A trainee examined a set of experimental data to find comparisons that "look promising" and calculated a family of Bonferroni confidence intervals for these comparisons with a 90 percent family confidence coefficient. Upon being informed that the Bonferroni procedure is not applicable in this case because the comparisons had been suggested by the data, the trainee stated:"This makes no difference. I would use the same formulas for the point estimates and the estimated standard errors even if the comparisons were not suggested by the data." Please disscuss.

Answer:

Answer for the question:

A trainee examined a set of experimental data to find comparisons that "look promising" and calculated a family of Bonferroni confidence intervals for these comparisons with a 90 percent family confidence coefficient. Upon being informed that the Bonferroni procedure is not applicable in this case because the comparisons had been suggested by the data, the trainee stated:"This makes no difference. I would use the same formulas for the point estimates and the estimated standard errors even if the comparisons were not suggested by the data."

Please disscuss.

Is explained in the attachment.

Step-by-step explanation:

Final answer:

The trainee's assertion is flawed as the Bonferroni method's assumption of independence doesn't hold when comparisons are derived from the data. For a smaller error bound at the same confidence level, sample size should be increased before the study. Moreover, reliance on null hypothesis significance testing can be problematic, and alternative evidence estimation methods may be more informative.

Explanation:

The trainee's use of Bonferroni confidence intervals with a 90 percent family confidence coefficient assumes independent comparisons. However, when comparisons are suggested by the data, the assumption of independence is violated, rendering the Bonferroni method inappropriate. The trainee errs by stating that using the same formulas for point estimates and estimated standard errors would not differ in the other scenario. When comparisons are data-derived, adjustments such as using resampling methods or adjusting for multiple testing should be considered to account for the increased risk of Type I error.

Regarding the desire for a smaller error bound while keeping the same level of confidence, one should increase the sample size of the study before it is conducted. This would enable a more precise estimate with a narrower confidence interval without altering the confidence level.

To avoid the limitations of null hypothesis significance testing (NHST), alternative approaches such as estimation of evidence strength through model comparison criteria like AIC or BIC, or using Bayesian methods, might be employed. These do not rely on arbitrary significance thresholds and often provide a more informative assessment of model's evidential support.

Learn more about Statistical Significance here:

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