Correlation and Causation

Every important business question is about cause. Will this discount increase sales? Did that advert work? Would closing this cafe help? A chart can show you what happened. It can't tell you what would have happened otherwise. And that gap is where the most expensive mistakes live.

• Every important question is causal
• Charts show what happened
• Not what would have happened

Simpson's paradox

Here's something that seems impossible. Cafe B has a better upsell rate overall. But split by day, cafe A is better on weekdays, and better on weekends too! How can A win both, yet lose overall? Run it. The reason is that B does most of its trade on weekends, when everyone upsells more. That's Simpson's paradox. The hidden variable, the type of day, flips the conclusion. So always ask what you might be missing.

import pandas as pd

df = pd.DataFrame({
    "cafe": ["A"] * 2 + ["B"] * 2,
    "weekday": ["Mon-Fri", "Weekend", "Mon-Fri", "Weekend"],
    "orders": [800, 200, 200, 800],
    "upsold": [160, 80, 30, 280],
})

overall = df.groupby("cafe")[["upsold", "orders"]].sum()
print((overall["upsold"] / overall["orders"]).round(3).to_string())
print()
print(df.assign(rate=lambda d: (d["upsold"] / d["orders"]).round(3))
        .pivot(index="cafe", columns="weekday", values="rate").to_string())

cafe
A    0.24
B    0.31

weekday  Mon-Fri  Weekend
cafe
A           0.20     0.40
B           0.15     0.35

Three ways to answer a causal question

There are three main routes. Best of all is a randomised experiment. If you can't do that, control for confounders, using regression. Or look for a natural experiment, where something changed for one group, but not for another. Each step down needs stronger assumptions, so say those assumptions out loud.

Summary