Original title: Two Kinds of Nothing: What Insignificant Results in Finance Actually Show
David Tan · August 2026
Researchers in finance often say they found "no evidence" that one thing affects another. People often wrongly assume this means the effect is zero. In reality, a test that is not statistically significant just means the data cannot rule out zero, while also failing to rule out many other possible effect sizes. The author shows how to fix this mistake by checking confidence intervals, which are the ranges of plausible values around an estimate. This check reveals two types of results that look identical in normal tables. First are bounded null claims, which rule out any meaningful real-world effects and provide a real answer. Second are vacuous null claims, which fail to rule out large effects and prove nothing at all. The author also notes that saying "no effect" hides split verdicts that are bounded in one direction but vacuous in the other.
You are trying to decide whether a new allergy pill really works. Your friend tries it and says she feels no difference after one day. But that single day might not be enough to detect a slow effect, so her 'no difference' could mean either that the pill is useless or that she gave up too soon. In this paper, a null claim in finance is like that friend's report — it could be informative (bounded) if the test was strong, or empty (vacuous) if the test was weak.
Every day, someone reads 'no effect' in a finance paper and assumes the result is zero. This paper shows that such a claim can hide two very different scenarios: one where the data truly rule out meaningful effects, and another where the data simply lack power to detect them. Without the distinction, readers may discard genuinely useful null findings or act on empty ones.
The abstract does not provide empirical evidence or examples; the author notes this is ongoing work. It also does not offer a systematic method for determining the smallest consequential effect size, leaving it to the researcher's discretion. The proposal relies on the availability of standard errors and coefficient estimates, which may not always be reported in applied finance papers.
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Two Kinds of Nothing: What Insignificant Results in Finance Actually Show — David Tan
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.