386. doi:10.1080/00031305.2015.1089789. review (Central limit theorem)
  24. Neyman, J. (1937). Outline of a theory of statistical estimation based on the classical theory of probability. Philosophical Transactions of the Royal Society of London A 236(767), 333–380. doi:10.1098/rsta.1937.0005. primary (Confidence intervals)
  25. NIST/SEMATECH (2012). NIST/SEMATECH e-Handbook of Statistical Methods, §7.1.4 What are confidence intervals?. National Institute of Standards and Technology. standard (Confidence intervals)
  26. Hoekstra, R., Morey, R. D., Rouder, J. N. & Wagenmakers, E.-J. (2014). Robust misinterpretation of confidence intervals. Psychonomic Bulletin & Review 21, 1157–1164. doi:10.3758/s13423-013-0572-3. primary (Confidence intervals)
  27. Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N. & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. European Journal of Epidemiology 31, 337–350. doi:10.1007/s10654-016-0149-3. review (Confidence intervals)
  28. Student (Gosset, W. S.) (1908). The probable error of a mean. Biometrika 6(1), 1–25. doi:10.1093/biomet/6.1.1. primary (Confidence intervals)
  29. Zabell, S. L. (2008). On Student’s 1908 article “The probable error of a mean”. Journal of the American Statistical Association 103(481), 1–7. doi:10.1198/016214508000000030. scholarship (Confidence intervals)
  30. Brown, L. D., Cai, T. T. & DasGupta, A. (2001). Interval estimation for a binomial proportion. Statistical Science 16(2), 101–133. doi:10.1214/ss/1009213286. primary (Confidence intervals)
  31. Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association 22(158), 209–212. doi:10.1080/01621459.1927.10502953. primary (Confidence intervals)
  32. Agresti, A. & Coull, B. A. (1998). Approximate is better than “exact” for interval estimation of binomial proportions. The American Statistician 52(2), 119–126. doi:10.1080/00031305.1998.10480550. primary (Confidence intervals)
  33. Wasserstein, R. L. & Lazar, N. A. (2016). The ASA statement on p-values: context, process, and purpose. The American Statistician 70(2), 129–133. doi:10.1080/00031305.2016.1154108. institutional (Confidence intervals)
  34. Benjamin, D. J. et al. (2018). Redefine statistical significance. Nature Human Behaviour 2, 6–10. doi:10.1038/s41562-017-0189-z. primary (P-values & power)
  35. Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences, 2nd edition. Lawrence Erlbaum Associates. ISBN 978-0-8058-0283-2. textbook (P-values & power)
  36. Button, K. S., Ioannidis, J. P. A., Mokrysz, C., Nosek, B. A., Flint, J., Robinson, E. S. J. & Munafò, M. R. (2013). Power failure: why small sample size undermines the reliability of neuroscience. Nature Reviews Neuroscience 14, 365–376. doi:10.1038/nrn3475. primary (P-values & power)
  37. Benjamini, Y. & Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society B 57(1), 289–300. doi:10.1111/j.2517-6161.1995.tb02031.x. primary Added by the verifier for the false-discovery-rate sentence in chapter 6. (P-values & power)
  38. Simmons, J. P., Nelson, L. D. & Simonsohn, U. (2011). False-positive psychology: undisclosed flexibility in data collection and analysis allows presenting anything as significant. Psychological Science 22(11), 1359–1366. doi:10.1177/0956797611417632. primary (P-values & power)
  39. Armitage, P., McPherson, C. K. & Rowe, B. C. (1969). Repeated significance tests on accumulating data. Journal of the Royal Statistical Society A 132(2), 235–244. doi:10.2307/2343787. primary (P-values & power)
  40. Ioannidis, J. P. A. (2005). Why most published research findings are false. PLoS Medicine 2(8), e124. doi:10.1371/journal.pmed.0020124. primary (P-values & power)
  41. Open Science Collaboration (2015). Estimating the reproducibility of psychological science. Science 349(6251), aac4716. doi:10.1126/science.aac4716. primary (P-values & power)
  42. NIST/SEMATECH (2012). NIST/SEMATECH e-Handbook of Statistical Methods, §7.2.2.2 Sample sizes required. National Institute of Standards and Technology. standard (Sample size calculator)
  43. Cochran, W. G. (1977). Sampling Techniques, 3rd edition (ch. 4, the estimation of sample size). John Wiley & Sons, New York. ISBN 978-0-471-16240-7. textbook (Sample size calculator)

Simplifications