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Three Stats Pitfalls Facing 

the New Data Scientist
Sean Owen
2
Do I Know You?
• Apache Spark committer, PMC

• “Advanced Analytics with Spark”

• Recently: Director, Data Science @
Cloudera
3
Correlation is not causation.
But then, what is causation?
4
Which Best-Fit Line Is Best?
lm(speed ~ dist, cars) lm(dist ~ speed, cars)
5
Which Treatment is Better?
Treatment A Treatment B
Small Stones 93% (81/87) 87% (234/270)
Large Stones 73% (192/263) 69% (55/80)
78% (273/350) 83% (289/350)
6
Now, Which Treatment is Better?
Treatment A Treatment B
Low Blood pH 93% (81/87) 87% (234/270)
High Blood pH 73% (192/263) 69% (55/80)
78% (273/350) 83% (289/350)
7
Carburetors and Axle Ratio Uncorrelated
lm(drat ~ carb, mtcars)
r = -0.09
8
… Except in Both Halves of the Data?
lm(drat ~ carb, mtcars[

which(mtcars$cyl >= 6),])
lm(drat ~ carb, mtcars[

which(mtcars$cyl < 6),])
r = 0.52 r = 0.22
9
3 Answers
Resolution: Causation
• Humans reason causally
• Data doesn’t contain causal information
• Data correlations consistent with multiple causal models
• Correct inference requires adding causal model
10
11
One Consistent with Causal Knowledge
disti = β0 + β1speedi + ϵi
12
DistanceSpeed
13
Controlling Confounders is Right
Treatment A Treatment B
Small Stones 93% (81/87) 87% (234/270)
Large Stones 73% (192/263) 69% (55/80)
78% (273/350) 83% (289/350)
14
OutcomeTreatment
Size
15
Controlling Mediators is Wrong
Treatment A Treatment B
Low Blood pH 93% (81/87) 87% (234/270)
High Blood pH 73% (192/263) 69% (55/80)
78% (273/350) 83% (289/350)
16
OutcomeTreatment
pH
17
Colliders Create Correlation
lm(drat ~ carb, mtcars)
r = -0.09
18
CarburetorsAxle Ratio
Cylinders
19
Causation and do-Calculus
20
do-Calculus
P(Y|X) ≠ P(Y|do(X))
Just because it’s more often raining when you

walk outside with an umbrella …

… doesn’t mean that you carrying an umbrella 

makes it more likely to be raining.
21
CancerSmoking
Genes?
Tar
22
P(C|do(S)) =
∑
t
P(C|do(S), t)P(t|do(S))
=
∑
t
P(C|do(S), do(t))P(t|do(S))
=
∑
t
P(C|do(S), do(t))P(t|S)
=
∑
t
P(C|do(t))P(t|S)
=
∑
s′
∑
t
P(C|do(t), s′)P(s′|do(t))P(t|S)
=
∑
s′
∑
t
P(C|t, s′)P(s′|do(t))P(t|S)
=
∑
s′
∑
t
P(C|t, s′)P(s′)P(t|S)
Conclusion
• Must bring causal info to data for proper interpretation
• Know common causal pitfalls!
• PGMs help reason about causal effects
• Do-calculus can clarify reasoning about intervention
23
Thank You
@sean_r_owen

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Three Stats Pitfalls Facing the New Data Scientist with Sean Owen