References

Algorithms

• Welford, B. P. (1962). "Note on a method for calculating corrected sums of squares and products." Technometrics, 4(3), 419–420. The one-pass variance algorithm used throughout this site.
• Knuth, D. E. (1998). The Art of Computer Programming, Volume 2: Seminumerical Algorithms, 3rd ed., section 4.2.2. The presentation of Welford's method that popularised it, and the analysis of why the naive formula fails.
• 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. The numerical comparison of variance algorithms.
• Abramowitz, M., & Stegun, I. A. (1964). Handbook of Mathematical Functions, formula 7.1.26. The error function approximation behind the normal CDF.
• Acklam, P. J. (2003). "An algorithm for computing the inverse normal cumulative distribution function." The inverse normal approximation.
• Press, W. H., et al. (2007). Numerical Recipes, 3rd ed., sections 6.1 and 6.4. The Lanczos log-gamma and the continued-fraction incomplete beta used for the t distribution.
• Hyndman, R. J., & Fan, Y. (1996). "Sample quantiles in statistical packages." The American Statistician, 50(4), 361–365. The nine quantile definitions, and the source of the "type 7" naming used on the methodology page.

Statistical conventions

• NIST/SEMATECH (2012). e-Handbook of Statistical Methods. Reference definitions for standard deviation, pooled standard deviation and weighted statistics.
• Higgins, J. P. T., et al. (eds.) (2023). Cochrane Handbook for Systematic Reviews of Interventions, version 6.4, section 6.5.2. Recovering a standard deviation from a reported confidence interval or standard error.
• Wan, X., Wang, W., Liu, J., & Tong, T. (2014). "Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range." BMC Medical Research Methodology, 14, 135. The range-to-SD and IQR-to-SD estimators implemented in the engine.
• Kish, L. (1965). Survey Sampling. The effective sample size used for reliability weights.
• Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences, 2nd ed. Pooled standard deviation as the denominator of the standardised effect size.

Precision limits in analytical and bioanalytical methods

• U.S. Food and Drug Administration, CDER (1994). Reviewer Guidance: Validation of Chromatographic Methods. Injection repeatability "RSD of ≤ 1% for n ≥ 5 is desirable", quoted on the relative standard deviation page.
• ICH (2022). M10 Bioanalytical Method Validation and Study Sample Analysis, adopted as FDA guidance, November 2022, section 3.2.5.2. Precision (%CV) not to exceed 15%, or 20% at the lower limit of quantification.

Software behaviour referenced

• Microsoft. STDEV.S, STDEV.P, VAR.S, VAR.P and AGGREGATE function documentation.
• R Core Team. `quantile` documentation: the type 1–9 definitions.
• Texas Instruments. TI-84 Plus CE Graphing Calculator Guidebook: 1-Var Stats output and the Sx / σx labels.
• Casio. fx-991EX / fx-570EX Quick Start Guide, Statistics.

A note on how these are used

Citations here are to the sources actually consulted in building the calculators, not a reading list assembled afterwards. Where a source's convention differs from another's (the quantile definitions being the clearest case), the methodology page states which one this site follows and why, rather than presenting one choice as if it were the only one.