6
$\begingroup$

Inspired by this: http://pss.sagepub.com/content/22/11/1359

In the context of open-ended data collection where the necessary sample size cannot be properly estimated, for the purpose of a frequentists test;

I understand that a stopping condition based on the main outcome is circular. For example, if I stop sampling once my p value happens to be below .05, my p value is biased (so much as to be mostly worthless). However, say I choose another stopping rule, such as the width of my 95% confidence interval (without regard for other aspects of the test, such as e.g. if the CI includes 0), am I introducing any bias (but for, of course, CI width and related statistics)?

As far as I understand it, this is not a problem in a Bayesian analysis, but I am wondering about the options for conditional stopping precluding frequentist tests.

$\endgroup$
3
  • 1
    $\begingroup$ I have seen this approach (aim for a given CI width, assessing it as you go) recommended by various authors (sorry no reference at hand). It seems related to the accuracy in parameter estimation approach. $\endgroup$ – Gala Jul 27 '13 at 13:58
  • $\begingroup$ Thank you for the link to AIPE @GaëlLaurans and if you happen to remember any of these "various authors", I'd love to look them up! $\endgroup$ – jona Jul 28 '13 at 10:03
  • $\begingroup$ This is certainly an interesting question, which I do not have an answer at the moment. But I did find this blog entry worthy of a read, even though it concerns the width bayesian credible intervals, rather than frequentist confidence intervals: doingbayesiandataanalysis.blogspot.com/2013/11/… $\endgroup$ – Andrew M Dec 4 '14 at 23:25
1
$\begingroup$

Jan Vanhove presented simulations showing that optional stopping based on the width of a confidence interval does not introduce biases. He simulated a situation where the null hypothesis was true, and simulated thousands of experiments that continued adding n until the confidence interval was narrower than a prespecified limit. Since the null hypothesis is known to be true, the p-values ought to be evenly spaced between 0 and 1, and this is exactly what he saw (figure below). Optional stopping did not bias the p-value.

enter image description here

In those simulations, each p-value at each sample size was computed as if the study was planned to use the sample size at that point. Kruschke points out the problem that each calculated p-value, in this case, depends on assumptions that aren't correct when the data are reanalyzed repeatedly as new data are added. But the simulations seem to show this method works fine. I am not sure how to tackle this discrepancy.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.