B05 · Intermediate
B05 · Applied project
Does paid social sell beans?
Fictional case
January 2028. An agency pitching for Lantern’s account sends Ana one chart: weekly paid-social spend against online order value for 2027, with “r = 0.95” in large type and the advice to double the budget. Ana asks you whether the data say that. You have the shop’s 52 weeks of 2027 (week 52 runs 24–31 December), which total the $189,400 of online sales in Lantern’s 2027 accounts (F03), and her marketing calendar. Everything about Lantern and the agency is fictional.
| Push | Weeks |
|---|---|
| Valentine’s Day | 6–7 |
| Mother’s Day | 18–19 |
| Father’s Day | 24 |
| The gift season | 46–52 |
She sets each push’s spend in proportion to how big she expects it to be. In the other weeks spend stays between $38 and $46 a week; the year’s total is $2,649 (part of the $11,500 of advertising in Lantern’s 2027 accounts). Week 33 (13–19 August) had a four-day checkout outage.
Work through the stages: look at the relationship as a whole and in ordinary weeks, deal with the outage, check what trends and the season do, avoid a tempting but wrong adjustment, look at the other signals in the data, and decide how Ana could find out what her spend really does.
What you will produce
- Pearson’s r and Spearman’s ρ for spend and order value, and why they differ so much.
- The correlation in the ordinary weeks, with its confidence interval, and what it does and doesn’t rule out.
- How the outage week affects the link between sessions and orders, and how to report it.
- What trends, the season and a mediator do to the correlations, and which adjustments are honest.
- Delivery days and ratings measured properly, and what testing 36 pairs at once means.
- A memo to Ana: what the 0.95 does and doesn’t show, and a test that would show what spend does.
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