Teachers’ Reference



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Teachers’ Reference
Lesson 2 Causal Inference-Mill’s Method in Causal Reasoning
Learning Objectives
Students will:

gain an understanding of Mill’s Method in causal reasoning;

be able to use Mill’s method to analyze and interpret observations for the purpose of drawing conclusions about the causal relationships they exhibit;

be able to understand the limitations of Mill’s method in causal reasoning.


Suggested Lesson Time: 90 minutes
Activity 1(a)

Disease X was recorded long time ago. People with disease X have shaking chills at regular time intervals (usually at mid-day between 11 a.m. to 12 noon), followed by high fever lasting for 2 to 6 hours. The patients may also have other symptoms like headaches, vomiting, delirium, anxiety and restlessness.


It was also discovered that the blood of the infected patients contained a micro-organism that was a new species of parasite at that time.
Some doctors also observed that

people sleeping outdoors were more susceptible to get the disease that those of sleeping indoors;

people sleeping near a camp fire were less susceptible to get the disease.
A doctor (Dr. R) made a lot of efforts in researching Disease X. He observed that disease X was widely spread in the following areas in 1895:


Place

Natural Environment

A

Near a river

B

Inside a forest

C

Near the marshes

D

Paddy fields

Dr. R also observed that there were a lot of mosquitoes in places A, B, C and D. He suggested that mosquitoes might be responsible for the transmission of the micro-organisms that caused Disease X.


Task 1(a):

1. Use flow charts / comparison tables / diagrams to illustrate how Doctor R arrived at his

proposition that mosquitoes might be responsible for the transmission of the micro-organisms

that cause Diseased X.




Place

Circumstance

Disease X

A (Near a river)

Water + mosquitoes + plants P1, P2, P3 … + animals A1, A2, A3 …

+

B (Inside a forest)

Water + mosquitoes + plants P1, P2, P3, P4 … + animals A1, A2, A3, A4 …

+

C (Near the marshes)

Water + mosquitoes + plants P1, P2, P3, P4, P5 … + animals A1, A2, A3, A4, A5 …

+

D (Paddy fields)

Water + mosquitoes + plants P1, P2, P3, P4, P5, P6 … + animals A1, A2, A3, A4, A5, A6 …

+




  • Either water or mosquitoes may be related to Disease X

With reference to the observation of some doctors, it is more likely for mosquitoes to spread Disease X.


Remarks:

After years of hard work on researching Disease X, Dr. R discovered that mosquitoes were the carriers of the parasite, which caused Disease X and such a great discovery has led Dr. R to get the Nobel Prize in Medicine in 1902. Disease X is Malaria and Dr. R was Ronald Ross.


2. Use simple diagrams to show the logic of the causal relationship in case 1(a).


Event/Case

Circumstance

Effect

1

E, R, Y, Z

e, r, y, z

2

E, P, Q, T

e, p, q, t

3

E, H, J, K

e, h, j, k

4

E, L, M, N

e, l, m, n




  • E and e has a causal relationship

Remarks:
Mill’s Method of Agreement: investigation of the cases in which the effect occurred revealed only one prior circumstance that all of them shared.
Activity 1(b)
In an uneventful afternoon, four students of School A suffered from severe diarrhea. All of them went to the hospital and the doctor naturally suspected that the symptom might be related to the food eaten by the students during lunch.
The doctor asked the students what they ate for lunch and their answers were as follows:

Student

Food items

1

pizza, orange juice, cookie, vegetable salad

2

hot dog, French fries, vegetable salad, iced tea

3

pizza, vegetable salad, coca cola, cheese cake

4

hamburger, orange juice, vegetable salad, cheese cake


Task 1(b)
1. Use a table / diagram to show the logic of the possible cause of diarrhea among the

students.



Case/event

Circumstance

Effect

1

B, C, D, A

x

2

E, F, A, G

x

3

B, A, H, I

x

4

J, C, A, I

x

Conclusion: A is the cause of x

2. Do you know the name of this method of establishing the causal relationship?

Mill’s Method of Agreement (求同法)


3. What is the precaution of applying the method (in (2)) in causal reasoning?

You may get the answer “vegetable salad” from the method of agreement. But

pathology tests showed that there were no bacteria causing diarrhea found in the

vegetable salad. The actual cause why these four students suffered from diarrhea

was that the forks they used to eat the vegetable salad were contaminated with

bacteria.

