Peanut Butter Cookies Lab326 recipes

Peanut Butter Cookies Lab

What moves together in 326 peanut butter cookie 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 326 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: 11 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 326 recipes (p of 0.05 or more).

Peanut butter and butter: rho 0.28, weak0.28Peanut butter and sugar: rho 0.33, weak0.33Butter and sugar: rho 0.45, moderate0.45Peanut butter and egg: rho 0.25, weak0.25Butter and egg: rho 0.34, weak0.34Sugar and egg: rho 0.40, weak0.40Peanut butter and leavening: rho 0.20, weak0.20Butter and leavening: rho 0.16, very weak0.16Sugar and leavening: rho 0.29, weak0.29Egg and leavening: rho 0.26, weak0.26Peanut butter and salt: rho 0.17, very weak0.17Butter and salt: rho 0.30, weak0.30Sugar and salt: rho 0.30, weak0.30Egg and salt: rho 0.01, negligible, not distinguishable from zero0.01Leavening and salt: rho 0.08, negligible, not distinguishable from zero0.08ButterSugarEggLeaveningSaltPeanut butterButterSugarEggLeavening
All 15 pairs as a table
Spearman correlation for every pair of ratios, strongest first
PairRhoStrengthp
Butter and sugar0.45moderateunder 0.001
Sugar and egg0.40weakunder 0.001
Butter and egg0.34weakunder 0.001
Peanut butter and sugar0.33weakunder 0.001
Butter and salt0.30weakunder 0.001
Sugar and salt0.30weakunder 0.001
Sugar and leavening0.29weakunder 0.001
Peanut butter and butter0.28weakunder 0.001
Egg and leavening0.26weakunder 0.001
Peanut butter and egg0.25weakunder 0.001
Peanut butter and leavening0.20weakunder 0.001
Peanut butter and salt0.17very weak0.002
Butter and leavening0.16very weak0.003
Leavening and salt0.08negligible0.17
Egg and salt0.01negligible0.87

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.

  1. Recipes with more butter tend to use more sugar

    rho 0.45 across 326 recipes · moderate · p under 0.001

    The third of recipes with the most butter use a median of 132% sugar; the third with the least butter, 88%.

    0%50%100%150%0%100%200%300%Butter, % of flour →↑ Sugar, % of flour

  2. Recipes with more sugar tend to use more egg

    rho 0.40 across 326 recipes · weak · p under 0.001

    The third of recipes with the most sugar use a median of 32% egg; the third with the least sugar, 24%.

    0%100%200%300%0%25%50%75%100%125%Sugar, % of flour →↑ Egg, % of flour

  3. Recipes with more peanut butter tend to use more sugar

    rho 0.33 across 326 recipes · weak · p under 0.001

    The third of recipes with the most peanut butter use a median of 115% sugar; the third with the least peanut butter, 97%.

    0%100%200%300%0%100%200%300%Peanut butter, % of flour →↑ Sugar, % of flour

Also strong, and left out above because both of its ingredients already appear: butter and egg (rho 0.34).

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 (0.01) and leavening and salt (0.08).

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 peanut butter 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.