MSTP Annual Retreat
June 27, 2020


danny_sack

Definitions

  • test statistic: “the distance between the data and the model prediction” — \(T,\space Z,\space X^2,\space \text{etc.}\) (Greenland et al, 2016)
  • p-value: “probability that the chosen test statistic would have been at least as large as its observed value if every model assumption were correct” (Greenland et al, 2016)
  • confidence interval: “over infinite repeated sampling, and in the absence of selection, information, and confounding bias, the \(\alpha\)-level confidence interval will include the true value in \(\alpha\)% of the samples for which it is calculated” (Naimi & Whitcomb, 2020)
  • p-value function: “testing all hypotheses null and non-null and recording the corresponding P values…[and] plotting the result[s]” (Infanger & Schmidt-Trucksäss, 2019)

Three Different Studies

Effect Estimate 95% Confidence Interval
Study 1 1.125 (1.022, 1.2383)
Study 2 1.750 (1.151, 2.661)
Study 3 1.750 (0.968, 3.165)

Visualizing Confidence Intervals

Effect Estimate 95% Confidence Interval
Study 1 1.125 (1.022, 1.2383)
Study 2 1.750 (1.151, 2.661)
Study 3 1.750 (0.968, 3.165)

References

  • Greenland, Sander, Stephen J. Senn, Kenneth J. Rothman, John B. Carlin, Charles Poole, Steven N. Goodman, and Douglas G. Altman. “Statistical Tests, P Values, Confidence Intervals, and Power: A Guide to Misinterpretations.” European Journal of Epidemiology 31, no. 4 (April 1, 2016): 337–50. https://doi.org/10.1007/s10654-016-0149-3.

  • Infanger, Denis, and Arno Schmidt‐Trucksäss. “P Value Functions: An Underused Method to Present Research Results and to Promote Quantitative Reasoning.” Statistics in Medicine 38, no. 21 (2019): 4189–97. https://doi.org/10.1002/sim.8293.

  • Naimi, Ashley I., and Brian W. Whitcomb. “Can Confidence Intervals Be Interpreted?” American Journal of Epidemiology. Accessed June 16, 2020. https://doi.org/10.1093/aje/kwaa004.