StreamCart, a grocery delivery app, noticed that users who receive more push notifications tend to place more weekly orders. The growth team wants to know whether sending more notifications causes higher order volume, or whether the relationship is only correlational.
You are given observational data split into two customer segments. At the overall level, push notifications and weekly orders appear positively correlated. Your task is to quantify that correlation, then explain why it does not establish causation and how segment-level analysis changes the conclusion.
| Segment | Users | Avg Push Notifications per Week | Avg Orders per Week |
|---|---|---|---|
| New users | 800 | 6.0 | 1.2 |
| Existing users | 1,200 | 2.0 | 3.8 |
A simple user-level regression on the full sample produced the following summary:
| Metric | Value |
|---|---|
| Overall correlation between notifications and orders | 0.42 |
| Regression coefficient on notifications | 0.18 |
| p-value for coefficient | 0.003 |
| Significance level | 0.05 |
Within each segment, the estimated relationship is:
| Segment | Correlation between Notifications and Orders |
|---|---|
| New users | -0.08 |
| Existing users | -0.05 |