code example (2): collider bias

https://mixtape.scunning.com/03-directed_acyclical_graphs

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Notice that the two variables are independent, random draws from the standard normal distribution, creating an oblong data cloud. But because “movie star” is in the top 85th percentile of the distribution of a linear combination of talent and beauty, the sample consists of people whose combined score is in the top right portion of the joint distribution. This frontier has a negative slope and is in the upper right portion of the data cloud, creating a negative correlation between the observations in the movie-star sample. Likewise, the collider bias has created a negative correlation between talent and beauty in the non-movie-star sample as well. Yet we know that there is in fact no relationship between the two variables. This kind of sample selection creates spurious correlations. A random sample of the full population would be sufficient to show that there is no relationship between the two variables, but splitting the sample into movie stars only, we introduce spurious correlations between the two variables of interest.

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