An effective numerical narrative guides a reader or audience member through a belief updating process in which the preferred theoretical story evolves from possible to plausible to probable. This approach is designed to emphasize mechanism-specific analyses.
I aspire to good numerical narrative in all of my research. And I often provide this guidance to authors in my role as Associate Editor for Administrative Science Quarterly
1. Establish the phenomenon.
Descriptive statistics (e.g., counts, rates, probabilities, scatter plots, time trends) characterize trends, means, distributions, etc. in raw data.
2. Affirm some audience priors about the phenomenon; deny others.
Scatter plots of raw data characterize the phenomenon and the at-risk set of observations in the sample (or population).
3. Demonstrate possibility by motivating multiple theoretical accounts.
Provide suggestive visual evidence of multiple accounts.
4. Demonstrate plausibility by presenting prima facie evidence of your preferred theoretical account.
Provide the strongest evidence consistent with your story.
5. Demonstrate probability by treating multivariate regressions as robustness checks on the narrative.
Regression becomes necessary when descriptive statistics become cumbersome. Resort to regression when a reasonable audience member is likely to believe your story is somewhere between plausible and probable.
6. Deliver “differences-in-inferences” for the audience.
Clearly present how inferences obtained from your approach differ from those obtained from alternative approaches. This highlights your distinct empirical contribution.
See Merton's (1987) "3 fragments" and Davis's (1971) "That's interesting!" for the original inspiration for this approach.
See Damadoran's book "Narrative and Numbers" for more on combining numbers and stories (summary here).
See Stolz's summary of "Coleman's bathtub" or Ylikoski's article for more on "mechanism-based theorizing."