9.2: Causal Reasoning
- Page ID
- 223911
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)We make causal judgments all the time. We think that the world is full of things causing other things to happen. He made me do it. The woman lost the race because she was anemic. The frog jumped off the leaf, causing it to shake and shower dew drops onto the ground below. You’re only cheating on this test because if you fail it, then you’ll have to drop out of college (don’t cheat, students, even if you are failing a course :) ). Roasting meat until it is charred and black causes cancer.
How, though, do we know that there’s a causal connection between two factors or events or things? We have to go through a particular process to demonstrate it. It’s sort of a more specific version of the hypothetical method we discussed above.
First, we establish that there is in fact a correlation between two things. There’s a correlation between alcohol use and liver disease. As one drinks more alcohol more regularly, one’s chances of developing liver disease increase proportionately.
Correlation, though, is cheap. There is a hilarious website called Spurious Correlations with a collection of graphs demonstrating the odd things that are correlated with one another. Check it out! It turns out Nick Cage films correlate quite closely with deaths by drowning in a pool. Per capita mozzarella consumption correlates with civil engineering doctorate awards. So we need to get beyond mere correlation in order to posit a causal connection. We need to give an account and run some tests.
Second, we need to develop a causal story or an account of how they actually might be correlated. The more doctorate awards are presented, the more wine and cheese receptions there are and the more wine and cheese receptions there are, the more mozzarella cheese is consumed. Plausible? Meh, not really. But that would be how we would fill in the gap between the two factors.
Gamma radiation exposure causes cancer. We know it is highly correlated, but beyond that, we actually have a story of how it causes cancer. Gamma radiation mutates cellular DNA, which either activates or creates genes which code for uncontrolled growth. That’s more or less the story of how gamma radiation and cancer are causally linked. We need this story because we need to understand how it possibly could be that gamma radiation has a causal effect on cancer.
Finally, we need to do perhaps the most important step: we need to test our hypothesis. We need to establish that the more radiation one is exposed to, the more likely one is to have cancer. Or if there were no civil engineering doctoral degrees awarded, then no one would consume mozzarella that year. We need to actually manipulate the variables involved until we have satisfied ourselves that by manipulating the cause we can manipulate the effect. For example, by removing the gamma exposure, we should dramatically decrease someone’s chances of developing cancer. If violent video games cause violent behavior, then we should see a drop in violent behavior after we get rid of violent video games.
1. Establish a prima facie correlation
2. Develop a causal theory or story or account
3. Test for concomitant variation
If we’ve only established a correlation between two variables or factors and then came up with a story about how they might share a causal connection, then we’ve stopped short of truly knowing that there is a causal connection between the two. We have to intervene between the two factors to be sure that one truly causes the other. Otherwise the cause might be something that we haven’t yet thought of.