Confidence Level: Non Normal Data

The choice of the confidence level in statistical analysis depends on the specific requirements of your study and the consequences of making Type I and Type II errors. The standard confidence levels are often 90%, 95%, and 99%, with 95% being the most commonly used. However, these levels are not set in stone, and there isn’t a universal “good” or “bad” choice for all situations.

Here are some considerations:

1. **95% Confidence Level (α = 0.05):**
— A 95% confidence level is commonly used in statistical analysis. It means that if you were to conduct the same study many times, you would expect the interval you calculate to contain the true parameter in about 95% of the cases. This level is often considered a good balance between precision and reliability.

2. **90% Confidence Level (α = 0.10):**
— A 90% confidence level provides a narrower interval than a 95% confidence level, but it comes with a higher risk of making a Type I error (incorrectly rejecting a true null hypothesis). This level might be appropriate if you are more concerned about precision and willing to accept a slightly higher risk of making Type I errors.

3. **99% Confidence Level (α = 0.01):**
— A 99% confidence level provides a wider interval but reduces the risk of Type I errors. This level might be chosen when a higher level of certainty is required, even at the cost of wider confidence intervals.

For a not-normal dataset, the choice of the confidence level may depend on the robustness of your statistical analysis method, the size of your sample, and the importance of avoiding Type I errors. If the dataset is large, the Central Limit Theorem may still apply, and a 95% confidence level could be reasonable. If the dataset is small or exhibits significant non-normality, you might consider a more conservative confidence level.

In summary, there isn’t a one-size-fits-all answer, and the choice of the confidence level should be made based on the specific context and requirements of your analysis. Consider consulting with a statistician or domain expert to make an informed decision based on the characteristics of your data and the goals of your study.