Banana Bread Lab
What moves together in 708 banana bread recipes
When a recipe uses more of one ingredient, does it tend to use more or less of another? For every pair of the 7 ingredient ratios (grams per 100 g of flour), this page ranks all 708 recipes on each and measures how closely the two rankings agree: Spearman's rho, from −1 (the more of one, always the less of the other) through 0 (unrelated) to 1 (always rise together).
21 pairs in all: 7 rise together at rho 0.20 or more, none move in opposite directions at −0.20 or less, and 9 are close to unrelated (between −0.10 and 0.10). This describes recipes as they are published; it does not say what changing one amount would do to a bake.
Every pair at once
Read a cell by its row and column. Caramel cells rise together, slate cells move in opposite directions, and the deeper the color the stronger the relationship. Pale cells with grey numbers are not distinguishable from no relationship with 708 recipes (p of 0.05 or more).
All 21 pairs as a table
| Pair | Rho | Strength | p |
|---|---|---|---|
| Sugar and fat | 0.52 | moderate | under 0.001 |
| Sugar and salt | 0.38 | weak | under 0.001 |
| Fat and egg | 0.38 | weak | under 0.001 |
| Banana and egg | 0.29 | weak | under 0.001 |
| Banana and fat | 0.25 | weak | under 0.001 |
| Banana and leavening | 0.23 | weak | under 0.001 |
| Sugar and egg | 0.23 | weak | under 0.001 |
| Banana and sugar | 0.18 | very weak | under 0.001 |
| Fat and salt | 0.17 | very weak | under 0.001 |
| Egg and leavening | 0.15 | very weak | under 0.001 |
| Banana and dairy | −0.13 | very weak | under 0.001 |
| Fat and dairy | −0.10 | very weak | 0.006 |
| Banana and salt | 0.09 | negligible | 0.013 |
| Egg and salt | 0.09 | negligible | 0.012 |
| Dairy and leavening | −0.08 | negligible | 0.027 |
| Fat and leavening | 0.08 | negligible | 0.040 |
| Sugar and dairy | 0.06 | negligible | 0.097 |
| Leavening and salt | −0.06 | negligible | 0.12 |
| Egg and dairy | −0.05 | negligible | 0.16 |
| Sugar and leavening | −0.02 | negligible | 0.63 |
| Dairy and salt | −0.01 | negligible | 0.75 |
The three clearest relationships
The strongest pairs that reach rho 0.20 either way with a p-value under 0.01. Each dot is a recipe; the line joins the median of the second ingredient within each fifth of recipes ranked by the first.
Recipes with more sugar tend to use more fat
rho 0.52 across 708 recipes · moderate · p under 0.001
The third of recipes with the most sugar use a median of 54% fat; the third with the least sugar, 33%.
Recipes with more sugar tend to use more salt
rho 0.38 across 708 recipes · weak · p under 0.001
The third of recipes with the most sugar use a median of 1.2% salt; the third with the least sugar, 0.2%.
Recipes with more fat tend to use more egg
rho 0.38 across 708 recipes · weak · p under 0.001
The third of recipes with the most fat use a median of 50% egg; the third with the least fat, 40%.
What moves on its own
- Dairy. Nearly independent of the rest: its strongest correlation with any other ingredient is −0.13, with banana. A recipe's amount of dairy says almost nothing about its other amounts.
The pairs closest to unrelated: dairy and salt (−0.01), sugar and leavening (−0.02), egg and dairy (−0.05) and leavening and salt (−0.06).
How the numbers are made
Spearman's rho is the ordinary correlation of the two rankings, so it measures whether one amount tends to rise with the other, in a straight line or not, and a single extreme recipe moves it little. A recipe with none of an ingredient ranks lowest on it. An ingredient fewer than 12 recipes use is left out of the matrix.
The p-value is the chance of a rho at least this far from zero if the two amounts were unrelated. With 21 pairs tested, about 1.1 would pass 0.05 by chance alone even if no ingredient were related to another, which is why the relationships explained above must pass 0.01 and reach 0.20.
Every number is divided by the same flour weight, so a recipe light on flour reads high on every ingredient at once. That nudges every correlation toward positive: part of a positive rho can be flour, not the two ingredients. A negative one holds despite it.
A correlation describes the recipes as published. “Recipes with more banana tend to use…” is a statement about what bakers write down together, not a rule that adding one forces the other. Plot any two ingredients to see the recipes behind a number.