The terms the films use, defined plainly, each with the film that explains it.
The variables you hold fixed to close every back-door path between a treatment and its outcome, without holding fixed anything the treatment causes or any collider. Often more than one set works, and you choose the one you can measure best. Sometimes none works, because a back door runs through something nobody measured.
Explained in 2.3 Confounders and the back door
Any route between a treatment and an outcome that starts with an arrow pointing into the treatment, such as organic certification, back to farm size, and on to efficiency. Back doors let through association that isn’t the treatment’s effect, so each must be closed by holding fixed a variable that sits on it.
Also called: back door, back-door criterion
Explained in 2.3 Confounders and the back door
Comparing an outcome before and after a change, such as Takaki’s navy voyages on different diets. It is the simplest evidence and, on its own, the weakest, because prices, weather, fashions and other policies change at the same time. Adding a comparison group, or measuring every link of a chain, makes it much stronger.
Also called: before and after, pre-post comparison
Explained in 3.3 Before and after, with a comparison, 1.3 Hidden in the food, 5.2 When farming changed the plate
Growing more of a nutrient into a crop itself, by breeding or by fertilising. Finland’s selenium fertiliser and orange-fleshed sweet potato, rich in beta-carotene, are examples. The convincing cases measure more than one link in the chain from crop to diet, and use a design that fits the question.
Explained in 5.2 When farming changed the plate
Grouping units that are alike, such as plots along the same side of a field or fields on the same farm, and randomising treatments within each group. Blocks soak up the differences you know about; randomisation handles the ones you don’t. Ronald Fisher set it out for field experiments in the 1920s.
Also called: blocks
Explained in 1.4 The wheat field, 5.3 From a pattern to a plan
Nine things Austin Bradford Hill listed in 1965 to weigh when deciding whether an association is causal, including its strength, its consistency, whether the cause comes first, and whether more dose brings more effect. He insisted they were aids to judgement, not a checklist.
Also called: Bradford Hill criteria
Explained in 1.6 Smoking and the sceptic
Methods that try to draw a causal map from data, by reading the patterns chains, forks and colliders leave behind, as the PC algorithm does. From observational data they usually narrow things to a family of maps, and they need strong assumptions. They are best used to draft a map for experts to check and test.
Also called: structure learning, PC algorithm
Explained in 4.4 Can AI find causes?
Hundreds of slightly different causal trees, averaged. Each tree splits the data with yes-or-no questions to find the groups whose treatment effects differ most. Set out by Stefan Wager and Susan Athey in 2018, causal forests estimate the average effect for units like a given one, not the effect on one particular field.
Also called: causal tree, generalised random forest
Explained in 4.2 Who benefits?
The discipline of telling a cause from a pattern: working out what would actually happen if you changed something, and how sure you can be. It combines a precise question, a causal map of the assumptions, a study design that can answer the question, and checks that try to break the answer.
Also called: causal analysis
Explained in Introduction: from field to plate, 5.4 What it takes to do this well
A diagram that draws each thing that varies as a box and each direct effect as an arrow, with no numbers. Also called a directed acyclic graph: arrows point one way and no route returns to its start. Sewall Wright’s path diagrams of 1921 were the first. A map puts assumptions where experts can check them.
Also called: DAG, directed acyclic graph, causal diagram, path diagram, causal graph
Explained in 2.1 Draw it before you analyse it, 1.5 Arrows and instruments, 2.7 How the map changes the work, 4.4 Can AI find causes?, 5.4 What it takes to do this well
Three variables in a line, where one affects a second that affects a third, like a foliar zinc spray raising leaf zinc, which raises grain zinc. Association flows along a chain, but holding the middle fixed blocks it, which is why adjusting for a mediator removes part of the effect.
Also called: causal chain
Explained in 2.2 Three shapes
A trial that randomises whole groups, such as communities, farms or herds, rather than individuals, because the treatment works through the whole group. Members of a cluster are alike, so the number of clusters matters more than the number of people: a hundred families in ten clusters tell you less than a hundred randomised singly.
