CAUSAL
REASONING
Yeung Chun Yin
1
CAUSAL REASONING
▪ One of the most important types of argument in our daily life.
▪ Concluding that something (A) is something’s (B) cause.
2
CORRELATION
▪ Positive correlation
▪ A positive correlation exists when one variable increases as the other
variable increases, or one variable decreases while the other decreases.
▪ Two variables move in the same direction.
▪ Negative correlation
▪ A negative correlation exists when one variable increases as the other
variable decreases, or one variable decreases while the other increases.
▪ They move in opposite direction.
▪ No correlation
▪ The change of the variables are independent of each other.
3
CORRELATION DOES NOT
IMPLY CAUSATION!
▪ Correlation does not imply causation
▪ When we find that A and B are positively correlated, there are
always other possible interpretations of the data
▪ Reverse causation
▪ A common cause C (third factor)
▪ Commonly called ‘confounder’ or ‘confounding variable’ in social
science
4
CORRELATION DOES
IMPLY CAUSATION!
NOT
▪ Correlation seems to suggest causation
▪ When A and B are positively correlated, it seems to suggest that A
causes B
P1. The time children spend on watching violent TV programme is
positively correlated to their tendency of using violence.
C. Watching violent TV is a cause of using violent.
▪ But generally speaking, such kind of causal argument is a
weak argument
5
REVERSE CAUSATION
▪ A and B are positively correlated.
▪ So it means A causes B? No!
▪ It maybe B causes A!
▪ Violent TV and tendency of using violence.
▪ You may think it is violent TV causes the children to use violence.
▪ But it may well be that the tendency of using violence causes them
to watch violent TV.
6
COMMON
(CONFOUNDER)
CAUSE
▪ A and B are positively correlated.
▪ But there may be a common cause C that causes both of A and
B.
▪ So it makes A and B positively correlated.
▪ Violent TV and tendency of using violence
▪ Perhaps the violent character of their parents is a common cause.
Violent parents cause their children to watch more violent TV and
their violent parents cause them to be more violent.
▪ But there is no direct causal linkage between watching violent TV
and using violence
7
INTERPRETATION OF DATA
▪ Some fun facts:
▪ The sales of ice-cream is positively correlated to the number of
people killed by sharks.
▪ The number of storks (送子鳥) found nesting in English villages
and the number of babies born in each of those villages.
▪ Does the former cause the latter in these cases?
▪ What is the real causal explanation?
8
INTERPRETATION OF DATA
▪ The sales of ice-cream is positively correlated to the number of
people killed by sharks.
▪ Common cause: Higher temperature causes more people to swim,
and so more people are killed by sharks. But higher temperature
also causes more people to buy ice-cream!
▪ The number of storks (送子鳥) found nesting in English villages and
the number of babies born in each of those villages.
▪ Reverse causation: when a new baby is born, the family members
will tend to stay more at home to take care of the baby. So they will
cook more. The higher temperature of the roof thus attract more
storks to nest at the top of those houses.
9
INTERPRETATION OF DATA
▪ You know what? Religion is really making men better!
▪ In Poland, the level of religiosity of a region is negatively
correlated to the crime rate.
▪ So religion makes people commit less crime!
10
COMMON CAUSE (THIRD
FACTOR)
11
COMMON CAUSE (THIRD
FACTOR)
▪ It turns out there is a common cause: urbanisation.
▪ The higher level of urbanisation, the higher level of crime
rate.
▪ The higher level of urbanisation, the lower level of religiosity.
12
FROM CORRELATION TO
CAUSE
▪ If we want to have a strong causal argument, using correlation
as the only premise would not be enough.
▪ We need to have more premises.
▪ To eliminate the possibility of reverse causation and the existence
of a common cause
13
FROM CORRELATION TO
CAUSE
▪ In our course, we will introduce three ways for eliminating the
other possibilities
▪ Controlled experiment
▪ Frequentism
▪ Experimentalism
14
CONTROLLED EXPERIMENT
▪ Done in laboratory context
▪ In controlled experiments, the same experiment is done in at
least two parallel experiments that differ in only one way, with
one experiment being the "control arm" and the other being
the "experimental arm".
15
CONTROLLED EXPERIMENT
▪ Violent TV programme
▪ We find two groups of children, who have no previous exposure to
violent TV. One group of them are instructed to watch violent
programme a certain period of time a day. The other group are
instructed continue not to watch violent TV.
