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SSR 3 > Lec. 20 - Critical Thinking about Causality > Flashcards

Lec. 20 - Critical Thinking about Causality Flashcards

1
Q

What to know after this lecture

A
  • what is a causal connection?
  • causal reasoning errors
  • what is a counterfactual?
    > counterfactuals in different designs
    > threats of causal inference
  • causal diagrams
    > specifying assumptions
    > identifying confounds
    > applied diagrams
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2
Q

What is a causal inference?

A
  • causality cannot be directly observed; it can only be inferred
  • you can’t measure causality directly, even through experiments you just see two events happening one after the other, but the causal relationship has to be investigated
    > e.g. when playing pool, you only see one ball moving after the other hit it, but you can’t directly see the causation between the two events
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3
Q

How is the causality inferred from an observational study called?

A
  • when a randomized control trial is not possible, we can use an observational study
  • “provisional causality”
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4
Q

What are Mill’s criteria to infer causality?

A

X causes Y if and only if:
- Priority: change in X precedes change in Y
- Consistency: change in X varies systematically with change in Y
- Exclusivity: there is no alternative explanation for the relationship
!! causality can be inferred only if ALL these criteria apply → if even just one criterion is not met, then it’s a correlation

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5
Q

What faulty reasoning is behind the priority criterion?
What is this fallacy called?

A

P1: X precedes Y
P2: if X precedes Y, X is the cause of Y
C: X is the cause of Y
- Post hoc ergo propter hoc

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6
Q

what faulty reasoning is behind the consistency criterion?

A

P1: X correlates with Y
P2: if X correlates with Y, X is the cause of Y
C: X is the cause of Y

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7
Q

what faulty reasoning is behind the exclusion criterion?

A

P1: X causes Y
P2: if X causes Y, then no Y without X
C: without X, no Y
! there can be other causes for Y
(see flashcards 12 and on)

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8
Q

what usually happens when study results don’t match theoretical explanation?

A

reserachers often say that there is something wrong with the measurement tools, and not with the theory

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9
Q

1) What causality criteria are met in this example? why?
“problematic academic achievements and drug abuse are related to low self-esteem → if we create a stronger positive sense of self-esteem, those other problems will also disappear”

A
  • Priority: not met (it’s not always the case that first there are problems, and then low self-esteem)
  • Consistency: ✓ (changes in one variable can lead to changes in the other variable)
  • Exclusivity: not met (there are other possible explanations behind both variables)
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10
Q

2) What causality criteria are met in this example? why?
“people with poor reading skills make more erroneous eye movements → abnormalities in eye movements cause poorer reading skills”

A
  • Priority: not clear
  • Consistency: ✓
  • Exclusivity: not clear
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11
Q

3) How was causality investigated in the disease example? What was concluded?
“a disease could be explained only by poor sanitary conditions (drinking infected water or poor nutrition)”

A
  • the researchers ate sweet balls with infected urine and scales → they did not get the disease
    = poor sanitary conditions were not the cause
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12
Q

What criteria are met in the disease example?

A
  • Priority: ✓
  • Consistency: not met (no disease after eating infected sweets, therefore poor sanitary conditions and disease not necessarily related)
  • Exclusivity: not met (poor nutrition could also be the cause of the disease
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13
Q

What is the exclusivity criterion? How can we assess it?

A
  • there is no alternative explanation for the relationship
    ! it does not mean that X is the only cause of Y !
    → INUS condition
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14
Q

What is an example of an INUS condition?
(this example will come in handy in the following flashcards)

A

“guns don’t kill people, people kill people”
- are guns a cause of death?
> Priority: ✓
> Consistency: ✓
> Exclusivity: ? (INUS condition!)

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15
Q

INUS condition

A
  • Insufficient but non-redundant part of an unnecessary but sufficient condition
    > it explains exclusivity criterion
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16
Q

(1) what does insufficient mean?

A
  • X is insufficient
    = X on its own will not lead to Y
    > gun itself will not lead to death: it has to be loaded, with gun powder, used, …
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17
Q

(2) what does non-redundant mean?

