*! version 1.1.1 24jan2017

Title

pkonfound -- Beta version: For published studies, this command calculates (1) % bias necessary to invalidate/sustain an inference; (2) the impact threshold of an omitted confounding variable to invalidate/sustain an inference.

Syntax

pkonfound
[{# # # #}]
[, options]

Main
First # the estimated value of the regression coefficient

Second # the standard error of the regression coefficient

Third # the sample size

Fourth # the number of covariates in the model

Description

pkonfound takes users' input of numerical values (e.g., from a published study) and calculates (1) the % bias
in an estimate necessary to invalidate/sustain an inference. The % bias necessary to invalidate/sustain an inference is
interpreted in terms of sample replacement; (2) the impact of an omitted variable necessary to invalidate/sustain an inference
for a regression coefficient. It also assesses how strong an omitted variable must be correlated with the outcome and with the predictor of interest
to invalidate/sustain the inference.

Four numbers must be input. The first number is the estimated value of the effect (e.g., the estimated regression coefficient); the second number is
the standard error of the estimated effect (regression coefficient); the third number is the sample size; the fourth number is
the number of covariates in the model.

Options

sig(#) Significance level of the test; default is 0.05 sig(.05).
To change the significance level to .10 use sig(.1)

nu(#) The null hypothesis against which to test the estimate. The
default is 0 nu(0)

onetail(#) One-tail or two-tail test;
the default is two-tail onetail(0);
to change to one-tail use onetail(1)

rep_0(#) For % bias to invalidate the inference, this controls the effect in the replacement cases;
the default is the null effect (which may or may not be 0) rep_0(0); to force replacing cases with effect of zero use rep_0(1)

Remarks

For a graphical illustration of the impact of a confounding variable see https://msu.edu/~kenfrank/research.htm#impact_diagram

For additional details of the calculations in a spreadsheet format and other supporting materials see https://msu.edu/~kenfrank/research.htm#causal.

For a web-based version of konfound see http://konfound-it.com.

Examples

## Assume in a study the estimate is 10, the standard error of the estimate is 2, the sample size is 100, and the number of covariates is 5

. pkonfound 10 2 100 5

. pkonfound 10 2 100 5, sig(0.1) nu(1) onetail(1) rep_0(1)

Authors

Kenneth A. Frank

Michigan State University

Ran Xu

Michigan State University

Please email ranxu@msu.edu if you observe any problems.

References

Frank, K.A. 2000. Impact of a Confounding Variable on the Inference of a Regression Coefficient. Sociological Methods and Research, 29(2), 147-194

Pan, W., and Frank, K.A. 2004. An Approximation to the Distribution of the Product of Two Dependent Correlation Coefficients. Journal of Statistical Computation and Simulation, 74, 419-443

Pan, W., and Frank, K.A., 2004. A probability index of the robustness of a causal inference. Journal of Educational and Behavioral Statistics, 28, 315-337.

*Frank, K. A. and Min, K. 2007. Indices of Robustness for Sample Representation. Sociological Methodology. Vol 37, 349-392. * co first authors.

Frank, K.A., Gary Sykes, Dorothea Anagnostopoulos, Marisa Cannata, Linda Chard, Ann Krause, Raven McCrory. 2008. Extended Influence: National Board Certified Teachers as Help Providers. Education, Evaluation, and Policy Analysis. Vol 30(1): 3-30.

Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. 2013. What would it take to Change an Inference?: Using Rubin’s Causal Model to Interpret the Robustness of Causal Inferences. Education, Evaluation and Policy Analysis. Vol 35: 437-460.