Zucchini Bread Lab243 recipes

Zucchini Bread Lab

What moves together in 243 zucchini bread 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 243 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: 10 rise together at rho 0.20 or more, none move in opposite directions at −0.20 or less, and 6 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 243 recipes (p of 0.05 or more).

Zucchini and sugar: rho 0.24, weak0.24Zucchini and fat: rho 0.22, weak0.22Sugar and fat: rho 0.56, moderate0.56Zucchini and egg: rho 0.41, moderate0.41Sugar and egg: rho 0.32, weak0.32Fat and egg: rho 0.33, weak0.33Zucchini and spice: rho −0.05, negligible, not distinguishable from zero−0.05Sugar and spice: rho 0.07, negligible, not distinguishable from zero0.07Fat and spice: rho 0.05, negligible, not distinguishable from zero0.05Egg and spice: rho −0.11, very weak, not distinguishable from zero−0.11Zucchini and leavening: rho 0.31, weak0.31Sugar and leavening: rho 0.12, very weak, not distinguishable from zero0.12Fat and leavening: rho 0.02, negligible, not distinguishable from zero0.02Egg and leavening: rho 0.29, weak0.29Spice and leavening: rho −0.08, negligible, not distinguishable from zero−0.08Zucchini and salt: rho 0.14, very weak0.14Sugar and salt: rho 0.26, weak0.26Fat and salt: rho 0.20, weak0.20Egg and salt: rho 0.17, very weak0.17Spice and salt: rho 0.11, very weak, not distinguishable from zero0.11Leavening and salt: rho 0.01, negligible, not distinguishable from zero0.01SugarFatEggSpiceLeaveningSaltZucchiniSugarFatEggSpiceLeavening
All 21 pairs as a table
Spearman correlation for every pair of ratios, strongest first
PairRhoStrengthp
Sugar and fat0.56moderateunder 0.001
Zucchini and egg0.41moderateunder 0.001
Fat and egg0.33weakunder 0.001
Sugar and egg0.32weakunder 0.001
Zucchini and leavening0.31weakunder 0.001
Egg and leavening0.29weakunder 0.001
Sugar and salt0.26weakunder 0.001
Zucchini and sugar0.24weakunder 0.001
Zucchini and fat0.22weakunder 0.001
Fat and salt0.20weak0.002
Egg and salt0.17very weak0.007
Zucchini and salt0.14very weak0.029
Sugar and leavening0.12very weak0.064
Spice and salt0.11very weak0.077
Egg and spice−0.11very weak0.082
Spice and leavening−0.08negligible0.21
Sugar and spice0.07negligible0.29
Zucchini and spice−0.05negligible0.41
Fat and spice0.05negligible0.41
Fat and leavening0.02negligible0.76
Leavening and salt0.01negligible0.89

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 fat

    rho 0.56 across 243 recipes · moderate · p under 0.001

    The third of recipes with the most sugar use a median of 65% fat; the third with the least sugar, 41%.

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

  2. Recipes with more zucchini tend to use more egg

    rho 0.41 across 243 recipes · moderate · p under 0.001

    The third of recipes with the most zucchini use a median of 52% egg; the third with the least zucchini, 40%.

    0%100%200%300%0%50%100%150%Zucchini, % of flour →↑ Egg, % of flour

  3. Recipes with more zucchini tend to use more leavening

    rho 0.31 across 243 recipes · weak · p under 0.001

    The third of recipes with the most zucchini use a median of 3.8% leavening; the third with the least zucchini, 2.9%.

    0%100%200%300%0%2.5%5%7.5%10%Zucchini, % of flour →↑ Leavening, % of flour

Also strong, and left out above because both of its ingredients already appear: fat and egg (rho 0.33) and sugar and egg (rho 0.32).

What moves on its own

  • Spice. Nearly independent of the rest: its strongest correlation with any other ingredient is 0.11, with salt. A recipe's amount of spice says almost nothing about its other amounts.

The pairs closest to unrelated: leavening and salt (0.01), fat and leavening (0.02), zucchini and spice (−0.05) and fat and spice (0.05).

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 zucchini 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.