Brownies Lab
What moves together in 1221 brownie 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 1221 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: 9 rise together at rho 0.20 or more, 3 move in opposite directions at −0.20 or less, and 5 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 1221 recipes (p of 0.05 or more).
All 21 pairs as a table
| Pair | Rho | Strength | p |
|---|---|---|---|
| Fat and egg | 0.65 | strong | under 0.001 |
| Fat and sugar | 0.60 | strong | under 0.001 |
| Chocolate and egg | 0.49 | moderate | under 0.001 |
| Sugar and egg | 0.48 | moderate | under 0.001 |
| Cocoa and sugar | 0.43 | moderate | under 0.001 |
| Sugar and salt | 0.37 | weak | under 0.001 |
| Cocoa and salt | 0.36 | weak | under 0.001 |
| Chocolate and fat | 0.35 | weak | under 0.001 |
| Fat and leavening | −0.34 | weak | under 0.001 |
| Egg and leavening | −0.30 | weak | under 0.001 |
| Sugar and leavening | −0.26 | weak | under 0.001 |
| Cocoa and fat | 0.24 | weak | under 0.001 |
| Chocolate and cocoa | −0.17 | very weak | under 0.001 |
| Chocolate and leavening | −0.17 | very weak | under 0.001 |
| Chocolate and sugar | 0.17 | very weak | under 0.001 |
| Fat and salt | 0.16 | very weak | under 0.001 |
| Cocoa and egg | 0.08 | negligible | 0.004 |
| Leavening and salt | −0.05 | negligible | 0.060 |
| Chocolate and salt | −0.05 | negligible | 0.081 |
| Egg and salt | 0.04 | negligible | 0.12 |
| Cocoa and leavening | 0.01 | negligible | 0.74 |
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 fat tend to use more egg
rho 0.65 across 1221 recipes · strong · p under 0.001
The third of recipes with the most fat use a median of 166% egg; the third with the least fat, 83%.
Recipes with more fat tend to use more sugar
rho 0.60 across 1221 recipes · strong · p under 0.001
The third of recipes with the most fat use a median of 313% sugar; the third with the least fat, 160%.
Recipes with more chocolate tend to use more egg
rho 0.49 across 1221 recipes · moderate · p under 0.001
The third of recipes with the most chocolate use a median of 163% egg; the third with the least chocolate, 100%.
What moves on its own
Every ingredient moves with at least one other: none has its strongest correlation under 0.15.
The pairs closest to unrelated: cocoa and leavening (0.01), egg and salt (0.04), chocolate and salt (−0.05) and leavening and salt (−0.05).
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 chocolate 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.