In Praise of Simplicity not Mathematistry! Ten Simple Powerful Ideas for the Statistical Scientist

Figures & data

Table 1 Simple ideas mentioned more than once in an informal poll of statisticians. Number of times mentioned in parentheses. Those in italics are related to the ideas discussed in the text

Histograms/plot the data/exploratory analysis (12)

Random selection/random treatment assignment (7)

Skepticism/understanding assumptions/model checking (5)

Resampling—bootstrap, permutation, jackknife (5)

Regression/ANOVA (4)

Monte Carlo Simulation—Gibbs/Metropolis-Hastings etc. (4)

Prediction from models that reflects uncertainty (4)

Factorial/fractional factorial designs (3)

Likelihood/maximum likelihood/likelihood principle(3)

Parsimonious models (3)

Understand the question/what data are needed (3)

Confounding/mediation (2); Potential outcomes (2)

Hierarchical models (2)

Observed = Fit + Residual/Pearson chi-square (2)

Smooth density estimation, loess, additive models (2)

Figure 1 Missing-data patterns. (a) Bivariate monotone data (Exs 1,2,6,7). (b) External calibration data (Exs 3,5). (c) Regression with two missing covariates (Ex 8).

Figure 2 (a) Root mean squared errors of estimates and (b) Noncoverage of 1000 confidence intervals (nominal = 50) of coefficient of X from four methods for handling measurement error in a covariate X, for external calibration data displayed in Figure 1. Naïve = no adjustment, CA = classical calibration, RP = regression prediction, MIEC = multiple imputation for external calibration. The online version of this figure is in color. (Continued)

Table 2 Example 9. Classifications by treatment and principal compliance: (a) Population proportions; (b) Population mean outcomes; (c) Observed means (sample counts)

(a) Population proportions
	Principal compliance C
	a	c	n	ALL
Randomized treatment R
0	(1−α)π a	(1−α)π c	(1−α)π n	1−α
1	απ a	απ c	απ n	α
ALL	π a	π c	π n
(b) Population mean outcomes
	Principal compliance C
	a	c	n	ALL
Randomized treatment R
0	μ0a	[μ0c ]*	[μ0n ]	μ0+
1	[μ1a ]	[μ1c ]	μ1n	μ1+
ALL	[μ+a ]	[μ+c ]	[μ+n ]
(c) Observed means (Sample counts)
	Principal compliance C
	a	c	n	ALL
Randomized treatment R
0
1
ALL	?	?	?
*[.] = not identifiable from the observable random variables without additional assumptions.