▪ After sometime, their tendency of using violence is traced
▪ If the tendency of the group who are instructed to watch violent TV
increases, then watching violent TV would be the cause
16
CONTROLLED EXPERIMENT
▪ Reverse causation?
▪ How to eliminate Revers causation?
▪ Common cause?
▪ How to eliminate common cause?
17
CONTROLLED EXPERIMENT
▪ But sometimes it is (1) difficult or (2) unethical to conduct
controlled experiment
▪ It is more so in the realm of social science
▪ Controlled experiment
▪ 介入式研究
▪ What we need….
▪ 觀察式研究
18
FREQUENTISM
▪ Let’s say, we find that believing in Christianity is positively
correlated to a person’s income
▪ How can we test if it is true that believing in Christianity cause
a higher income?
P1. Believing in Christianity is positively correlated to a person’s income
C. Believing in Christianity causes a higher income
▪ It is currently a weak argument!
19
FREQUENTISM
▪ We may try the following method:
▪ Find a large group of people (the number must be large) who
are all newly converted to Christianity
▪ And then we can trace their income in, say, 10 years
▪ If the income after 10 years is positively correlated to their
believing in Christianity, then there is prima facie reason to
believe that believing in Christianity causes the increase in
income
20
FREQUENTISM
▪ How reverse causation is eliminated?
▪ Because all those people are newly converted to Christianity,
believing in Christianity happens before the increase in income,
so reverse causation is impossible
21
FREQUENTISM
▪ How a common cause is eliminated?
▪ First, we need to identity what those possible common causes are.
▪ For example, original income, educational level, personality, etc
▪ And we try to eliminate these hypothesis by looking at whether
they are correlated to believing in Christianity and income
increase at the same time
▪ If any one of them is correlated, then probably there is a more
complicated causal relation
▪ If none of them are correlated, then it seems we are justified to
believe that believing in Christianity causes the increase in income
22
FREQUENTISM
▪ Frequentism is so called because it keeps using the idea of
“correlation” to eliminate other possibilities.
▪ If there is a common cause, the common cause must be
correlated to the two variables.
▪ So we can prove that there is no common cause by showing
that all the possible candidates of common cause are not
correlated to the variables.
23
FREQUENTISM
▪ Famous example
▪ Democracy and level of GDP
▪ Will democracy promote the growth of GDP?
▪ Bad health status and income level
▪ Will bad health status causes a lower income level?
24
EXPERIMENTALISM
▪ Some very clever social scientists can often find some rare
chance to conduct research that is similar to a controlled
experiment
▪ “Natural experiment”
▪ The so-called experiment is not really an experiment. It happens
naturally and is not controlled by the researcher. But it has an effect
similar to a real experiment.
25
EXPERIMENTALISM
▪ Does joining the military cause a lower income?
▪ It is found that previous participation in the military is
negatively correlated to income
▪ How can we eliminate other interpretation of data?
▪ Reverse causation
▪ Lower income causes the people to join the military
▪ Common cause
▪ Family background, educational level, etc cause them to join th
military and cause them to have a lower income
26
EXPERIMENTALISM
▪ During the time of Vietnam War, the U.S. government used
random lottery to draw adult men from a certain age into the
military
▪ Because the lottery is purely random, all other factors became
irrelevant
▪ This naturally created two group of people
▪ Main point: they are nearly equal but one
▪ One group: no military participation
▪ Another group: with military participation
27
EXPERIMENTALISM
▪ It is like conducting a controlled experiment
▪ Because there two groups of subjects who are nearly equal
but one factor
▪ Then observing the difference between these two group will
give us the result whether factor A is the cause of factor B
▪ Result: Joining the military will lower the income
28
EXPERIMENTALISM
▪ How is reverse causation eliminated?
▪ This possibility is eliminated because if the causal direction is
reverse (lower income cause people to join the military, but joining
the military will not cause them to have lower income), then joining
the military will not cause them to have lower income
29
EXPERIMENTALISM
▪ How a common cause is eliminated?
▪ Because the people is naturally divided into two groups. Perhaps
there are still some other third factors that will affect both of the
variables, but the effect will be cancelled out.
▪ For example, perhaps education level will affect both the chance of
joining the military and the income level, but because the two
groups of people are randomly divided, so there will be similar
portion of people will high education level and low education level
in the two groups. So the effect of education level is cancelled out.
