Bialys Lab
What moves together in 22 bialy recipes
When a recipe uses more of one ingredient, does it tend to use more or less of another? For every pair of the 5 ingredient ratios (grams per 100 g of flour), this page ranks all 22 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).
3 pairs in all: none rise together at rho 0.20 or more, none move in opposite directions at −0.20 or less, and 2 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 22 recipes (p of 0.05 or more).
Marked n/a: sugar or malt and fat, which too few recipes use to rank.
All 3 pairs as a table
| Pair | Rho | Strength | p |
|---|---|---|---|
| Water and yeast | 0.18 | very weak | 0.42 |
| Salt and yeast | −0.09 | negligible | 0.70 |
| Water and salt | −0.04 | negligible | 0.87 |
No strong relationships
No pair reaches rho 0.20 with a p-value under 0.01, the bar for calling a relationship here. With 22 recipes, the ingredients look chosen largely independently of one another.
What moves on its own
- Salt. Nearly independent of the rest: its strongest correlation with any other ingredient is −0.09, with yeast. A recipe's amount of salt says almost nothing about its other amounts.
The pairs closest to unrelated: water and salt (−0.04) and salt and yeast (−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 3 pairs tested, about 0.2 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 water 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.