People will be blinded by apparent causal relationship but in fact there are real reasons other than that of observed. For instance, in the malaria case above, people believed that the cause of malaria was marsh but the true reasons are that the parasites that cause malaria can be carried by mosquitoes that breed in water.
Activity 2:

Michael Faraday’s Experiment



1. Assemble the above experimental set-up.
2. Place a bar magnet into the copper coil (no movement of the magnet) and observe the reading of the ammeter.
3. Place a bar magnet into the copper coil and move the bar magnet forward and backward. Observe the reading of the ammeter.
4. Repeat steps (3) and (4) by replacing the bar magnet with an iron bar.
Task 2:
1. Design a table to record the results of the above experiment.


Movement of magnet

Movement of the pointer of ammeter

Yes

Yes

No

No




Movement of iron

Movement of ammeter

Yes

No

No

No

2. Suggest the cause of change (if any) in Faraday’s Experiment.


It’s the movement of the magnet that causes the pointer of the ammeter to move.
Conclusion: Change of magnetic field causes generation of electricity.

3. Use a comparison table / diagram to show the logic of the discovery by Faraday.




Case/event

Circumstance

Effect

1

A, B, C

x

2

- B, C

-

Conclusion: A is the cause of x

4. Do you know the name of the method (in (3)) of establishing the causal

relationship?

Mill’s Method of Difference (求異法)
Remarks: Mill’s Method of Difference includes Experimental and Control groups.

5. What is the precaution of applying the method (in (4)) in the causal reasoning?

If there are more than one variables in the experimental design, the results

obtained are not conclusive.



Activity 3

Dr. Sun Simiao (孫思邈) (AD 581-682) was a very famous doctor in Tang Dynasty. There were several rich people living in the capital of China, Changon. All of them were suffered from a strange disease at the same time and they all had similar symptoms, including leg edema, muscle pain, fatigue and tiredness. All the famous doctors could not treat the diseases.


Dr. Sun was invited to treat one of the patients. He went to the kitchen of one of the rich patients. The cook told him that his master did not like to eat too much meat or fish but he liked to eat polished rice (white rice which had been polished several times). Dr. Sun also paid visits to several rich patients who suffered from the same diseases. He found that these patients had a similar habit of eating polished rice.
He then noted that the diseases were not found among the poor people who ate coarse rice. He concluded that the cause of the disease was related to the eating of polished rice. He then asked the patients to eat coarse rice instead. Luckily, all the patients were cured within half a month.
Task 3:

1. Use a table / diagram to show the logic of the discovery of the cause of the

disease.


Case




Conditions




Symptom



W

X


Y

(ate polished rice)



leg edema, muscle pain,

fatigue and tiredness



Patient A

(rich) (+ve gp)



Yes

No

Yes

Yes

Patient B

(rich) (+ve gp)



No

No

Yes

Yes

C

(poor) (-ve gp)



Yes

No

No

No

D

(poor) (-ve gp)



No

Yes

No

No

2. Do you know the name of the method (in (1)) of establishing the causal relationship?

Mill’s Joint Method of Agreement and Difference (求同求異並用法)
3. What is the precaution of applying the method (in (2)) in causal reasoning?

We should consider and compare as many conditions and symptoms as possible among the +ve and –ve groups in order to minimise the chance factor.


Activity 4
THE DISCOVERY OF RADIUM by Marie Curie

In Marie Curie’s time a radioactive substance, uranium was discovered. When uranium compound was placed onto a photographic plate covered with black paper, it produced an impression analogous to that which light would make on that plate. The impression is due to uranium rays that traverse the paper. One day when Marie Curie and his husband were doing research on some samples containing uranium, they discovered that the radioactivity measured was far greater than that of uranium. They began to suspect that the sample contained other radioactive active substances. Then they carried out numerous experiments to search for the unknown radioactive substance. Finally, after 45 months’ hard work the couple isolated a very minute quantity of black power, radium chloride in 1902.