A
  • X is relevant predictor in set of predictors
  • X adds explanatory power to set of different factors
  • does this factor (X) make a difference in set of factors?
    > set of factors: gun + loaded + gun powder + used + …
    > gun: non-redundant
    → gun is relevant in set of factors; even if all other factors are met, without the gun there would be no death
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18
Q

(3) What does unnecessary mean?

A
  • other set of factors are also possible
    > people can still be killed in different ways
    > gun (+ factors) are not the only cause of death, therefore to produce death they are not necessary
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19
Q

(4) what does sufficient mean?

A
  • this set of factors is enough
    > gun (+ factors) are enough to produce death
    > they are not the only possible cause, but when present they are sufficient
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20
Q

Does a match cause a fire?
- INUS condition applied to “match example”

A
  • Insufficient: a match does not lead to fire without other factors (e.g. oxygen, …)
  • non-redundant: a match is relevant predictor in set of factors (it is substantially different from a situation without a match)
  • unnecessary condition: other combos are also possible (sunlight, dry grass, …)
  • sufficient condition: combination of paper, oxygen, matches, … is sufficient to produce fire
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21
Q

How can we check for non-redundancy?

A

through a counterfactual

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22
Q

What is a counterfactual?

A
  • a perfect counterfactual is knowledge of what would have happened to each participant if they had not undergone a certain manipulation
    → if we compare that knowledge with what actually happened, we know what the effect of the manipulation is
  • counterfactuals are situations with only one specific difference from initial (control) situation
    > what if things were different? → what if there were no guns? What if the lecturer had a wig?
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23
Q

How are counterfactuals? How do we account for this?

A

! there is no perfect counterfactual in reality !
- there is no perfect version of reality where everything is the same except for specific thing that you want to change
> we can create experiments with a control condition and experimental condition (it’s as close as we’ll ever get to a counterfactual)

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24
Q

“What is the effect of hazing in fraternities?”
- how can the effect of hazing be manipulated? What is the problem with each experiment?

A
  • quasi experiment
    > seeing effect of fraternities where there is hazing and fraternities where there isn’t (existing groups)
    ! there are many confounds with this quasi experiment !
    > eg people choose different fraternities based on prior factors → systematic differences
  • therefore, random assignment
    > 3 conditions (intense, mild and no hazing)
    ! ethics concerns
  • the counterfactual is the control condition
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25
Q

What is the causal diagram of this example?
How does it change when controlling for confounds?

A

see image 1 & 2

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26
Q

what can the effect of treatment be confused with?

A
  • outside factors
  • effects of selection
  • unintended effects of study itself
  • statistical artifacts
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27
Q

Outside factors

A
  • History
    > influences (outside of intervention) over teh course of the research, which influence outcome
  • Maturation
    > natural changes that may be confused with effect treatment
28
Q

Effects of selection

A
  • Selection
    > selection criteria for treatment related to outcomes of treatment
  • Attrition
    > participants’ dropout, systematically correlated with attrition
29
Q

Selection
- in what cases should it be investigated?

A
  • especially important in quasi experiments
    > random allocation solves it
  • it happens before experiment
30
Q

Attrition
- why should it be investigated?

A
  • cause of attrition might be very relevant to what the study is investigating
  • e.g. when studying effects of posting facebook update on emotions, 1/4 of participants stopped posting
    > attrition here might be caused by negative emotions, and should therefore NOT be ignored
  • it happens during experiment
31
Q

Example to explain attrition and its importance

A
  • planes coming back from war are full of bullet holes
  • where should the extra armor be added?
    = where there are no bullet holes!
    → those parts were probably hit in planes that did not come back
32
Q

Unintended effects of study itself

A
  • Instrumentation
    > change in measuring instrument resulting in a difference between pre- and post-measurement
  • Testing
    > effect of measurement itself of subsequent measurements (fatigue, habituation, …)
33
Q

statistical artifacts

A
  • Regression to the mean
    > extreme scores will be followed by less extreme scores
34
Q

Regression towards the mean
- example

A
  • athletes that do well in their first year end up in cover magazine
  • in second year they do worse: curse?
    > doing well is skill + luck (random factor)
    > in second year, luck changes
    > skill remains, but will probably do a bit worse
35
Q

How do researchers deal with causality?

