Figure 1.

(a) Reproducibility rate of a true result decreases with measurement error in a misspecified simple linear regression model. Reproducibility rate is estimated by the proportion of times the $95\text{\%}$ confidence interval captures the true effect. Sample sizes are 50 (small) and 500 (large). The true regression coefficient of the predictor variable is 2 (small effect) and 20 (large effect). Model details are given in appendix D. (b) Example data (black points) generated under simple linear regression model E(Y) = 2 + 20X. Measurement and sampling error are normally distributed with standard deviations equal 3. Regression lines are fit under measurement error model (magenta line) and the correct model (blue line) with a sample size of 100. The $95\text{\%}$ confidence interval for the regression coefficient obtained under the measurement error model is (7.94, 12.37), which does not include the true value 20. By contrast, the $95\text{\%}$ confidence interval for the regression coefficient obtained under the correct model, (19.86, 20.21), includes the true value. For the code generating all simulations and figures in the article, please see the electronic supplementary material.