Also called: cluster randomized trial, cluster trial
Explained in 3.1 The trial on the farm
A variable with two arrows pointing into it, such as whether a grain sample reaches the lab when either good soil or a new treatment can send it there. A collider blocks association between its causes until you hold it fixed, by adjusting for it or selecting on it. Then a link appears from nowhere.
Explained in 2.2 Three shapes, 2.4 Mediators, 2.5 Colliders and selection, 4.4 Can AI find causes?
A false link created by holding a collider fixed. Joseph Berkson described it in 1946: two unrelated illnesses appeared linked among hospital patients because either one could put a patient in hospital. Analysing only lab samples, or only animals that reached slaughter, can do the same.
Also called: Berkson’s bias
Explained in 2.5 Colliders and selection
Something that affects both a decision and its outcome, so a comparison mixes the treatment’s effect with its own. At a feedlot, the risk a vet sees on arrival drives both which groups get antibiotics and which animals die. When the confounder is the very reason for treating, it is called confounding by indication.
Also called: confounding variable, confounding, confounding by indication
Explained in P1 Right for the wrong reason, 2.2 Three shapes, 5.1 The chain from soil to health
Giving similar subjects different treatments under the same conditions, then comparing the results, as James Lind did with twelve sailors with scurvy in 1747. If the groups start alike and are treated alike apart from the treatment, a difference at the end points to the treatment. Letting chance decide who gets what makes it stronger.
Explained in 1.1 1747: twelve sailors and a cure nobody could explain
A single number for how closely two things move together, developed by Francis Galton in the 1880s. A correlation can be strong without either thing causing the other: something else may drive both, influence may run the other way, or two trends may simply be moving over the same years.
Also called: association
Explained in 1.2 “If the first had not been”, Introduction: from field to plate
What would have happened instead. A field had an extra pass of nitrogen and made thirteen per cent protein: would it have made thirteen per cent without it? Counterfactual questions sit on the top rung of Pearl’s ladder, and every causal effect compares an outcome that happened with one that didn’t.
Explained in P1 Right for the wrong reason, 1.2 “If the first had not been”
A label for any column in a data set that isn’t the treatment or the outcome. It is not a role: a covariate might be a confounder to adjust for, a mediator to leave out, or a collider never to adjust for. Only a causal map tells you which, and adding the wrong one can create bias.
Explained in 2.3 Confounders and the back door
Splitting the data into groups, training a model on all but one, predicting the one left out, and rotating until every unit has a prediction from a model that never saw it. A model judged on data it has memorised looks far better than it is, and cross-fitting stops that flattery leaking into the answer.
Also called: sample splitting
Explained in 4.1 Double machine learning, step by step, P2 Machines and causes
Comparing the change in a treated group with the change in a group that wasn’t treated, both measured before and after. If they were moving in parallel beforehand, the comparison group’s change shows what would have happened anyway, and the treated group’s extra change is the estimate. It rests on the parallel-trends assumption.
Also called: diff-in-diff, DiD
Explained in 3.3 Before and after, with a comparison
When a plant grows more mass, faster, the minerals it takes up can be spread more thinly through it. Breeding for bigger yields is the leading explanation for some declines in crop minerals: in the Broadbalk archive, grain minerals fell after high-yielding varieties arrived while the soil’s levels did not.
Explained in 5.1 The chain from soil to health
A pattern in which more of a cause brings more of the effect. Among British doctors, the risk of dying of lung cancer climbed with every step up in how much they smoked. It is one of Bradford Hill’s viewpoints for weighing whether an association is causal.
Also called: dose-response, biological gradient
Explained in 1.6 Smoking and the sceptic
A method that uses two nuisance models: one predicts the treatment from the background, the other the outcome, and the leftovers, or residuals, are compared. It is built so the models’ errors matter only when multiplied, a property called orthogonality, and uses cross-fitting. It still assumes no unmeasured confounding.
Also called: DML, debiased machine learning, nuisance model, residual, orthogonality
Explained in 4.1 Double machine learning, step by step, P2 Machines and causes
A variable that changes how big an effect is, like zone for the maize response to fertiliser in Ghana, or farm size for the efficiency gain from organic olives. You don’t adjust a modifier away and report one number; you report the effect for each group, because a single average can be wrong almost everywhere.
