Irish Soda Bread Lab123 recipes

Irish Soda Bread Lab

What moves together in 123 Irish soda 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 6 ingredient ratios (grams per 100 g of flour), this page ranks all 123 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: 4 rise together at rho 0.20 or more, 1 moves 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 123 recipes (p of 0.05 or more).

Buttermilk and baking soda: rho 0.10, very weak, not distinguishable from zero0.10Buttermilk and butter: rho 0.00, negligible, not distinguishable from zero0.00Baking soda and butter: rho 0.00, negligible, not distinguishable from zero0.00Buttermilk and sugar: rho −0.10, very weak, not distinguishable from zero−0.10Baking soda and sugar: rho −0.21, weak−0.21Butter and sugar: rho 0.48, moderate0.48Buttermilk and egg: rho 0.08, negligible, not distinguishable from zero0.08Baking soda and egg: rho −0.06, negligible, not distinguishable from zero−0.06Butter and egg: rho 0.54, moderate0.54Sugar and egg: rho 0.41, moderate0.41Buttermilk and salt: rho 0.14, very weak, not distinguishable from zero0.14Baking soda and salt: rho 0.24, weak0.24Butter and salt: rho 0.02, negligible, not distinguishable from zero0.02Sugar and salt: rho −0.05, negligible, not distinguishable from zero−0.05Egg and salt: rho 0.00, negligible, not distinguishable from zero0.00Baking sodaButterSugarEggSaltButtermilkBaking sodaButterSugarEgg
All 15 pairs as a table
Spearman correlation for every pair of ratios, strongest first
PairRhoStrengthp
Butter and egg0.54moderateunder 0.001
Butter and sugar0.48moderateunder 0.001
Sugar and egg0.41moderateunder 0.001
Baking soda and salt0.24weak0.008
Baking soda and sugar−0.21weak0.018
Buttermilk and salt0.14very weak0.12
Buttermilk and baking soda0.10very weak0.25
Buttermilk and sugar−0.10very weak0.26
Buttermilk and egg0.08negligible0.36
Baking soda and egg−0.06negligible0.52
Sugar and salt−0.05negligible0.58
Butter and salt0.02negligible0.84
Baking soda and butter0.00negligible0.72
Buttermilk and butter0.00negligible0.31
Egg and salt0.00negligible0.34

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 egg

    rho 0.54 across 123 recipes · moderate · p under 0.001

    82% of the third of recipes with the most butter use some egg, against 19% of the 47 with no butter.

    0%10%20%30%0%10%20%30%Butter, % of flour →↑ Egg, % of flour

  2. Recipes with more butter tend to use more sugar

    rho 0.48 across 123 recipes · moderate · p under 0.001

    78% of the third of recipes with the most butter use some sugar, against 31% of the 47 with no butter.

    0%10%20%30%0%10%20%30%Butter, % of flour →↑ Sugar, % of flour

  3. Recipes with more baking soda tend to use more salt

    rho 0.24 across 123 recipes · weak · p 0.008

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

    0%1%2%3%0%1%2%3%Baking soda, % of flour →↑ Salt, % of flour

Also strong, and left out above because both of its ingredients already appear: sugar and egg (rho 0.41).

What moves on its own

  • Buttermilk. Nearly independent of the rest: its strongest correlation with any other ingredient is 0.14, with salt. A recipe's amount of buttermilk says almost nothing about its other amounts.

The pairs closest to unrelated: buttermilk and butter (0.00), egg and salt (0.00), baking soda and butter (0.00) and butter and salt (0.02).

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 buttermilk 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.