In fact, we have already seen the back-door adjustment when we discuss Simpson’s Paradox. We have calculated the weighted average of the rate of heart attacks with the drug in men and that in women to get the overall effect of the drug in the general population adjusted for the confounder, age. We can write …

## Simpson’s Paradox

Last time, we have talked about Monty Hall Problem and Berkson’s Paradox. This time, let’s discuss another paradox called Simpson’s Paradox. Let’s consider the following table: This is not a randomized experiment. The data is observed. By looking at the data, you can observe the following: Female in Control Group has 5% chance of getting …

## Should You Switch Your Choice of Doors? The Month Hall Problem

I want to illustrate this problem using a causal diagram. Here is the rule of the game: Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the …

## Cornfield’s inequality Causation v.s. Correlation

In the last post, I have shared about a debate: Today, I would like to show the proof on Corenfield’s Inequality, an inequality that settled the debate. I have read the original proof on the paper. Although the author said it is obvious, I don’t think so (always find reading maths discouraging LOL). I spent …

## Does smoking cause lung cancer? A case on causation v.s. correlation

The debate was neither tobacco nor cancer. It was the word “cause”. Many people smoke their whole lives and never get lung cancer. Some get it without lighting up a single cigarette. Previously when we discussed RCT, we know that it is an excellent way to establish a causal relationship. However, we cannot randomly assign …

## Some Puzzles to Understand How to Eliminate Confounders

To better understand this article, you need to first read these two articles: A confounder is like some backdoor paths from X to Y. To eliminate the confounder, you just need to block those backdoor paths. A randomized Controlled Trial did exactly that. But there is another way if we have a hypothesis on the …

## How Confounding Was Defined?

Before talking about how confounding should be defined, let’s talked about how it was defined before. Some declarative defintions A confounder is any variable that is correlated with both X and Y. A confounder X and Y is a variable Z that is (1) associated with X in the population at large, and (2) associated …

## How Randomized Controlled Trial Deconfounds the Confounding Bias

What is confunding bias? Imagine you are a farmer trying to determine applying fertilizer A to the field will increase the yield of crops. In other words, you are trying to establish a causal relationship between fertilizer A and yield. Our tricky Nature tells you that the effect of the fertilizer is mixed with a …

## Causal Diagram and Bayesian Network (Part 2)

There are three building blocks of Baysian Network. Remember that a Bayesian Network is nothing but some arrows connecting with different nodes representing the conditional probability table. The so-called building blocks are just the three types of arrow patterns. Arrow Pattern Easy To RMB Name Description A –> B –> C Chain Fire -> Smoke …

## Causal Diagram and Bayesian Network (Part 1)

After looking at how statistics pay little attention on causation compared with correlation, the author talks about Bayesian Network, in which he is one of the main contributors, and its relation with causal diagram. Bayes Theorem and Inverse Probability Bayes theorem provides a mathematical description of two events, the hypothesis (D) occurring before the evidence …