▪ The only difference in effect would be caused by the participation
in the military.
▪ It is why the two groups are said to be nearly equal but one factor.
30
EXPERIMENTALISM
▪ Other famous examples
▪ 英國霍亂
▪ 生女孩的議員會較傾向自由主義嗎？
31
SOURCE OF CHOLERA
▪ 1853-54年，英國爆發大規模霍亂。當時大部份人都認為，霍亂由
空氣傳染。而一個麻醉師Snow卻認為，霍亂透過污水而非空氣傳
染。Snow最重要的證據，就是來自一場natural experiment。
▪ Snow當時把染病人口數量畫在地圖上，使他懷疑Board
近的一個水泵就是疾病的來源。
Street附
▪ 那時倫敦有兩間供水公司，而因為種種原因，哪間房子由哪間公司
供水是十分隨機的。可能這間房子由甲公司供水，旁邊的已由乙公
司供水。而且甲乙兩公司同時會供水給富人窮人，大屋小屋。所以
這制造了兩群nearly equal but one的群體。
32
SOURCE OF CHOLERA
▪ 當年，其中一間公司要把它們的intake
pipe移到泰吾士河上游，
所以他們的供水不再經過Board Street的水泵。
▪ Snow於是再記錄染病人口與他們所用的供水公司，就發現用沒有
搬遷那間公司的人口染病人數/比例明顯較高，所以證實了霍亂由
污水傳染。
▪ 這次natural experiment中，我們排走了諸如房子大小、家境富裕
與否、職業等不同的可能原因。因為甚麼人使用哪間公司的供水可
說是完全隨機。兩組人的唯一分別就是他們用哪一間供水公司。所
以這些其他因素的影響就給排走了。
▪ 而我們可能得出一個有力的證據，證明污水才是染病的原因。
33
REGRESSION
DISCONTINUITY
▪ A kind of common natural experiments, so a kind of
experimentalism
▪ Does a social policy have a certain effect?
▪ Is receiving an award have positive effect on students’ academic
performance?
▪ Is university education useful to increasing a student’s income?
▪ All these questions are difficult to study
▪ There are some other factors affecting the result
34
EXAMPLE
▪ Is receiving an award have positive effect on students’ academic
performance?
▪ But is it normal that students having received awards is
academically better?
▪ Simply because they are better ! (so they got the award)
35
METHOD
▪ We can focus on those students who just missed the award
and who just got the award
▪ Then it creates two nearly equal but one group
▪ The two groups are almost equal but different in one aspect
▪ One group have received the award and one haven‘t
▪ 我們可以把這兩組學生在曾否獲獎以外看成大致相同。因為你可
以想象，其實剛剛能拿到獎的學生，跟剛剛不能拿到獎的學生，大
致上沒真正差別。
36
METHOD
▪ 例如有個獎是給1000學生中考頭20名的學生，你可以想象，考第
20的跟考第21的學生，其實沒甚麼真正差別，只是考好一個考高一
名。
▪ 又或者，有個獎項是GPA 3.5的可以拿，但3.49的就不能。那考3.5
的跟3.49的，其實大致上沒有真正差別。
▪ 如果這是真的，那麼我們追縱這兩組學生得獎/沒得獎後的成績變
化，就能知道得獎與否會不會影響學生的成績
▪ 當然數字要夠大，這兩組學生的其他差異才能互相抵消(所以可以
追縱連續很多年的學生)
37
REGRESSION DISCONTINUITY:
ADVANTAGE
▪ A natural experiment
▪ Some might think that it is difficult to find natural experience
▪ But Regression Discontinuity gives us a way to look into data and
‘create’ natural experiment systematically
▪ 舉例說，一個社會福利政策能否有效幫助長者，我們也可做類似研
究
▪ 找那些剛好夠年紀拿這福利的人，和那些剛好不夠年紀(可能只差一段
短時間)拿這福利的人，看看這兩組人之後的變化有沒有分別，就可以知
道這福利有沒有用
38
EXPERIMENTALISM
FREQUENTISM
VS.
▪ Experimentalism
▪ Requires two sample groups which are “nearly equal but one” to
eliminate reverse causation and common cause (as if it is a
controlled experiment)
▪ Frequentism
▪ Uses time sequence to eliminate reverse causation
▪ Shows that there is no correlation between the proposed common
cause with the other factors to eliminate a common cause
39