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					          Mill’s Methods
   a) Identify the method used
 b) Indicate how the method is
used in the particular example
 In H. Davies' experiments on the decomposition of water by galvanism, it was
  found that besides the two components of water, oxygen and hydrogen, an
  acid and an alkali were developed at opposite poles of the machine. Since
  the theory of the analysis of water did not give reason to expect these
  products, their presence constituted a problem. Some chemists thought that
  electricity had the power of producing these substances of itself. Davies
  conjectured that there might be some hidden cause for this part of the effect-
  the glass might suffer decomposition, or some foreign matter might be in the
  water. He then proceeded to investigate whether or not the diminution or total
  elimination of possible causes would change or eliminate the effect in
  question. Substituting gold vessels for glass ones, he found no change in the
  effect and concluded that glass was not the cause. Using distilled water, he
  found a decrease in the quantity of acid and alkali involved, yet enough
  remained to show that the cause was still in operation. He inferred that
  impurity of the water was not the sole cause, but was a concurrent cause. He
  then suspected that perspiration from the hands might be the cause, as it
  would contain salt which would decompose into acid and alkali under
  elec-tricity. By avoiding such contact, he reduced the quantity of the effect still
  further, till only slight traces remained. These might be due to some impurity
  of the atmosphere decomposed by the electricity. An experiment determined
  this. The machine was put under an exhaust receiver and when it was thus
  secured from atmospheric influences, no acid or alkali was produced.
Method?

Method of Residues

ABC—xyz
B is the cause of y
C is the cause of z
A is the cause of x
Method of Residues
Some tips:

Typically used when we remove from the
 phenomenon the casual features that we
 already know, and what remains (the
 residue) is (probably) causally related.
Resembles a process of elimination.
 In H. Davies' experiments on the decomposition of water by galvanism, it
  was found that besides the two components of water, oxygen and hydrogen,
  an acid and an alkali were developed at opposite poles of the machine.
  Since the theory of the analysis of water did not give reason to expect
  these products, their presence constituted a problem. Some chemists
  thought that electricity had the power of producing these substances of itself.
  Davies conjectured that there might be some hidden cause for this part of
  the effect-the glass might suffer decomposition, or some foreign matter might
  be in the water. He then proceeded to investigate whether or not the
  diminution or total elimination of possible causes would change or
  eliminate the effect in question. Substituting gold vessels for glass ones,
  he found no change in the effect and concluded that glass was not the
  cause. Using distilled water, he found a decrease in the quantity of acid and
  alkali involved, yet enough remained to show that the cause was still in
  operation. He inferred that impurity of the water was not the sole cause, but
  was a concurrent cause. He then suspected that perspiration from the hands
  might be the cause, as it would contain salt which would decompose into
  acid and alkali under elec-tricity. By avoiding such contact, he reduced the
  quantity of the effect still further, till only slight traces remained. These might
  be due to some impurity of the atmosphere decomposed by the electricity.
  An experiment determined this. The machine was put under an exhaust
  receiver and when it was thus secured from atmospheric influences, no acid
  or alkali was produced.
Method of Residues
ABC—xyz
B is the cause of y
C is the cause of z
A is the cause of x

Galvanized water produces: hydrogen, oxygen and an alkali and acid.
    The alkali and acid were unexpected. What was the cause?
Was it the water?
Was it the electricity?
Was it the glass vessel the water was in?
It was then hypothesized that the acid and alkali were caused by
    impurities, impurities in the water, on the hands of the
    experimenters, and in the atmosphere. Experiments bore this out…
A 1994 study by Dr. Stephen Moses, published in
  the International Journal of Epidemiology,
  showed that around the world men who were not
  circumcised were three to four times likelier to be
  infected with H.I.V. than circumcised men. One
  hypothesis suggested was that the virus may be
  transmitted through tears in the foreskin during
  intercourse. A study reported in Scientific
  American in March of 1996 claimed to show that
  "only one factor" seemed to correlate with
  susceptibility to H.I.V. infection in Africa: lack of
  circumcision.
Method?

Method of Agreement

  ABCD precedes abcd
  AEFG precedes aefg
  A is the cause of a
Method of Agreement
 This method works by looking for an agreement
  between A (cause) and a (effect) in varied
  situations.

 In this case, the “varied situations” are all the
  different men around the world who are
  susceptible to H.I.V. infection.
 The agreement between all these differences is
  that all these different men are not cicumcised.
Method of Agreement
   ABCD precedes abcd
   AEFG precedes aefg
   A is the cause of a

Man 1 is not circumcised and is susceptible to HIV infection
Man 2 is not circumcised and is susceptible to HIV infection
……….
Man n is not circumcised and is susceptible to HIV infection
-----------------------------
"only one factor" seemed to correlate with susceptibility to
   H.I.V. infection in Africa: lack of circumcision.
 Careful studies have been made of the incidence of leukemia in the
  survivors of the atomic bombs burst over Hiroshima and Nagasaki. These
  survivors received exposures ranging from a few roentgens to 1000
  roentgens or more. They are divided into four groups.... The first group, A,
  consists of the estimated 1,870 survivors who were within 1 kilometer of the
  hypocenter (the point on the surface of the earth directly below the bomb
  when it exploded). There were very few survivors in this zone, and they
  received a large amount of radiation. The second group, B, consists of the
  13,730 survivors be-tween 1.0 and 1.5 kilometers from the hypocenter; the
  third, C, of the 23,060 between 1.5 and 2.0 kilometers; and the fourth, D, of
  the 156,400 over 2.0 kilometers from the hypocenter. The survivors of
  zones A, B, and C have been dying of leukemia during the period of careful
  study, the eight years from 1948 to 1955, at an average rate of about 9 per
  year.... Many more cases of leukemia occurred in the 15,600 survivors of
  zones A and B than in the 156,400 survivors of zone D, who received much
  less radiation. There is no doubt that the increased incidence is to be
  attributed to the exposure to radiation. ... The survivors of zone A received
  an estimated average of 650 roentgens; those of zone B, 250; those of zone
  C, 25; and those of zone D, 2.5.... To within the reliability of the numbers, the
  incidence of leukemia in the three populations A, B, and C is proportional to
  the estimated dose of radiation, even for class C, in which the estimated
  dose is only 25 roentgens.
Method?