A
  1. ignoring causality
    > they only write down correlations found but without mention of causality
    > not really satisfying in scientific community
  2. statements of causality, but unclear assumptions
    > unclear assumptions about what confounds should be included
  3. pseudo-correlational statements
    > no direct statements, but clear implication of causality
    > e.g. “the role of attachment style on relationship satisfaction”
    = “swamp of ambiguity” about causality
36
Q

What is a causal diagram?

A
  • diagram that shows causal relationships between variables, and their confounds
  • also called DAG: directed acyclic graph
    ! arrows go just in direction of causality
    ! if a variable is not included, we assume it plays no role
37
Q

What are two main characteristics of DAGs?

A
  • their structural stability
    > an intervention in one component fo the model does not alter the broader structure
    > intervening on a variable may change how it relates to other variables statistically
  • it assumes a perference for simplicity and probabilistic stability
38
Q

What are simplicity and stability?

A
  • simplicity: models representing data with fewer links are preferred
  • stability: robustness of a set of relationships across a range of possible magnitudes
    > it makes it clear that if there is no link, there is no causal relationship
39
Q

what are key features of DAGs?

A
  • not linear nor parametric (it shows causal links, but choice of covariates is a separate decision)
  • contains no bidirectional arrows implying simultaneity
    > if two variables are simultaneously related, the DAG would treat them as a common cause
40
Q

what types of causal diagrams are there?

A
  • mediation
  • confound (common cause)
  • collider (common effect)
    > see image 3
41
Q

Why is it important to distinguish between the three?

A
  • we must know what role the variable Z plays on the effect between X and Y (our initial two variables)
  • once we know the role, we know whether we should control for Z or not
42
Q

what is another expression for “controlling for”?

A
  • “conditioning on”
43
Q

In which cases do we control for Z?

A
  • Mediation: depends (only if we want to find direct effect)
  • Confound: always YES
  • Collider: absolutely NO
    = in general, we control for Z when the arrow points towards X
44
Q

Mediation
- what is it? what does it show?
- when do we control for it?

A
  • X has effect on Z, and Z has effect on Y
  • it shows indirect effects between two variables X and Y
    > control for it only when interested about direct effect of X on Y
45
Q

Controlling for a mediator
- when?
- example

A
  • only if we want to investigate a direct effect
  • e.g. quality of music causes changes in temperature on dance floor
    > mediator: people dancing (a lot / a little)
    → control for people dancing only if you want direct effect of music on temperature
46
Q

see image 14
- should we control for something?

A
  • if you want to investigate the total effect of testosterone on the likelihood of using a headgear, then do not control for baldness
  • if you control for insecurity, you control for baldness, and that’s something that in this case we don’t want to do
47
Q

Confounding
- what is it?

A
  • “common cause”
  • it is a common cause for both X and Y
    > X and Y have no connection other than that
  • we should always control for Z when it is a counfounder
    ! also called as “backdoor path”
48
Q

what is a spurious correlation?

A
  • correlation that will disappear while we control for confound
  • biased correlation
49
Q

How can we control for a confound?

A
  • we look at correlation between two variables at every level of the confound
  • when dividing the levels, correlation disappears
50
Q

Noncollapsibility

A

” if you suspect a confounder, try adjusting for it and try not adjusting for it. If there is a difference, it is a confounder, and you should trust the adjusted value. If there is no difference, you are off the hook”

51
Q

Controlling for confounds
- skull example

A
  • when measuring width and length of 50 skulls, correlation was found
  • when dividing skulls in subgroups based on gender (female vs male), correlation was not found
    = gender was a confound!
    → looking at correlation between X and Y in all levels of Z
  • image 13
52
Q

Controlling for confounds
- amount of electrical appliances (X) and birth controll pills (Y) in a household example

A
  • correlation found between amount of electrical appliances and amount of birth control pills in household
  • confound: SES
  • when controlling for SES, correlation disappears
    > we look at correlation between X and Y at every level of SES
53
Q

Collider
- what is it?

A
  • “common effect”
  • both X and Y independently cause Z
  • we NEVER control for collider
    > it would create a spurious relationship between X and Y, which can inflate or suppress a true causal effect
54
Q

“there is a negative correlation between smoking and getting covid”
- what is the collider?
- should we control for it? why (not)?

