Infer causal relations. Philosophy and Logic Unit 5 Section 5.6

Transcription

1 Infer causal relations Philosophy and Logic Unit 5 Section 5.6

2 So, to this point, we have Drawn a Sample from a population Measured each member of the sample Computed some statistic which summarizes those measurements And Generalized that summary back to the population from which the sample was drawn What s left?

3 How about: use it to answer some question that is important to you! Is this professor biased against conservatives? Does this stereo model sound better than that one at high volume? Are sports utility vehicles safer than cars? Does second hand smoke pose a significant risk to non-smokers? Does use of ecstasy kill serotonergic neurons?

4 To answer any of these You must follow all of the steps so far (Sample, Measure, Compute, Generalize) for two groups, and then make a comparison between them. On the basis of that comparison, you infer some causal relation.

5 Causal Relations The most important relation to know about (for our purposes) is a causal relation: that x happens because y happens. Perhaps people who drive SUVs have lower death rates because the vehicles are safer. Perhaps spouses of smokers are more likely to get cancer because second hand smoke causes cancer.

6 Mistakes in causal inference 1. Comparing Unlike Groups 2. Post Hoc Ergo Propter Hoc (after this, therefore because of it)

7 A key diagnostic indicator 1. Comparing Unlike Groups 2. Post Hoc Ergo Propter Hoc (after this, therefore because of it) Both of these fallacies have a conclusion of the form "x causes y". They are the only two fallacies that have that conclusion.

8 Rival hypotheses Both fallacies have a conclusion that claims that x causes y. In both, you can accept all the premises as true but (reasonably) reject the conclusion, which is not sufficiently established by the premises. The reason you can reject that conclusion: rival hypotheses can be provided hypotheses that agree with all the premises but assert a different causal claim.

9 1. Comparing Unlike Groups Using statistics to infer some relation between two groups, when other differences between the groups explain the difference in the statistics.

10 1. Comparing Unlike Groups Using statistics to infer some relation between two groups, when other differences between the groups explain the difference in the statistics. So the conclusion has to be a causal claim. The premises have to describe two different groups. And there are other differences between those groups that could account for the different effects observed.

11 To avoid the fallacy Look at the two groups very carefully. Ask yourself Do these groups differ from one another in any other way that could be relevant? Could that difference account for the difference in statistics? If yes: you ve got unlike groups.

12 Huff, p 83 The death rate in the Navy during SpanishAmerican War was 9 out of The death rate for civilians in NYC during the same period was 16 out of Therefore: Death rates show it s safer to join the Navy than to stay in New York. Enlist now!

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14 Comparing unlike groups The groups are defined by some variable G. (Example: male vs. female.) We measure each group, and find that the two groups have different values on some statistic. (Example: average take home pay. Women earn 78 cents per dollar earned by men. ) Conclude that the difference in the statistic results from variable G. ( Gender discrimination is rampant in the workplace. )

15 Sexist Pig Philosophers: The Philosophy Department at UConn has only 2.5 female professors, out of a total of thirteen. Women faculty at UConn earn on average 75% of what the men faculty earn. Philosophers here are sexist pigs.

16 But the groups are also different in other ways that can explain the difference in the statistic workforce participation rates. Parity between men & women only reached in 1994! hence, age: There are fewer women in the workplace that have the same number of years of experience education. Even today only about 30% of MBA students are female. disciplinary interests. Some 90% of technical & engineering degrees are earned by males

17 First problem: Ignore the inputs. Only one out of six of all those with Ph.D.s in Philosophy who are alive in the US today are women. 13 x (1/6) = 2.2 (Source: APA Proceedings and Addresses, Committee on the Status of Women in Philosphy, vol 68, no. 2-4, 1995)

18 Second issue: ignore age Suppose everyone in each age bracket is paid exactly the same amount. Everyone gets equal raises as they age. Each year you save just one tenth of what you have left after expenses. Net worth is recorded at the beginning of each age bracket.

19 Socialist utopia? Age Annual income Annual expense Annual savings Net worth 20 $10,000 $5,000 $ ,000 5,000 1,500 5, ,000 5,000 2,500 20, ,000 5,000 3,500 45, ,000 5,000 4,500 80, , ,000

20 The inequitable results The top 17 percent earn five times what the bottom 17 percent earn. Those in the top 17 percent have 25 times the savings of those in the bottom. The top 17 percent own 45 percent of all the capital in the society.

21 Huff, p 85.

22 2. Post Hoc Ergo Propter Hoc After this, therefore because of it: First X happened. Then Y happened. Hence, X caused Y.

23 A piece of superlative canine reasoning I bark in the afternoon (all afternoon!) I get fed in the evening. Hence, I am fed because I bark. Woof woof! Good for a dog, but I hope its owners know about post hoc

24 More generally The premises state nothing but a correlation. The conclusion makes some sort of causal claim. X and Y are correlated (occur together). Hence X causes Y.

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26 Some rival hypotheses (a) Y causes X (b) some third factor Z causes both X and Y (c) the correlation is pure coincidence.

27 Examples cigarette smoking (pp 87 90). value of education (pp ).

28 This Week magazine (Huff, 94)

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33 Why we need experiments To establish the existence of causal relations, one must do more than simply observe; one must experiment. That is, one must show that changing X will change Y. This requires a controlled manipulation: go in and change X alone, then see what happens. Passive observation cannot replace this!

34 End