Challah Lab
What moves together in 72 challah recipes
When a recipe uses more of one ingredient, does it tend to use more or less of another? For every pair of the 6 ingredient ratios (grams per 100 g of flour), this page ranks all 72 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).
15 pairs in all: 5 rise together at rho 0.20 or more, 2 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 72 recipes (p of 0.05 or more).
All 15 pairs as a table
| Pair | Rho | Strength | p |
|---|---|---|---|
| Egg and oil | 0.29 | weak | 0.013 |
| Egg and yeast | 0.29 | weak | 0.014 |
| Oil and yeast | 0.27 | weak | 0.024 |
| Water and salt | −0.25 | weak | 0.032 |
| Egg and water | −0.25 | weak | 0.037 |
| Oil and sweetener | 0.25 | weak | 0.037 |
| Sweetener and salt | 0.22 | weak | 0.062 |
| Sweetener and yeast | −0.15 | very weak | 0.21 |
| Oil and water | −0.13 | very weak | 0.27 |
| Water and yeast | −0.12 | very weak | 0.33 |
| Sweetener and water | 0.10 | negligible | 0.41 |
| Egg and salt | 0.09 | negligible | 0.44 |
| Oil and salt | −0.08 | negligible | 0.52 |
| Egg and sweetener | 0.06 | negligible | 0.59 |
| Salt and yeast | 0.03 | negligible | 0.82 |
No strong relationships
No pair reaches rho 0.20 with a p-value under 0.01, the bar for calling a relationship here. The nearest is egg and oil (rho 0.29, p 0.013), short of it with 72 recipes.
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: salt and yeast (0.03), egg and sweetener (0.06), oil and salt (−0.08) and egg and salt (0.09).
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 15 pairs tested, about 0.8 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 egg 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.