A
  • collider: getting a positive covid test
    > if we control for collider, we are just looking at subset of people that test positive
    > when looking at people who test positive, they either have covid or they smoke
    > if it’s less likely that they smoke, it’s more likely that they have covid (and viceversa)
    > we create a negative spurieus correlation between smoking and having covid by controlling for positive covid test
  • see image 5
55
Q

we are looking at the correlation between rain and a sprinkler by conditioning on the lawn being wet
- what is the problem with this?
- what is instead the answer when we don’t condition on the lawn being wet?

A
  • when the lawn is wet, there are three possible causes: either the sprinkler, the rain or both
    > not possible that there is neither the sprinkler nor the rain, at least one must be present
  • when we condition on the collider of the lawn being wet, we’ll see a negative correlation between rain and the sprinkler
    = we know that the effect occurred (the lawn is wet), therefore there must be a cause (either rain or the sprinkler or both)
    → if we don’t condition on collider, and we look at lawns either wet or dry, we don’t see a correlation between rain and sprinkler
  • see image 6
56
Q

correlation found between height and speed in NBA players
- what is the collider?
- why is this a problem?

A
  • collider: NBA players
  • to be an NBA player you have to be either tall, or fast, or both, but you can’t be an NBA player if you are neither
  • by looking at subset of NBA players, we will find a correlation between height and speed
    → when we don’t control for collider, correlation is not there anymore (non-NBA players can also be neither tall or fast
  • see image 7
57
Q

can you now explain the same reasoning process for image 8 & 9?

A
  • ps image 9 talks about the quality of hamburger and fries in restaurants you are willing to visit
58
Q

We calculate the probability of getting either heads or tails in a coin toss
- First throw: X
- Second throw: Y
- Z: 1 when at least one heads, 0 when no heads
~ is there a correlation between X and Y?
~ what about when we condition on Z?
> see image 10

A
  • originally, no correlation between X and Y (each combination has .25 probability)
    > if we know that Y is tails, X still has 50% chance of being heads
  • when conditioning on only getting at least one head (Z=1), now probabilities change (each combination has .33 probability)
    > if we know that Y is tails, now we have 100% chance that X is heads, because we conditioned on Z=1
59
Q

see image 11
- what does it show?
- why?

A
  • it shows a negative correlation (red) even though there is no correlation in overall group (blue+red)
  • this is because we are conditioning on subset
60
Q

Purification principle
- is it true?
- what does it lead to?

A
  • idea that the more variables we control for, the more accurate the estimation of the causal effect is (e.g. age, gender, SES, …)
  • WRONG! → it depends on whether variable is confounder or collider
    > overcorrection
    > collider bias

! overall, when all confounders are controlled for, the correlation between treatment and outcome can be seen as causal !

61
Q

Overcorrection

A
  • controlling for mediators on the causal path could lead to an underestimation of the total causal effect
  • overcorrection = underestimation of effect
62
Q

Collider bias

A
  • controlling for common effects will bias the estimation of a causal relationship between two variables
  • (explained in the next flashcards)
63
Q

I am willing to date only attractive, or nice, or both, people. When looking at people I select on tinder, I can see a negative correlation between the two.
- How come?
- What is the collider?

A
  • see image 12
  • collider: only people I would want to date
  • we see correlation because we are not looking at the entire population of people
64
Q

Confounder vs Collider
(summary, as it was on the slides)

A
  • whether or not to condition on a third variable depends on how you think these variables are actually related to each other
  • this assumptions is crucial for how you further analyse the data, and needs to be substantiated
    > based on prior research
    > based on common assumptions
  • the fact that you condition on a third variable must therefore be explicitly stated and substantiated
    > a causal diagram is an insightful way to make these assumptions explicit
65
Q

What should you know by now?

A
  • what a cause-effect relationship is (+ Mill’s criteria)
  • what an INUS condition is, and apply it to reasoining about causes of psychological states
  • what a counterfactual is and where it is derived from in different research settings
  • the most important threats of causal inference in Quasi experimental research and how to apply them
  • understand the three main ways in which a third variable can give a distorted picture of the relationship between two variables
  • difference between mediator vs confounder vs collider
  • recognize them in causal diagram
66
Q

Exercise

A

look at image 15 and try to explain the graphs
(graphs should be seen vertically)

SSR 3 (14 decks)

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