Also called: effect modification, moderator
Explained in 2.6 Modifiers, instruments and the unmeasured, 4.2 Who benefits?
A family of causal maps that fit the same observational data equally well. A chain and a fork leave the same fingerprint, so data alone can’t tell them apart, and causal discovery usually ends with an equivalence class rather than a single map.
Also called: Markov equivalence class
Explained in 4.4 Can AI find causes?
One variable affecting two others, like bran fraction raising both zinc and fibre in grain. The two outer variables move together although neither causes the other. Holding the middle fixed removes the link, if the fork is the whole story. When the shared cause also drives a treatment, it is a confounder.
Also called: common cause
Explained in 2.2 Three shapes
Bias that arises because people who choose a treatment differ from those who don’t, often by being healthier to begin with. Women who chose hormone therapy tended to be healthier, wealthier and more health-conscious, which made observational studies suggest a benefit that the trial didn’t find.
Also called: healthy user effect
Explained in 3.6 When observation lied
An effect that differs from place to place or unit to unit, such as a maize response to fertiliser of 2.8 tonnes a hectare in one zone of Ghana and 0.9 in another. An average effect answers “does it work, on the whole?”; a farmer asks “will it work on my farm?”
Also called: heterogeneous treatment effect, effect heterogeneity
Explained in 4.2 Who benefits?
A rule in causal forests: one half of the data chooses where to split, and the other half estimates the effect in each group. A tree can’t pick a group because it looks impressive and then report that same impressive number, which is what makes a forest’s uncertainty ranges trustworthy.
Also called: honest estimation
Explained in 4.2 Who benefits?
Whether the data can answer a causal question at all, decided before any model runs. A causal map shows which back doors must be closed and whether the variables needed to close them were measured. If not, the honest answer is “not yet”, because a cleverer model would only give a confident wrong answer.
Explained in 2.7 How the map changes the work
Something that pushes the treatment around but has no other route to the outcome, like growing conditions shifting the supply of flaxseed in Philip Wright’s 1928 study, or a cow’s genes for milk yield. An instrument lets you measure an effect from outside, but it fails if it leaks through a back route.
Also called: instrumental variable, IV
Explained in 1.5 Arrows and instruments, 2.6 Modifiers, instruments and the unmeasured
A long run of measurements before and after a change, compared with the trend projected from before it. It works best with a comparison group too. Without one, anything else that changed at the same time, such as a pandemic, could be part of the estimate.
Also called: ITS
Explained in 3.3 Before and after, with a comparison
A deliberate change to the world, as opposed to watching it. “If I put another pass of nitrogen on this field, what will happen to its protein?” is an intervention question, on the second rung of Pearl’s ladder. Data gathered only by watching can’t answer it on their own.
Explained in P1 Right for the wrong reason
Judea Pearl’s three rungs of causal questions. Seeing: given what I’ve seen, what should I expect? Doing: what happens if I intervene? Imagining: what would have happened instead? Most AI learns on the bottom rung, and data from it can’t climb to the next without an experiment or a causal model.
Also called: Pearl’s ladder
Explained in P1 Right for the wrong reason
Building a fair comparison without randomising, by pairing each treated unit with an untreated one that looks the same on everything measured, such as size, soil, rainfall and enterprise. A balance check then confirms the groups line up. Matching balances what you measured, never what you didn’t.
Also called: balance check, matched comparison
Explained in 3.2 Comparing like with like, 2.3 Confounders and the back door
A variable on the path from treatment to outcome: how the effect gets there, like leaf zinc between a spray and the grain, or diet between farm support and child growth. Adjusting for a mediator blocks the route the treatment works through, so the rule is never to adjust for anything the treatment causes.
Also called: mediating variable
Explained in 2.4 Mediators, 5.2 When farming changed the plate
Using genes as an instrument. Genes are dealt out at conception, before anyone decides anything, so comparing individuals by genes linked to a trait is like a natural lottery. In tens of thousands of Holstein cows it gave evidence that higher milk yield raises the risk of mastitis. It fails if the genes act another way.
