Carrot Cake Lab260 recipes

Carrot Cake Lab

What moves together in 260 carrot 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 7 ingredient ratios (grams per 100 g of flour), this page ranks all 260 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: 6 rise together at rho 0.20 or more, none 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 260 recipes (p of 0.05 or more).

Carrot and sugar: rho 0.16, very weak0.16Carrot and fat: rho 0.12, very weak, not distinguishable from zero0.12Sugar and fat: rho 0.46, moderate0.46Carrot and egg: rho 0.30, weak0.30Sugar and egg: rho 0.11, very weak, not distinguishable from zero0.11Fat and egg: rho 0.20, very weak0.20Carrot and spice: rho −0.03, negligible, not distinguishable from zero−0.03Sugar and spice: rho 0.31, weak0.31Fat and spice: rho 0.19, very weak0.19Egg and spice: rho −0.05, negligible, not distinguishable from zero−0.05Carrot and leavening: rho 0.14, very weak0.14Sugar and leavening: rho 0.05, negligible, not distinguishable from zero0.05Fat and leavening: rho 0.04, negligible, not distinguishable from zero0.04Egg and leavening: rho 0.34, weak0.34Spice and leavening: rho −0.04, negligible, not distinguishable from zero−0.04Carrot and salt: rho 0.02, negligible, not distinguishable from zero0.02Sugar and salt: rho 0.46, moderate0.46Fat and salt: rho 0.13, very weak0.13Egg and salt: rho −0.06, negligible, not distinguishable from zero−0.06Spice and salt: rho 0.40, weak0.40Leavening and salt: rho −0.11, very weak, not distinguishable from zero−0.11SugarFatEggSpiceLeaveningSaltCarrotSugarFatEggSpiceLeavening
All 21 pairs as a table
Spearman correlation for every pair of ratios, strongest first
PairRhoStrengthp
Sugar and salt0.46moderateunder 0.001
Sugar and fat0.46moderateunder 0.001
Spice and salt0.40weakunder 0.001
Egg and leavening0.34weakunder 0.001
Sugar and spice0.31weakunder 0.001
Carrot and egg0.30weakunder 0.001
Fat and egg0.20very weak0.001
Fat and spice0.19very weak0.002
Carrot and sugar0.16very weak0.011
Carrot and leavening0.14very weak0.023
Fat and salt0.13very weak0.032
Carrot and fat0.12very weak0.061
Leavening and salt−0.11very weak0.072
Sugar and egg0.11very weak0.075
Egg and salt−0.06negligible0.32
Sugar and leavening0.05negligible0.44
Egg and spice−0.05negligible0.44
Fat and leavening0.04negligible0.50
Spice and leavening−0.04negligible0.53
Carrot and spice−0.03negligible0.63
Carrot and salt0.02negligible0.75

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 sugar tend to use more salt

    rho 0.46 across 260 recipes · moderate · p under 0.001

    The third of recipes with the most sugar use a median of 1.2% salt; the third with the least sugar, 0.1%.

    0%100%200%300%0%1%2%3%4%Sugar, % of flour →↑ Salt, % of flour

  2. Recipes with more sugar tend to use more fat

    rho 0.46 across 260 recipes · moderate · p under 0.001

    The third of recipes with the most sugar use a median of 87% fat; the third with the least sugar, 65%.

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

  3. Recipes with more spice tend to use more salt

    rho 0.40 across 260 recipes · weak · p under 0.001

    The third of recipes with the most spice use a median of 1.2% salt; the third with the least spice, 0.05%.

    0%2%4%6%8%0%1%2%3%4%Spice, % of flour →↑ Salt, % of flour

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: carrot and salt (0.02), carrot and spice (−0.03), spice and leavening (−0.04) and fat and leavening (0.04).

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 carrot 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.