Correlation and Causation

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What is correlation ?

Test of relationship between 2 variables ; change in one variable may or may not cause a change in other variable

What is causation?

Implies that if the value of one variable is changed, the other variable changes accordingly

Correlation does not mean Causation :

- two unrelated variables can have a strong correlation by sheer coincidence - ex., Money spent on Pets and Number of lawyers in California;

-Causation is Asymmetric : X causes Y , does not mean , Y causes X; -Correlation is symmetric; X is correlated to Y , means Y is Correlated to X

-X and Y variable may be correlated with each other , because both are driven by same third variable Z ;

ex., Say if , Ice-cream sales and drowning deaths are correlated; they both might be driven by High temperature - that causes higher ice-cream sales and Water-based activities;

How to distinguish correlation from Causation?

t-test : is used to test if the difference in the means of the two groups is likely to have occurred because of an actual difference between the two groups instead of random chance.

if p-value (likelihood of getting the observed difference by random chance) < 5% , difference between the 2 groups is statistically significant

What is A/B Testing : Randomized testing where A - Control group ; B - Treatment group ;

With Randomization it is safe to assume that most extraneous factors affect the treatment group and control group equally , with the exception of the treatment, so that we can attribute the differences between the two groups to the treatment effect.

this helps in distinguishing causation from correlation

Panel testing:

Collect the data (Ex., sales of a book, Ratings) on the same subject over different time periods ; assess the changes in the variables and see if they correlate well (change in sales vs change in ratings)

Assumption is that the unobserved Z (book quality) remains unchanged over time. while for books it may be true,Panel data may not be effective for measuring restaurant quality as it can change over time.

Matching:

is the process of choosing well-matched samples of treatment and control groups so that we can replicate a randomized experiment as closely as possible

issue is that unobserved factors may affect the assignment to treatment and outcome , and so the treatment group and control group are not comparable. Requires large sample size to ensure the matching

Regression Discontinuity:

choose a threshold value; pick the test units barely above the threshold (control) and those that are barely below the threshold (treatment) so that the two groups are comparable;

issue is : Requires large samples ; how do you identify the threshold ? Are the conclusions valid for the population far away from the threshold?