Also called: Mendelian randomization
Explained in 2.6 Modifiers, instruments and the unmeasured, 3.4 Nature’s experiments
An arrow left off a causal map, which claims there is no direct effect at all. It is the strongest claim on any map, because the analysis leans on it: if the claim is wrong, the answer is wrong however much data you collect. Every missing arrow is a question for the experts in the room.
Explained in 2.1 Draw it before you analyse it
A change nobody designed that still splits the world into comparable groups. Eijkman’s chickens, switched to unpolished rice by accident, and John Snow’s houses, supplied by different water companies, are classic examples. The work is arguing that the split really was as good as random for the question being asked.
Explained in 1.3 Hidden in the food, 3.4 Nature’s experiments
An outcome the treatment can’t possibly affect, used to check an analysis. This year’s nitrogen can’t change last year’s yield, so if an analysis says it did, something is confounding the comparison. Negative controls can expose hidden confounding that the causal map missed.
Also called: negative control outcome
Explained in 4.3 Try to break your own answer
The assumption that every kind of unit had some chance of getting either treatment. If the best fields always got the extra pass of nitrogen, there are no comparable fields without it, and no method can supply the missing comparison.
Also called: positivity, common support
Explained in 4.1 Double machine learning, step by step
The key assumption of difference-in-differences: without the change, the treated and comparison groups would have kept moving together. You can check whether they moved in parallel before the change, by tracking both groups over the earlier period, but not afterwards, so it always stays an assumption.
Also called: parallel trends assumption
Explained in 3.3 Before and after, with a comparison
Replacing the real treatment with a fake one, shuffled at random, and running the whole analysis again. The effect should vanish. If the method finds a big effect of a treatment that never happened, it is finding patterns in the noise, and its real result shouldn’t be trusted either.
Also called: placebo treatment
Explained in 4.3 Try to break your own answer
The outcome a unit would have under each possible treatment. A field has a yield if fertilised and another if not, and the effect is the difference. Only one is ever seen, which is the fundamental problem of causal inference. Jerzy Neyman wrote these outcomes into mathematics for crop varieties on plots.
Also called: potential outcomes
Explained in 1.2 “If the first had not been”
A unit’s probability of being treated, given everything measured about it. Paul Rosenbaum and Donald Rubin showed in 1983 that units with the same score are, on average, balanced on all those characteristics at once, so you can match or weight on one number instead of many. It balances only what was measured.
Also called: propensity score matching
Explained in 3.2 Comparing like with like, 3.5 When neighbours matter
The smallest step that can answer the question. Not every promising pattern calls for a field trial; many questions need only one or two steps, such as completing the records, measuring what’s missing or learning from changes already happening. A trial, which asks the most of a farm, is chosen when the evidence points to it.
Explained in 5.3 From a pattern to a plan, 2.7 How the map changes the work, 5.4 What it takes to do this well
A stand-in for something hard to measure, like arrival weight for a calf’s disease risk, or a laboratory result for the true composition of the grain. Proxies help, but they leave some confounding behind. On a causal map, a proxy hangs off the thing it measures.
Also called: proxy variable
Explained in 2.6 Modifiers, instruments and the unmeasured
Letting chance decide which unit gets which treatment. Then no difference between units, known or unknown, can line up with the treatment except by luck, and statistics can say how big that luck might be. Ronald Fisher developed it for field trials at Rothamsted; it is the only method that handles confounders nobody has thought of.
Also called: random allocation, randomization
Explained in 1.4 The wheat field, 1.1 1747: twelve sailors and a cure nobody could explain, 5.3 From a pattern to a plan
A study in which chance decides which units get the treatment, and the groups are then compared. On farms the units can be strips, plots, animals, herds or whole communities. Because no hidden judgement can line up with the treatment, a randomised trial still beats every other design when it can be run.
Also called: randomised trial, RCT, randomized controlled trial
Explained in 3.1 The trial on the farm, 1.4 The wheat field
A design that uses a sharp rule. If a grant goes only to farms above 50 hectares, farms just either side of the line are nearly identical apart from the grant, so comparing them is close to a randomised trial for farms near the threshold. It fails if units can shift themselves across the line.
