Is the fallacy limited to the second table?

No; the name refers to a common reporting pattern.

Are all non-primary coefficients necessarily biased?

No; their validity depends on the target and assumptions.

Can one model answer several causal questions?

Sometimes, but each interpretation needs its own justification.

AI Glossary / Statistics and probability / Intermediate

Table 2 fallacy

Definition

The Table 2 fallacy is the mistake of interpreting every coefficient from one multivariable regression as though each estimated the intended causal effect of its own variable. A model designed to estimate one exposure's effect may adjust appropriately for that exposure while producing coefficients for other variables that answer different questions or lack a valid causal interpretation.

What it means

Regression output often lists many variables in one table, giving their coefficients a visually similar status. Yet the reasons for including them differ. One may be the exposure of interest, another a confounder, another a mediator, and another an effect modifier.
The same adjustment set need not be appropriate for every variable treated in turn as the exposure. The fallacy concerns interpretation, not the table number itself. Publishing additional coefficients can be useful for transparency, provided their roles and limits are clear.

How it works

Start by defining the causal question and target effect. Specify which exposure is being compared, which outcome matters, and whether the interest is a total effect or a more restricted effect such as one holding an intermediate variable fixed.
Use substantive knowledge to describe the causal relationships among variables. A directed acyclic graph can help identify which variables are confounders for the chosen exposure and which lie on a pathway from it to the outcome.
Select adjustment variables for that specific target. A variable that needs adjustment when estimating one exposure's effect may be a mediator when estimating another's total effect. Its role depends on the question and assumed causal structure.
Fit a model compatible with the target and data. Even an appropriate adjustment set does not protect against incorrect functional form, measurement error, selection bias, or unmeasured confounding. Causal interpretation requires more than adding covariates to an equation.
Read each coefficient as a conditional model parameter before attaching a causal meaning. Holding the other listed variables fixed may remove part of the effect a reader expects to include. It can also introduce bias if the adjustment conditions on an inappropriate variable.
Consider interactions. When an exposure interacts with another variable, a main coefficient may describe the exposure contrast only at a reference value of the modifier. It is not automatically an overall average effect across the study population.
If effects of several exposures are genuinely of interest, define each estimand and evaluate its own identification assumptions. Separate models, standardization, or other methods may be needed. One convenient coefficient table is not a substitute for that reasoning.
Report the primary effect with its interpretation and uncertainty. Other coefficients can be included as model details or explicitly labeled associations, but avoid presenting them as a ranked list of causal drivers without justification.
For predictive models, coefficients may be useful for understanding fitted relationships without representing interventions. Prediction accuracy and causal effect identification are different goals, and a model's adjustment choices should be evaluated against the goal actually claimed.

Three practical examples

AI adoption research: avoid interpreting every adjustment coefficient as the causal impact of a separate organizational policy.
Customer studies: distinguish a product exposure's total effect from coefficients for variables that may mediate other relationships.
Dashboard reporting: prevent a regression table from becoming an unjustified list of independent causal levers.

Think of it this way

Think of building a map for one journey. The chosen route may answer that journey well, but it does not automatically give the right route for every other starting point. Likewise, an adjustment set chosen for one exposure does not automatically answer every causal question represented by the table's rows.

Worked example

Consider an original hypothetical causal system with variables X, M, and Y. Let M = 4X + U and Y = 2X + 3M + V, where X, U, and V are mutually independent, mean-zero variables with nonzero variances. Assume these equations describe interventions as well as observed relationships.
In a regression of Y on both X and M, the population coefficients are 2 for X and 3 for M. Holding M fixed, increasing X by one unit changes Y by two units in this stipulated system.
But allowing M to respond normally, a one-unit increase in X increases M by four. The total effect on Y is 2 + 3 times 4 = 14. The coefficient 2 therefore does not estimate X's total effect.
If the original question concerns the effect of M on Y, adjusting for X addresses the common cause X in this toy structure. It does not make the X coefficient a total-effect estimate. The calculations illustrate the fallacy under explicit causal assumptions; regression output alone would not establish those assumptions.

Illustrative case study

Fictional case: Spruce Operations studies whether training increases use of an AI tool and whether tool use affects productivity. Its regression includes both training and tool use, and a report calls each coefficient a total causal effect. Analysts explain that tool use may mediate part of training's impact. They revise the report to distinguish the training total-effect question from a conditional comparison holding use fixed, and identify which additional assumptions each interpretation would require.

Common misconceptions and mistakes

Do not assume that adjusting for more variables makes every coefficient more causal. A small p-value does not fix the wrong estimand. A confounder for one exposure can have a different role for another. An interaction coefficient is not a universal effect across all subgroups. The solution is not simply to hide tables, but to align interpretation with explicitly justified questions.

Business use

Use the concept when reviewing analytical reports that identify multiple business drivers from a single regression. Ask what intervention each claimed effect represents and whether the adjustment set is suitable for it. Preserve model transparency while separating descriptive associations, predictive contributions, and supported causal estimates.

Check your understanding

What is X's conditional coefficient in the example?

Answer: Two.

What is its total causal effect under the stipulated equations?

Answer: Fourteen.

Why do they differ?

Answer: Holding M fixed removes the pathway through M.

Related terms

Causal estimand
Confounding
Mediation (statistics)
Regression coefficients
Directed acyclic graph
mediation
direct effect
total effect
regression coefficient
interaction

Learn next

Study adjustment-set selection and mediation diagrams, then practice rewriting coefficient-table claims as explicit intervention questions. Examine when standardization is needed to translate model parameters into the desired population effect.

Sources

Westreich and Greenland, The Table 2 Fallacy: Presenting and Interpreting Confounder and Modifier Coefficients: https://doi.org/10.1093/aje/kws412 Primary article record: https://pubmed.ncbi.nlm.nih.gov/23371353/ The structural-equation example is original.

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