The Method of Concomitant Variation

ABC—abc
A+BC—a+bc
A and a are connected, but not necessarily
  the cause
The Method of Concomitant Variation
Look out for cases where there are
 fluctuating levels in the cause/effect
 corresponding to fluctuating levels in the
 effect/cause.

In this case, there is a correlation between
 amount of radiation a group is exposed to
 and the incidence of leukemia in that
 group.
The Method of Concomitant Variation
ABC—abc
A+BC—a+bc
A and a are connected, but not necessarily the cause

Exposed to 650 R results in high incidences of leukemia.
Exposure to 250 R, a little less…
Exposure to 25 R, still less…
------------------------------
Therefore: To within the reliability of the numbers, the
   incidence of leukemia in the three populations A, B, and
   C is proportional to the estimated dose of radiation, even
   for class C, in which the estimated dose is only 25
   roentgens.
Inflammation-swelling, redness, and pain-plays a key role in
   rheumatoid arthritis and in the process that leads to diabetes. Can
   the gene that causes inflammation be identified? Dr. Donald N.
   Cook, a pathologist at the University of North Carolina at Chapel
   Hill, was able to do so using what are called "knockout mice." Like
   humans, mice suffer inflammation as a result of many infections,
   and like humans they possess the gene MIP-1 alpha, suspected of
   producing the protein that begins the process of inflammation. Dr.
   Cook and his team bred mice that lacked the gene MIP-1 alpha, and
   then infected those mice, and a control group of normal mice, with
   the influenza virus and the coxsackie virus (which can cause heart
   damage in children and young adults). In response to the infection,
   all the normal mice developed extreme inflammation, with swelling
   and redness. But the mice lacking the MIP-1 alpha gene had only
   slight inflammation. The experiment, said Dr. Cook, proves that the
   MIP-1 alpha gene promotes inflammation in response to virus
   infection. This finding, he suggested, could lead to the development
   of drugs that would allow the body to fight viral infections without the
   damaging effects of inflammation.
Method?

Method of Difference

  ABCD precedes abcd
  BCD precedes bcd
  A is the cause of a
Method of Difference

Tip:

The Method of Difference usually utilizes a
 control group (a sample that is just like the
 typical sample/population, except that it is
 missing one feature)
In this case, the knock-out mice lacked the
 gene MIP-1 alpha
Method of Difference
  ABCD precedes abcd
  BCD precedes bcd
  A is the cause of a

  Mice with the MIP-1 alpha gene that were infected with
    the coxsackie virus developed inflammation.
  Mice without the MIP-1 alpha gene (the knockout mice)
    did not develop inflammation when infected the
    coxsackie virus.
  Therefore, MIP-1 alpha gene promotes inflammation in
    response to virus infection.
Pasteur ... carried out at least one spectacular experiment
  having to do with the effect of temperature on
  susceptibility to infection. Puzzled by the fact that hens
  were refractory to anthrax, he had wondered whether
  this might not be explained by their body temperature,
  which is higher than that of animals susceptible to this
  disease. To test his hypothesis, he inoculated hens with
  anthrax bacilli and placed them in a cold bath to lower
  their body temperature. Animals so treated died the next
  day, showing numerous bacilli in their blood and organs.
  Another hen, similarly infected and maintained in the
  cold bath until the disease was in full progress, was then
  taken out of the water, dried, wrapped, and placed under
  conditions that allowed rapid return to normal body
  temperature. Mirabile dictu, this hen made a complete
  recovery. Thus, a mere fall of a few degrees in body
  temperature was sufficient to render birds almost as
  receptive to anthrax as were rabbits or guinea pigs.
Method?

Joint Method of Agreement and Difference

ABC—xyz              ABC—xyz
ADE—xtw              BC—yz
Therefore A is the effect or the cause of x
Joint Method of Agreement and
Difference
The use of this joint method is what often
 underlies what are called “double-arm” or
 crossover experiments. This is quite
 common, e.g., in medical experiments.
  One group receives a new treatment while
   another group does not, and then in a second
   phase those who did not receive the treatment,
   do so, and those who did, have it withdrawn.
Joint Method of Agreement and
Difference
                                   Agreement
Rabbits have a normally low temperature and are susceptible to anthrax.
Guinea pigs have a normally low temperature and are susceptible to anthrax.
Hens whose body temperature has been lowered (by cold bath) to a below
   normal temperature are susceptible to anthrax.
Therefore, “a mere fall of a few degrees in body temperature was sufficient to
   render birds almost as receptive to anthrax as were rabbits or guinea pigs”

                                    Difference
Hens whose body temperature has been lowered to a below normal
   temperature and contract anthrax will die.
Hens whose body temperature has been lowered to a below normal
   temperature and contract anthrax and are then warmed to their normal
   temperature recover from anthrax.
Therefore, “a mere fall of a few degrees in body temperature was sufficient to
   render birds almost as receptive to anthrax as were rabbits or guinea pigs”