The Benjamini-Hochberg correction is a method for controlling the False Discovery Rate (FDR) using sequential modified Bonferroni correction for multiple hypothesis testing. It is used to adjust p-values obtained from multiple statistical tests to control the expected proportion of false discoveries among the rejected hypotheses. The Benjamini-Hochberg procedure is a step-up procedure that controls the FDR at level alpha.

To apply the Benjamini-Hochberg correction after calculating multiple correlations and doing two regression analyses, you can follow these steps:

The Benjamini-Hochberg procedure, also known as the False Discovery Rate (FDR) correction, is commonly used to control for multiple comparisons when conducting hypothesis tests on multiple variables or conducting multiple tests. It is a more lenient method compared to the Bonferroni correction and is suitable for controlling the proportion of false discoveries in your analysis.

To apply the Benjamini-Hochberg procedure, you need a set of p-values from your hypothesis tests. These p-values represent the strength of evidence against the null hypothesis for each individual test. In your case, you have multiple correlations and regression analyses, each producing a set of p-values.

When using the Benjamini-Hochberg procedure, you need to sort the p-values in ascending order. Then, you calculate the critical p-value threshold for significance based on the desired false discovery rate (FDR) control level. For example, if you want to control the FDR at 0.05, you would calculate the critical p-value threshold accordingly.

Next, you compare each sorted p-value to its corresponding critical threshold. You start from the lowest p-value and move upwards until you encounter a p-value that is larger than its corresponding critical threshold. All the p-values up to and including that point are considered significant, and the corresponding null hypotheses are rejected. The remaining p-values above that point are not considered significant.

Regarding your question about p-values below 0.001, it is common to report such p-values as "< 0.001" or simply as p < 0.001. In the context of the Benjamini-Hochberg procedure, you can treat these p-values as their approximate value, such as p = 0.001. This is because the FDR control level is based on the rank order of the p-values rather than their precise numerical values.

To summarize, to apply the Benjamini-Hochberg procedure:

Remember that the Benjamini-Hochberg procedure controls the FDR, allowing for a controlled proportion of false discoveries among the rejected null hypotheses. It's important to interpret and report the results accordingly, considering the nature of your study and the specific research questions you are addressing.