A confidence interval or significance test is called stable if the confidence level or P-value does not change very much when the conditions for use of the procedure are violated
The stability of a confidence interval or significance test refers to the sensitivity of the results when the conditions required for the procedure are violated. In other words, it assesses whether the outcome (confidence level or p-value) remains relatively constant or changes significantly when the assumptions of the analysis are not met.
To determine if a confidence interval or significance test is stable despite violations of the assumptions, you can perform sensitivity analysis. Here's how you can do it:
1. Identify the assumptions: Start by understanding the conditions or assumptions that are required for the particular confidence interval or significance test. For example, assumptions might include normality of the data, independence, or equal variances between groups.
2. Simulate violations: Introduce potential violations by simulating scenarios that deviate from the assumptions. For instance, if you are assuming normality, you can create datasets with non-normal distributions.
3. Calculate confidence intervals or p-values: Apply the chosen confidence interval or significance test to each simulated dataset. Calculate the confidence intervals or p-values under the violated conditions.
4. Compare results: Compare the confidence levels or p-values obtained under the different simulated scenarios. Assess whether there are significant changes in the results when the assumptions are violated. If the confidence levels or p-values vary significantly, the procedure may be considered unstable. On the other hand, if the differences are minimal, the procedure can be seen as stable.
It is important to note that the stability of a confidence interval or significance test does not imply that the procedure is valid or reliable under the violated assumptions. It just suggests that the results are less sensitive to the violations. Therefore, if the assumptions are strongly violated, it is recommended to consider alternative procedures that are appropriate for the specific situation, rather than relying solely on stability.