Causal fallacies; Causation and experiments. Phil 12: Logic and Decision Making Winter 2010 UC San Diego 2/26/2010

Transcription

1 Causal fallacies; Causation and experiments Phil 12: Logic and Decision Making Winter 2010 UC San Diego 2/26/2010

2 Review Diagramming causal relations - Variables as nodes (boxes) - Causal relations as arrows Not tracing the flow of activity, but causal relations - If there are conditions under which changing one variable will result in change of another variable, include a arrow between the variables Sometimes there are important intermediate causes such that a more ultimate cause only produces its effect through a more proximate cause Match struck [yes, no] Tip temperature [>350, <350 ] Match lit [yes, no]

3 Review - 2 Common cause - A positive correlation between two variables may be the result of a common cause for both Pine needles [on tree, dropped] Fish [alive, dead] Toxic waste [no, yes] If the causation is direct, there should be no way to screen off E from C X

4 Analyzing causation: what causes malaria Consider the variable Has malaria - Round up the suspects (aka develop hypotheses) Bitten by mosquito [yes, no] Inoculated [yes, no] Has sickle cell gene [yes, no] Drinks gin and tonics regularly [yes, no] To determine the relation between these and Has malaria we need to consider the possible values on these variables and whether, for each variable, there is a case in which it makes a difference

5 Is being bitten a cause of malaria? Assignment Variable 1: BITTEN BY MOSQUITO Variable 2: INOCULATED Variable 3: HAS SICKLE CELL GENE Variable 4: DRINKER OF GIN AND TONICS 1 True True True True False 2 True True True False False 3 True True False True False 4 True True False False False 5 True False True True False 6 True False True False False 7 True False False True True 8 True False False False True 9 False True True True False 10 False True True False False 11 False True False True False 12 False True False False False 13 False False True True False 14 False False True False False 15 False False False True False 16 False False False False False Effect: MALARIA

6 Is being bitten a cause of malaria? Assignment Variable 1: BITTEN BY MOSQUITO Variable 2: INOCULATED Variable 3: HAS SICKLE CELL GENE Variable 4: DRINKER OF GIN AND TONICS 1 True True True True False 2 True True True False False 3 True True False True False 4 True True False False False 5 True False True True False 6 True False True False False 7 True False False True True 8 True False False False True 9 False True True True False 10 False True True False False 11 False True False True False 12 False True False False False 13 False False True True False 14 False False True False False 15 False False False True False 16 False False False False False Effect: MALARIA

7 Is being bitten a cause of malaria? Assignment Variable 1: BITTEN BY MOSQUITO Variable 2: INOCULATED Variable 3: HAS SICKLE CELL GENE Variable 4: DRINKER OF GIN AND TONICS 1 True True True True False 2 True True True False False 3 True True False True False 4 True True False False False 5 True False True True False 6 True False True False False 7 True False False True True 8 True False False False True 9 False True True True False 10 False True True False False 11 False True False True False 12 False True False False False 13 False False True True False 14 False False True False False 15 False False False True False 16 False False False False False Effect: MALARIA

8 Is being inoculated a cause of malaria? Assignment Variable 1: BITTEN BY MOSQUITO Variable 2: INOCULATED Variable 3: HAS SICKLE CELL GENE Variable 4: DRINKER OF GIN AND TONICS 1 True True True True False 2 True True True False False 3 True True False True False 4 True True False False False 5 True False True True False 6 True False True False False 7 True False False True True 8 True False False False True 9 False True True True False 10 False True True False False 11 False True False True False 12 False True False False False 13 False False True True False 14 False False True False False 15 False False False True False 16 False False False False False Effect: MALARIA

9 Is having sickle cell gene a cause of malaria? Assignment Variable 1: BITTEN BY MOSQUITO Variable 2: INOCULATED Variable 3: HAS SICKLE CELL GENE Variable 4: DRINKER OF GIN AND TONICS 1 True True True True False 2 True True True False False 3 True True False True False 4 True True False False False 5 True False True True False 6 True False True False False 7 True False False True True 8 True False False False True 9 False True True True False 10 False True True False False 11 False True False True False 12 False True False False False 13 False False True True False 14 False False True False False 15 False False False True False 16 False False False False False Effect: MALARIA

10 Is drinking gin and tonics a cause of malaria? Assignment Variable 1: BITTEN BY MOSQUITO Variable 2: INOCULATED Variable 3: HAS SICKLE CELL GENE Variable 4: DRINKER OF GIN AND TONICS 1 True True True True False 2 True True True False False 3 True True False True False 4 True True False False False 5 True False True True False 6 True False True False False 7 True False False True True 8 True False False False True 9 False True True True False 10 False True True False False 11 False True False True False 12 False True False False False 13 False False True True False 14 False False True False False 15 False False False True False 16 False False False False False Effect: MALARIA

11 Causal graph for malaria Bitten by mosquito [yes, no] Inoculated [yes, no] - Has sickle cell gene - [yes, no] Malaria [yes, no] Drinks gin and tonics regularly [yes, no]

12 Mistakes in reasoning about causes There are a variety of ways in which people mistakenly infer causal relations when they do not exist

13 1. Treating coincidence as cause Joe gets a chain letter that threatens him with dire consequences if he breaks the chain. He laughs at it and throws it in the garbage. On his way to work he slips and breaks his leg. When he gets back from the hospital he sends out 200 copies of the chain letter, hoping to avoid further accidents.

