In network motif algorithms, it seems quite common to return both a p-value and a Z-score for a statistic: "Input network contains X copies of subgraph G". A subgraph is deemed a motif if it satisfies
- p-value < A,
- Z-score > B and
- X > C, for some user-defined (or community-defined) A, B and C.
This motivates the question:
Question: What are the differences between p-value and Z-score?
And the subquestion:
Question: Are there situations where the p-value and Z-score of the same statistic might suggest opposite hypotheses? Are the first and second conditions listed above essentially the same?