Randomization Breaks OVB

Section one

Key concepts

The claim the deck makes, and the picture behind it.

Key concepts

The observational problem.

In a study of caffeine and heart rate, stress and sleep are omitted variables — and they are connected to both caffeine consumption and heart rate.

If we can’t measure stress and sleep quality to include in our study it will cause bias: we can’t confidently say caffeine is the factor driving the increase in heart rate, or if it co-occurs with the other factors that are actually increasing heart rate.

What randomization does.

Randomization breaks the correlations between the variable that has been randomized and the rest of the variables in the study — except the outcome, if the relationship is in fact causal.

Assigning caffeine doses at random severs the arrows from stress and sleep into caffeine. They may still affect heart rate; they no longer travel through the treatment.

The test this creates.

If the relationship was spurious then caffeine dosage no longer predicts heart rate.

A relationship that survives randomization is causal. A relationship that disappears was riding on the omitted variables all along.

In Venn terms.

X₂ overlapping X₁ → will cause bias when omitted
X₂ not overlapping X₁ → will not cause bias when omitted

Randomization moves every other variable from the first picture to the second.

The same logic applies to program participation.

Whoever chooses to participate in a program differs from those who do not, on things you cannot measure. Randomizing participants into treatment groups breaks those correlations exactly as it does for a dose.

Section two

Key relationships

The mental map. How the pieces connect, and how to read the deck.

Randomization sets one term of the bias formula to zero

This deck is short because it only needs one line from p-07:

bias = α₁ · β₂

where α₁ is the slope of the omitted variable regressed on the treatment. Randomization makes the treatment independent of everything that was determined before assignment, so α₁ = 0 for every such variable, and therefore bias = 0 · β₂ = 0.

Note what it does not do. It does not make β₂ zero — stress still affects heart rate, and sleep still affects heart rate. Those variables remain in the residual, where they inflate your standard errors. Randomization buys you accuracy, not precision.

That is why randomized studies still use control variables: type-A controls (uncorrelated with the treatment, which after randomization means all of them) shrink the residual and tighten the interval. Under randomization, every control is a type-A control.

The two failure routes, and which one randomization closes

An observed association between caffeine and heart rate could be either:

Causal — caffeine raises heart rate directly.
Spurious or confounded — stress causes people to drink more coffee and raises heart rate, so the two move together without one causing the other.

The naïve regression cannot tell these apart, because both produce the same correlation. Randomization can, and the mechanism is worth stating carefully: once dose is assigned by a coin flip, stressed people are no more likely to get a high dose than anyone else. Any remaining association cannot be running through stress.

Hence the deck’s sharpest slide: if the relationship was spurious then caffeine dosage no longer predicts heart rate. Randomization does not merely reduce bias — it converts the study into a test that a spurious relationship fails.

Why this is the strongest answer to p-07’s problem

p-07 ended in an uncomfortable place. Observational studies always omit something; you can sometimes sign the bias but rarely remove it; and the correlated controls that would fix it are expensive and never provably complete.

Randomization sidesteps the entire problem rather than solving it case by case. You do not need to know what the confounders are, or measure them, or even be able to name them. Whatever they are — measured, unmeasured, unmeasurable — random assignment breaks their correlation with the treatment simultaneously.

That is a qualitatively different kind of guarantee from “we controlled for everything we could think of,” and it is the reason experiments sit at the top of the evidence hierarchy.

What randomization does not fix

Worth being clear about the limits, since the deck focuses on the win:

It does not remove noise. The omitted variables still explain part of Y, so standard errors are unaffected.
It only breaks correlations with things determined before assignment. Anything that happens after — attrition, non-compliance, differential measurement — can reintroduce exactly the same problem.
It says nothing about whether your effect generalises beyond the units you randomized.

Where this sits

p-06 — correlated controls cost precision.
p-07 — omitting them costs accuracy; bias = α₁β₂.
this deck — randomization sets α₁ = 0, so the trade-off disappears.
taxonomy — how to classify controls when you cannot randomize.

How to read the slides

Slides	What they are doing	What to take away
2–4	Setup: is a relationship causal?	The question randomization answers.
5	The observational case	Stress and sleep connect to both caffeine and heart rate.
6	The key claim	Randomization severs correlations with the treatment.
7	The consequence	A spurious relationship disappears after randomization.
8–9	Venn versions	Overlap with X₁ → bias; no overlap → no bias.
10–11	Program participation	The same logic for who enrols, not just how much.

Section three

What should be clear in my mind?

Four things to be able to answer without notes.

What randomization actually does. It breaks the correlation between the randomized variable and everything else determined beforehand — it does not remove those variables’ effects on the outcome.
Why that eliminates bias. Because bias = α₁β₂, and randomization forces α₁ = 0.
Why it does not improve precision. The omitted variables still sit in the residual, so standard errors are unchanged. Controls are still useful in a randomized study.
What the spuriousness test is. If an association vanishes once the treatment is randomized, it was never causal.

Key takeaways

Randomization zeroes α₁, and a product with a zero in it is zero.
It buys accuracy, not precision. Bias goes away; noise does not.
You do not need to name the confounders. Random assignment handles unmeasured and unmeasurable ones at the same time.
After randomization every control is a type-A control — safe to add, and useful for shrinking standard errors.
A spurious relationship fails the randomized test, which is what makes an experiment a test rather than a description.
Only pre-assignment correlations are broken. Attrition and non-compliance can bring confounding back in.