Chocolate Cake Lab
What moves together in 357 chocolate cake recipes
When a recipe uses more of one ingredient, does it tend to use more or less of another? For every pair of the 8 ingredient ratios (grams per 100 g of flour), this page ranks all 357 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).
28 pairs in all: 12 rise together at rho 0.20 or more, 2 move in opposite directions at −0.20 or less, and 7 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 357 recipes (p of 0.05 or more).
All 28 pairs as a table
| Pair | Rho | Strength | p |
|---|---|---|---|
| Cocoa and salt | 0.46 | moderate | under 0.001 |
| Cocoa and liquid | 0.44 | moderate | under 0.001 |
| Liquid and salt | 0.42 | moderate | under 0.001 |
| Sugar and liquid | 0.40 | moderate | under 0.001 |
| Cocoa and sugar | 0.37 | weak | under 0.001 |
| Cocoa and chocolate | −0.36 | weak | under 0.001 |
| Sugar and salt | 0.36 | weak | under 0.001 |
| Cocoa and leavening | 0.33 | weak | under 0.001 |
| Liquid and leavening | 0.30 | weak | under 0.001 |
| Chocolate and salt | −0.29 | weak | under 0.001 |
| Sugar and fat | 0.27 | weak | under 0.001 |
| Chocolate and egg | 0.25 | weak | under 0.001 |
| Fat and egg | 0.20 | weak | under 0.001 |
| Leavening and salt | 0.20 | weak | under 0.001 |
| Sugar and egg | 0.19 | very weak | under 0.001 |
| Sugar and leavening | 0.19 | very weak | under 0.001 |
| Chocolate and leavening | −0.15 | very weak | 0.004 |
| Chocolate and fat | 0.14 | very weak | 0.008 |
| Chocolate and liquid | −0.14 | very weak | 0.009 |
| Fat and leavening | −0.11 | very weak | 0.046 |
| Egg and liquid | −0.10 | very weak | 0.050 |
| Cocoa and egg | 0.07 | negligible | 0.16 |
| Fat and salt | −0.06 | negligible | 0.23 |
| Cocoa and fat | 0.06 | negligible | 0.30 |
| Chocolate and sugar | −0.06 | negligible | 0.30 |
| Egg and leavening | 0.05 | negligible | 0.37 |
| Fat and liquid | −0.03 | negligible | 0.54 |
| Egg and salt | −0.03 | negligible | 0.56 |
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 cocoa tend to use more salt
rho 0.46 across 357 recipes · moderate · p under 0.001
The third of recipes with the most cocoa use a median of 1.8% salt; the third with the least cocoa, 0%.
Recipes with more cocoa tend to use more liquid
rho 0.44 across 357 recipes · moderate · p under 0.001
The third of recipes with the most cocoa use a median of 175% liquid; the third with the least cocoa, 118%.
Recipes with more sugar tend to use more liquid
rho 0.40 across 357 recipes · moderate · p under 0.001
The third of recipes with the most sugar use a median of 184% liquid; the third with the least sugar, 125%.
Also strong, and left out above because both of its ingredients already appear: liquid and salt (rho 0.42).
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: egg and salt (−0.03), fat and liquid (−0.03), egg and leavening (0.05) and cocoa and fat (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 28 pairs tested, about 1.4 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 cocoa 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.