14 2-3. Assuming and ignoring common causes 2. Assuming common causes: Based on a correlation between two variables, assume there must be a common cause of them both 3. Ignoring common causes: Based on a correlation between two variables, assume a direct causal relationship, when there really is a common cause for both Test for common cause: - must identify the cause and determine that varying it alone alters both effects - If varying the purported cause fails to alter both effects, there is no common cause, but rather two correlated causes

15 4. Confusing cause and effect Even when a causal relation seems likely, it is not always clear which is cause and which is effect. - Is a child difficult because the parents are short-tempered? - Or are the parents short of temper because the child is difficult? Parents short-tempered [no, yes] Child difficult [no, yes]

16 5. Post hoc, ergo propter hoc We are prone to see causation when one event precedes another - You are feeling sick. You go to the doctor. A few days later you begin to feel better. - Conclusion: Go to doctor [no, yes] Get better [no, yes]

17 5. Post hoc, ergo propter hoc - 2 When the street lights start to come on, the sun goes down. Thus, the turning on of the street lights causes the sun to go down. Roosters crow just before the sun rises. Therefore, roosters crowing causes the sun to rise. You have a headache so you stand on your head and six hours later your headache goes away. Therefore,... You put acne medication on a pimple and three weeks later the pimple goes away. Therefore,...

18 Clicker question 1 What causal fallacy is illustrated in this example: You observe that people who have lung cancer also smoke, and conclude that cancer causes smoking. A. Ignoring a common cause B. Treating coincidence as a cause C. Post hoc, ergo propter hoc D. Confusing cause and effect

19 Clicker question 2 What causal fallacy is illustrated in this example: Immigration to Alberta from Ontario increased. Soon after, the welfare rolls increased. Therefore, the increased immigration caused the increased welfare rolls. A. Ignoring a common cause B. Treating coincidence as a cause C. Post hoc, ergo propter hoc D. Confusing cause and effect

20 Clicker question 3 What causal fallacy is illustrated in this example: Bob is visiting his cousin Fred on his farm. While standing in Fred s hay field, Bob gets watery eyes and starts sneezing. Bob claims that his watery eyes caused him to sneeze. A. Ignoring a common cause B. Treating coincidence as a cause C. Post hoc, ergo propter hoc D. Confusing cause and effect

21 Need for Experiments or Well-Controlled Observations The best evidence as to whether something is a cause of some effect is whether manipulating it changes the value of the effect When that isn t possible, one must rely on controlled observations that rule out other possible causes (confounds)

22 The basic idea of an experiment If the independent variable is the cause of the dependent variable, then a manipulation of the independent variable should produce a change in the value of the dependent variable - And if it were not the cause, we would not expect such a result from manipulation Manipulation Independent variable [values]? Dependent variable [values]

23 Experiments on regular deterministic systems When there is no variance in the population being studied, statistical analysis is not necessary The main danger is affirming the consequent - The key is to test a causal hypothesis in which you would not expect the effect to occur unless you were right about the cause. Manipulation (vary the object dropped) Object dropped [no, yes]? Object falls [no, yes]

24 Variability in non-deterministic systems Different systems of the same kind will vary in their responses depending on - their particular composition (genetics, etc.) - their particular history, etc. The same system may respond differently on different occasions - Your reaction time will differ depending on how much sleep you have had what you have had to drink, etc. Challenge: how to detect causal relations in the face of background variability (noise)?

25 Experiments on non-deterministic systems Since complex systems biological cognitive social are not perfectly regular in their behavior: - Researchers cannot simply do an experiment on one instance and draw a conclusion about the whole population - Must rather work with samples and draw conclusions based on statistical analysis Are the differences in the values of the dependent variable greater than expected by chance?

26 Confounding Variables The reason different individuals behave differently is that among extraneous variables, some may be related to the effect of interest. When such variables may be responsible for the effect produced in the study, they are called confounds - There are two kinds that are particularly important: Subject variable confounds: - Differences between subjects in the study Procedural variable confounds: - Differences in the way different groups are treated - If these variables are correlated with the independent variable and are also causes of the dependent variable, the experiment is confounded

27 Strategies for controlling confounding variables Randomization - Most commonly used to control confounding subject variables Locking - Most commonly used to control confounding procedural variables Matching subjects on confounding variables Making confounding variables into studied variables