Also called: RDD, regression discontinuity design
Explained in 3.4 Nature’s experiments
Testing each treatment on several units, such as several plots or strips, so that one odd plot can’t decide the answer. Replication lets a trial tell a real effect from the ordinary variation between plots, and repeating a test across farms and years is how a lead becomes knowledge.
Also called: replicates
Explained in 1.4 The wheat field, 5.3 From a pattern to a plan
A single number from Carlos Cinelli and Chad Hazlett, in 2020: how much of the variation in both the treatment and the outcome a hidden confounder would need to explain to bring the effect to zero. Compared with how much measured factors such as soil type or rainfall explain, it shows how sturdy a result is.
Explained in 4.3 Try to break your own answer
Bias that comes from which units end up in the data: farms that volunteer, fields with complete records, animals that reach slaughter, studies that get published. Selection that depends on the treatment and the outcome, or their causes, creates collider bias. Counting every unit that started, not just those that finished, is often the fix.
Also called: survivorship bias, publication bias
Explained in 2.5 Colliders and selection
Asking how strong an unmeasured confounder would have to be to overturn a result, and comparing that with confounders you did measure. Jerome Cornfield’s 1959 answer to Fisher about smoking was the first. If the hidden factor would need to be far stronger than soil type, you can be fairly confident.
Explained in 4.3 Try to break your own answer, P2 Machines and causes, 1.6 Smoking and the sceptic, 5.4 What it takes to do this well
When one unit’s treatment changes another unit’s outcome. On farms, pests, pollinators, spray drift, water, disease and ideas cross the hedge: Bt maize cut corn borer numbers for neighbours who never planted it. Spillovers can be designed around with whole-area randomisation and buffer strips, or measured directly.
Also called: interference, spillover effect
Explained in 3.5 When neighbours matter
A measurement that stands in for the outcome you really care about, such as a one-off drink choice on a screen instead of what children drink over months, or methane per kilogram of feed instead of a farm’s footprint. A trial is only as useful as its outcome is close to the real one.
Also called: surrogate endpoint, surrogate
Explained in 3.1 The trial on the farm
A way to build a twin for a single treated place: combine untreated regions, weighted so that together they track the treated region’s past as closely as possible. After the change, the gap between the real place and its synthetic twin is the estimate, as with California’s 1988 tobacco control programme.
Also called: synthetic control method
Explained in 3.4 Nature’s experiments
Writing down the randomised trial you wish you could run, then making an observational analysis copy it: who is eligible, exactly what the treatment is, and a time zero when everyone’s clock starts. Starting everyone at the same moment stops long-term users being compared with newcomers.
Also called: target trial, time zero
Explained in 3.6 When observation lied
A prediction a causal map makes that data could contradict. If bran is a common cause of zinc and fibre, then among samples with the same bran fraction, zinc and fibre should stop moving together. Checking implications like this can rule a rival explanation in or out before anything is changed on the farm.
Explained in 2.7 How the map changes the work
The total effect is what happens to the outcome when the treatment changes, by every route together; it is usually what a farmer wants to know. The direct effect is the part that doesn’t travel through a chosen mediator: protein if extra nitrogen were added but yield somehow stayed the same. Splitting an effect needs extra assumptions.
Also called: total effect, direct effect
Explained in 2.4 Mediators
A common cause of treatment and outcome that was never recorded, such as a grower’s skill or a stockperson’s eye. On a causal map it is drawn as a dashed box. Its back door can’t be closed by adjustment, so you randomise, use a design that sidesteps it, or test how strong it would need to be.
Also called: hidden confounder, unobserved confounding
Explained in 2.6 Modifiers, instruments and the unmeasured, 1.6 Smoking and the sceptic
An alternative to matching that gives each unit a weight based on its propensity score, so that units which were unlikely to be treated but were count for more. The weighted groups then line up on what was measured. Like matching, weighting can’t balance anything that wasn’t recorded.
Also called: inverse probability weighting
Explained in 3.2 Comparing like with like
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