Based on the information provided from the scientific article, here's an assessment of how pathway enrichment analysis was conducted:

1. **Tool Used for Pathway Enrichment Analysis:**  
   The tool used is Metacore®.

2. **Tool Version Number Provided:**  
   Not described in the article.

3. **Gene Set Library Queried:**  
   Gene Ontology (GO) cell process enrichment was performed, as indicated by references to gene ontologies and specific ontology terms related to cellular processes.

4. **Background Gene List Defined for Pathway Enrichment Analysis:**  
   It is implied that phospho-regulated proteins IDs were matched to corresponding genes which were then used for the analysis, but a specific background list is not described in detail.

5. **Statistical Test Used for Enrichment Analysis:**  
   A p-value and false discovery rate (FDR) are mentioned as part of the enrichment analysis process, suggesting that statistical significance testing was involved, though the exact test type isn't specified.

6. **False Discovery Rate Correction Used:**  
   Yes, false discovery rate (FDR) correction is used to control for false positives in the pathway enrichment analysis, as indicated by references to FDR in the tables.

This information can be organized into a table format if needed for further analysis or reporting.