1. Show the logic (method) in the cause of the discovery of radium by Marie Curie. Symbolically, the Method of residues can be represented as:

A, B, C occur together with x, y, z

B is known to be the cause of y

C is known to be the cause of z

Therefore, A is the cause of x.
e.g.

Let A be Uranium and “a” be the radioactivity measured due to the effect of A.

Let B be the unknown radioactive substance and “b” be the radioactivity measured due to the effect of B.

Since the radioactivity measured was higher than expected (a+b>a), then the source of the radioactivity must come from radioactive substance(s) other than A.


2. Do you know the name of the method (in (1)) of establishing the causal

relationship?

The induction method is called Method of Residues.
3. What is the precaution of applying the method (in (2)) in causal reasoning?
Sometimes it is difficult to use the Method of Residue to find the causal relationship because the remaining factor found is a compound factor. As in the discovery of radium, Marie Curie first isolated Po (plutonium) and then found radium which contributed to the major difference in the observed radioactivity of the uranium sample
Activity 5
Air Pollution Increases Hospital Admissions for Patients

with Chronic Obstructive Pulmonary Disease in Hong Kong
In Hong Kong, Chronic Obstructive Pulmonary Disease (COPD) was the 5th leading cause of death, and accounted for at least 4% of all public hospital acute admissions in 2003. The prevalence of COPD among elderly Chinese (age ≥70 years) living in Hong Kong is estimated to be 9%. Previous studies have shown that pulmonary function and quality of life among patients with COPD were adversely affected by frequent exacerbations.
A study has just been published in the journal THORAX and was carried out by the Department of Medicine and Therapeutics and the Department of Community and Family Medicine of the Chinese University of Hong Kong and. This study assessed the relationship between the levels of ambient air pollutants and the hospitalisation rate due to COPD in Hong Kong.
Data of daily emergency hospital admissions to 15 major hospitals in Hong Kong for COPD and indices of air pollutants (sulphur dioxide [SO2], nitrogen dioxides

[NO2], ozone [O3], particulates with an aerodynamic diameter of less than 10 m [PM10] and 2.5 m [PM2.5]) and meteorological variables from January 2000 to December 2004 were obtained from several government departments.

Significant associations were found between hospital admissions for COPD with all five air pollutants. For every 10mg/3m increase in SO2, NO2, O3, PM10 and PM2.5, there was 0.7%, 2.6%, 3.4%, 2.4% and 3.1% increases in the rates of COPD hospitalisation respectively. O3 had the strongest effect on COPD hospitalisation. The effect of SO2, NO2 and O3 had a stronger effect on COPD admissions in the cold season (December to March) than during the warm season.
Adverse effects of ambient concentrations of air pollutants on hospitalisation rates for COPD are evident, especially during the winter in Hong Kong. Measures to improve air quality are urgently needed.
(Press Release of CUHK 6 March 2007)

Task 5:


1. Use one or two sentences to describe the findings of the Chinese University of

Hong Kong?

Air Pollution Increases Hospital Admissions for Patients with Chronic

Obstructive Pulmonary Disease in Hong Kong.


2. Please use a table/diagram to represent the logic in establishing the causal

relationship.




Case/event

Circumstance

Effect

1

A, B, C

x

2

A+, D, E

x+

3

A-, F, G

x-

Evidence: There is a direct correlation between the degree to which the cause occurred and the degree to which the effect occurred.

Conclusion: A and x has a causal relationship

A is the cause of x

3. The name of the above method in causal reasoning is called Method of

Concomitant Variation.

4. What is the precaution of applying the method (in (2)) in causal reasoning?
(a). Two events have correlation but it is not necessary for them to have causal

relationship. For instance, many overweight people would die at young ages.

However, overweight is not a direct cause of early death.
(b). Many irrelevant factors would increase or decrease concomitantly. For

instance, both of the average rain falls per year and the birth rates in Hong

Kong have been decreasing. It is not likely that the amount of rainfall affects

the birth rate.


(c). There is a limit to degree of change in circumstance and effect.
(d). The circumstance must be the only cause for the effect.
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