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Reasoning about causality

Q: When is a variable a collider?

X-->C<--Y C, is a collider here because in this path both arrows point towards it.

Q: What happens when you control for a collider?

The back door path that was closed by the collider is opened again.

Q: If you control a collider, how can you close the path it's on again?

By controlling for another variable that is on that path.

33 important questions on Reasoning about causality

How do we call a study in which people are allocated at random (by chance alone) to receive one of several clinical interventions?

A randomized controlled trial.

What are the two benefits of using randomization?

It eliminates confounder bias
it enables the researcher to quantify his uncertainty

How can you find a confounder?

Try adjusting for the confounder, and try not adjusting for the confounder
if there is a difference in results, the confounder is real and should be adjusted for.
if there isn't any difference, use the non-adjusted results.

What is the definition of a confound?

Anything that makes P(Y | X) differ from P(Y | doing X).

When should a confounder be controlled for?

If the confounder influences X, but not if it just influences Y.

In a relationship diagram, what is a backdoor?

All the paths from x to y that start with an arrow pointing away from x.

How do you close a back- or front door route in a relationship diagram?

Control any variable that is in that route.

How do you choose which variables to control for?

Always choose the least amount of variables.
identify all the possible paths from x to y
choose the variables that cause the back doors to close, while the front doors stay open.

How do we call controlling for something that your treatment causes, causing you to shut down some of the effect of your treatment on the outcome?

Post treatment bias

When is a variable a collider?

X-->C<--Y
C, is a collider here because in this path both arrows point towards it.

What happens when you control for a collider?

The back door path that was closed by the collider is opened again.

If you control a collider, how can you close the path it's on again?

By controlling for another variable that is on that path.

What is a quasi experiment?

An experiment where the participants aren't randomly assigned to the different conditions.

What are the three criteria of a causal relationship?

X causes Y if:

X precedes Y; priority
change in X varies systematically with change in Y; consistency
there is no alternative explanation for the relationship.; exclusivity

Describe post hoc ergo propter hoc

Mistake correlation for causality
"X precedes Y, therefor X must cause Y"

Describe the inversion of cause and effect.

Mistake covarying with causality
"X causes Y, therefor the absence of X causes the absence of Y"

What does it mean when we talk about an inus condition instead of a single cause?

By itself not sufficient to cause something, but part of a group of factors that cause something

Apply the inus condition on a match as a cause for a fire.

Insufficient: a match cant start a fire on it's own, it needs oxygen etc.
non-redundant (niet overbodig): relevant part of the situation
unnecessary: there are other tools to start a fire with
sufficient condition: together with friction, oxygen and fuel it will start a fire.

What is a counterfactual?

Knowledge of what would have happened to a participant had they not undergone a certain manipulation.

How can counterfactuals be used to check for non-redundancy?

Compare the counterfactual to what actually happened
the difference between the situations can be attributed as an effect of the manipulation so we know if its non-redundant.

What are ways to cut the paths between causes and different confounds (backdoors)

Matching and randomization

What are the threats of causality?

History: unplanned events unrelated to the intervention that might impact the outcome
maturation: natural changes that may be confused with treatment effect.
selection: biased assignment to groups
attrition: systematic correlated with condition participant dropping
instrumentation: changes in scoring rubric or instrument caliber such as rater fatigue
testing: the effect of taking a pre test on the outcome of the study (familiarity with questions etc.)

How do you determine what the counterfactual should be?

What if everything was the same except for.....

Put the following in a DAG: the effect of X on Y is mediated by Z.

X->Z->Y

Put the following in a DAG: X and Y have a common effect Z

X->Z<-Y

Put the following in a DAG: X and Y have a common cause Z

X<-Z->Y

How do we call the idea that the more controlled variables are included in the model, the more accurate the estimation of the causal effect is?

The erroneous purification principle.

Which two problems come from the erroneous purification principle?

Problem of overcorrection
collider bias

How do we call it when controlling for common effects will bias the estimation of a causal relationship between two variables.

Collider bias

How do we call it when controlling for mediators on the causal path could lead to an underestimation of the total causal effect?

Problem of overcorrection

Why is it important to control for a common cause?

By controlling for a common cause, you avoid finding spurious correlations

Describe Berkson's paradox

When a spurious correlation is found between two variables due to collider controlling.
when two diseases in a hospital are correlated this is because you're already in a hospital. So when you don't have one disease the chances are higher that you have the other disease because you are already sick.
when you also look at people outside the hospital, the correlation is not found.

How can a correlation between attractiveness and character be found in an individual's dates be explained by berkson's paradox.

You're only looking at a specific subset of people. The dates of one individual.
if the person is ugly and not nice you wouldn't go out in the first place.
so if you're date is ugly chances increase that he's very nice.

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scientific and statistical reasoning and psychological testing

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