can you give me an specific example illustrating using a robust analysis？

Sure! Here's an example:

Let's say you're analyzing the effect of a new drug on patients' blood pressure. You collect data from two groups: a control group and a treatment group. However, when you analyze the data, you notice that there are a few outliers in the treatment group who have significantly higher blood pressure readings than the rest of the group.

In this case, you could use a robust analysis method to account for these outliers and ensure that they don't skew your results. One possible approach is to use a trimmed mean, which involves discarding a certain percentage of the highest and lowest values in the data and calculating the mean of the remaining values. This can help to reduce the impact of extreme values and provide a more accurate estimate of the average blood pressure in the treatment group.

Another option is to use a nonparametric test, such as the Wilcoxon rank-sum test or the Mann-Whitney U test, which don't make any assumptions about the underlying distribution of the data and are less sensitive to outliers. These tests can still provide a reliable measure of the difference between the control and treatment groups, even if the data is not normally distributed.

By using a robust analysis method in this scenario, you can ensure that your results are not unduly influenced by a few extreme values, and that you're getting an accurate estimate of the effect of the drug on blood pressure.