Lecture 16Correlation andCausation

I"d like to make a few commentsabout correlation and also causation. That is frequently said the a correlation betweentwo variables walk not suggest causation. This is generally true. Just becausethe lot of time invested working on an test is positively correlated with thegrade on the exam does not median that spending an ext time ~ above an exam willnecessarily lead to a better grade. The two might be correlated for part otherreason.

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In part instances, the adage aboutcorrelation and causation is actually no true. Take into consideration the instance in whichwe have actually a well conducted experiment the compares 2 groups. Us compute acorrelation coefficient and there is a far-reaching relationship in between theexperimental change (i.e., group membership) and the dependency variable. Thiswould, the course, it is in the exact same as conducting a t-test. Assuming us haveeliminated any kind of confounds and we provided random assignment, we should be maybe toconclude the the independent variable brought about the dependency variable. For this reason inthis case a correlation between the live independence variable and the dependentvariable suggests that the elevation variable led to the dependency variable.

If a non-experimental study isconducted, there is likely to it is in some alternative explanations because that arelationship between the independent and also the dependency variable, since we didnot randomly assign participants to speculative conditions.

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A couple of CommonAlternative Explanations for a Correlation between X and also YThere room three general reasons us cannot conclude that X caused Y simply becauseX and also Y are associated (in situations where X is not experimentally manipulated).First, us don"t know for certain that Y go not cause X. I"ll use arrows toindicate causation.

X----> Y (X reasons Y)

but, it might be that Y reasons X asin the following diagram:

Y-----> X (Y causes X)

Second, us don"t recognize that theydon"t cause each other:

Finally, over there is regularly a thirdvariable that might cause both X and Y together this diagram clues out:

The latter is described as the"third change problem". Mine favorite instance of the third variableproblem is the correlation between the variety of fire hydrants in a city andthe variety of dogs in a city. Cities with more fire hydrants have tendency to have moredogs. Why the relationship? A third variable. Any guesses what the third variablemight be?