Why does the stats summary say there’s no relationship when details show differences?
It’s not a contradiction. AddMaple runs several complementary tests that answer slightly different questions:
- Global chi-square (table-level): asks “Is there any relationship at all between these two categorical columns?” If assumptions aren’t met (e.g., too many expected counts < 5), we suppress or downweight the result and may show “no significant relationship.”
- Category vs. rest analysis (per-category): asks “Is this specific category different from all others combined?” This can surface strong differences for individual categories even when the overall table-level test doesn’t clear our thresholds.
- Cell-level z-scores with significance shading (per cell): asks “Is this specific cell higher or lower than expected?” We color cells based on standardized residuals (z), adjust p-values within each column using Holm-Bonferroni, and apply practical-effect guards so only reliable signals get stronger shading. See Significance Testing.
Important: Before interpreting results, filter out or merge very small categories to avoid sparse cells (low expected counts). This stabilizes the tests and reduces the chance that the global chi-square is suppressed while finer-grained analyses still show signals. You can merge categories in the Legend or filter to focus on well-populated groups.
Why the summary can say “no relationship”
- Assumption checks matter: The global chi-square requires that at least 80% of expected counts are ≥ 5 and none are < 1 for the usual inference to be valid. If your contingency table has sparse cells (common when segments are granular), we won’t claim a strong table-level relationship.
- Different questions, different thresholds: The per-category and per-cell analyses answer narrower questions and can still show meaningful signals for particular categories or intersections, even when the overall relationship is weak or unstable.
How to interpret the mixed signals
- Start with the summary: If it says “no significant relationship,” treat the overall linkage as weak/inconclusive—often due to sparse data.
- Check “Further Insights Between Column Categories”: Use this to identify which specific categories are notably different vs. the rest. These are directional findings you can investigate further.
- Use significance shading in a pivot table: Turn on Significance Testing. Stronger shades indicate reliable, adjusted differences at the cell level. Keep sample sizes in mind; small totals or expected counts can suppress stronger tiers.
- Stabilize the analysis when needed:
- Combine/merge very small categories in the Legend or filter to focus on well-populated groups.
- Consider broader groupings (e.g., recode long tails) to raise expected counts.
- Verify that you’re comparing categorical vs categorical; numeric vs categorical uses ANOVA/t-tests alongside the z-score table.
Quick definitions
- Global chi-square: Table-level test of any association; summarized in the top “Stats Overview.”
- Cramér’s V: Effect size for chi-square; 0 = none, 1 = perfect.
- Category vs. rest: Per-category test showing which categories drive differences.
- Z-score shading: Per-cell standardized residuals with Holm adjustment and practical-effect guards for reliable highlights.
Practical takeaway
- You can rely on the per-category and per-cell findings as targeted insights—especially when they pass our adjusted thresholds—even if the table-level summary is conservative due to sparse data. For client documents, describe them as “specific category differences” or “cell-level differences,” not as a blanket relationship between the entire pair of columns.
For related background, see: