"Precision is expressed by an international standard, viz., the standard error. It measures the average of the difference between a complete coverage and a long series of estimates formed from samples drawn from this complete coverage by a particular procedure or drawing, and processed by a particular estimating formula." (W Edwards Deming,On the Presentation of the Results of Sample Surveys as Legal Evidence", Journal of the American Statistical Association Vol 49" (268), 1954)
"Tests of the null hypothesis that there is no difference between certain treatments are often made in the analysis of agricultural or industrial experiments in which alternative methods or processes are compared. Such tests are [...] totally irrelevant. What are needed are estimates of magnitudes of effects, with standard errors." (Francis J Anscombe,Discussion on Dr. David’s and Dr. Johnson’s Paper", Journal of the Royal Statistical Society B 18, 1956)
"Evaluation of the statistical reliability of a set of results is not mere calculation of standard errors and confidence limits. The statistician must go far beyond the statistical methods in textbooks. He must evaluate uncertainty in terms of possible uses of the data. Some of this writing is not statistical but draws on assistance from the expert in the subject-matter." (W Edwards Deming,Principles of Professional Statistical Practice", Annals of Mathematical Statistics, 36(6), 1965)
"Pencil and paper for construction of distributions, scatter diagrams, and run-charts to compare small groups and to detect trends are more efficient methods of estimation than statistical inference that depends on variances and standard errors, as the simple techniques preserve the information in the original data." (William E Deming,On Probability as Basis for Action" American Statistician Vol. 29" (4), 1975)
"I contend that the general acceptance of statistical hypothesis testing is one of the most unfortunate aspects of 20th century applied science. Tests for the identity of population distributions, for equality of treatment means, for presence of interactions, for the nullity of a correlation coefficient, and so on, have been responsible for much bad science, much lazy science, and much silly science. A good scientist can manage with, and will not be misled by, parameter estimates and their associated standard errors or confidence limits." (Marks Nester,A Myopic View and History of Hypothesis Testing", 1996)
"The standard error of most statistics is proportional to 1 over the square root of the sample size. God did this, and there is nothing we can do to change it." (Howard Wainer,Improving Tabular Displays, With NAEP Tables as Examples and Inspirations", Journal of Educational and Behavioral Statistics Vol 22" (1), 1997)
"The bounds on the standard deviation are pretty crude but it is surprising how often the rule will pick up gross errors such as confusing the standard error and standard deviation, confusing the variance and the standard deviation, or reporting the mean in one scale and the standard deviation in another scale." (Gerald van Belle,Statistical Rules of Thumb", 2002)
"The estimate of the standard error (SE) is more sensitive to the Normality assumption than the estimate of the coefficients. There are two options available which do not require this assumption; these are the bootstrap and the robust standard error." (Michael J Campbell, "Statistics at Square Two: Understanding modern statistical applications in medicine" 2nd Ed., 2006)
"Scholars feel the need to present tables of model parameters in academic articles" (perhaps just as evidence that they ran the analysis they claimed to have run), but these tables are rarely interpreted other than for their sign and statistical significance. Most of the numbers in these tables are never even discussed in the text. From the perspective of the applied data analyst, R packages without procedures to compute quantities of scientific interest are woefully incomplete. A better approach focuses on quantities of direct scientific interest rather than uninterpretable model parameters. [...] For each quantity of interest, the user needs some summary that includes a point estimate and a measure of uncertainty such as a standard error, confidence interval, or a distribution. The methods of calculating these differ greatly across theories of inference and methods of analysis. However, from the user’s perspective, the result is almost always the same: the point estimate and uncertainty of some quantity of interest." (Kousuke Imai et al,Toward a Common Framework for Statistical Analysis and Development", Journal of Computational and Graphical Statistics vol. 17, 2008)
"Overlapping confidence intervals do not mean two values are not significantly different. Checking confidence intervals or standard errors will mislead. It’s always best to use the appropriate hypothesis test instead. Your eyeball is not a well-defined statistical procedure." (Alex Reinhart,Statistics Done Wrong: The Woefully Complete Guide", 2015)
"We thus echo the classical Bayesian literature in concluding that ‘noninformative prior information’ is a contradiction in terms. The flat prior carries information just like any other; it represents the assumption that the effect is likely to be large. This is often not true. Indeed, the signal-to-noise ratio s is often very low and then it is necessary to shrink the unbiased estimate. Failure to do so by inappropriately using the flat prior causes overestimation of effects and subsequent failure to replicate them." (Erik van Zwet & Andrew Gelman,A proposal for informative default priors scaled by the standard error of estimates", The American Statistician 76, 2022)
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