Scientific and Statistical Reasoning Lecture Notes - Interim 3

Scientific and Statistical
Reasoning Lecture Notes Interim
3
Contents
Lecture 20 - Critical Thinking About Causality........................................................................................2
Lecture 21 - Correlation and Simple Regression..................................................................................11
Lecture 22 - Critical Thinking about Psychological Measurement........................................................41
Lecture 23 - Critical thinking about psychological theory....................................................................51
Lecture 24 - Multiple Regression.........................................................................................................74
Lecture 25 - Critical Thinking About Individual Differences & Mechanisms.........................................79
Lecture 26 - Mediation Analysis...........................................................................................................88
Lecture 27 - Moderation Analysis........................................................................................................96
Lecture 28 - Critical Thinking About Psychological Constructs...........................................................103
Lecture 29 - Against Methodolatry....................................................................................................112

,Lecture 20 - Critical Thinking About Causality
Scientific & Statistical Reasoning
Critical thinking about causality

"Let them first discuss a more simple question, namely, the operations of body and brute
unintelligent matter; and try whether they can there form any idea of causation and necessity,
except that of a constant conjunction of objects, and subsequent inference of the mind from
one to another."
(Hume, 1777)


Swipe left?
 I think it's important that the people I'm dating are attractive or nice. Of the people I select
from Tinder for a date it seems like they get more annoying the more attractive they are.
And the nice persons are often a bit ugly. So I think a beautiful personality and a beautiful
face are mutually exclusive.


Today
 'Correlation does not imply causation'
o What is a causal connection?
o Causal reasoning errors
o What is a counterfactual?
 Counterfactuals in different designs
 Threats of causal inference

 Beyond 'correlation does not imply causation'.
o Causal graphs: Specifying Assumptions
o Causal graphs: Identifying Confounds vs Colliders



Causality
"Let them first discuss a more simple question, namely, the operations of body and brute
unintelligent matter; and try whether they can there form any idea of causation and necessity,
except that of a constant conjunction of objects, and subsequent inference of the mind from one to
another."
(Hume, 1777)


Causality
'That which produces any simple or complex idea, we denote by the general name cause, and that
which is produced, effect' (Locke, in Shadish, 20007, p38)


A classical definition of causal relationships
Criteria John Stuart Mill:
X causes Y if and only if:
 Priority: Change X precedes change Y
 Consistency: Change X varies systematically with change Y
 Exclusivity: There is no alternative explanation for the relationship

,  Problematic academic achievements, drug abuse, pregnancy at a very young age related to
low self-esteem.




 If we create a stronger positive sense of self-esteem, those other problems will disappear by
themselves.


 People with poor reading skills make more erroneous eye movements, go back to the
beginning of sentence more often (regression) and have more fixations per line of text.




 Abnormalities in eye movements (oculomotor skills) cause poorer reading skills


Reasoning errors
Post hoc ergo propter hoc

 Classic definition of causality:

 X causes Y like:

1. X precedes Y (Priority)
2. X covaries with Y (Consistency/correlation)
3. X is the only possible cause of Y (Exclusivity)

P1 X precedes Y
P2 If X precedes Y, X is the cause of Y
C X is the cause of Y

Mistaking correlation for cause

1. X precedes Y (Priority)
2. X covaries with Y (Consistency/correlation)
3. X is the only possible cause of Y (Exclusivity)

P1 X correlates with Y

, P2 If X correlates with Y, X is the cause of Y
C X is the cause of Y

Inversion of cause and effect

1. X precedes Y (Priority)
2. X covaries with Y (Consistency/correlation)
3. X is the only possible cause of Y (Exclusivity)

P1 X causes Y
P2 Is X causes Y, then no Y without X
C Without X, no Y

Causality
 "Weapons don't kill people, but people kill people."

 What is the cause?
 Is there only one cause?
 Often highly polarized political debates about what the 'real' cause of something is

 Are there single causes that are, strictly speaking, both sufficient and necessary?

 Research is about INUS conditions, not about ultimate causes

Causality
 INUS condition:

Insufficient but non-redundant part of an unnecessary but sufficient condition

Insufficient → A match does not lead to fire without other conditions
(e.g., oxygen)
Non-redundant → Substantially different from situation without a match
Unnecessary → Which is not necessary: other combos are also possible
(sunlight, dry grass, oxygen)
Sufficient → Combination of paper, oxygen, matches, friction is
sufficient to produce fire

Causality
 In research we try to compare observations we make with a good counterfactual:

 A perfect counterfactual is knowledge of what would have happened to each participants 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.

 That "perfect" variant is physically impossible
 A different version of the world where everything is the same except that on specific
thing.