Advance 1 and 3
Use Promotion 1 as the numerical leader, not a proven winner over 3.
Campaigns
& sales.
Three promotions. One menu launch.
What actually won?
01 / A menu launch, three waysSame question.
Same question.
Different promotions.
A fast-food chain is launching a new menu item. Before a wider rollout, it wants to know which of three promotions brings in more sales.
The trial covers 137 stores over four weeks. Each store runs one promotion. That gives us 548 weekly sales records, but only 137 distinct stores.
The test, store by store
One mark = one storeSales are reported in thousands. The dataset does not specify a currency or record promotion costs.
02 / The first impressionThe leader depends
The leader depends
on what you count.
Promotion 3 leads in total sales. But it also runs in four more stores than Promotion 1. Compare the average per store per week, and Promotion 1 moves ahead.
Average weekly sales per store, thousands
A fairer starting point
Not a one-week spikeA steady order
A steady order
across all four weeks.
Promotion 1 leads the weekly averages each time. Promotion 2 stays last.
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03 / Beyond the leaderboardA higher average
A higher average
isn't a clear win.
Promotion 1 averages 2.73 thousand more than Promotion 3. But the observed gap is small relative to the variation between stores.
The documented tests find a clear difference between either of these promotions and Promotion 2, not between Promotions 1 and 3.
How strong is the difference?
Difference in average sales+2.73thousand per store per week
Two-sided p-value0.121
The evidence behind the p-value
A p-value is the probability of a result at least this extreme if the true means were equal and the test assumptions held. It is not the probability that a promotion works.
Four weeks aren't four independent stores.
The weekly tests treat all 548 records as independent. A new sensitivity check uses each store's four-week average instead. Uncertainty grows, but the main pattern remains: 1 and 3 ahead of 2, with no clear separation between 1 and 3.
Neither approach accounts for shared market-level conditions. Non-significance does not establish that two promotions are equivalent.
04 / Location mattersA different market.
A different market.
A different baseline.
Large markets average 70.12 thousand in weekly sales, compared with 57.41 in small markets and 43.99 in medium markets.
Promotion 2 ranks last in every market size. Promotion 3 edges ahead of 1 in large markets. These are observed averages, not proof of a different causal effect.
Three promotions, three market sizes
Average weekly sales, thousandsMarket profile and statistical comparisons
| Market | Stores | Mean store age | Weekly sales |
|---|
All three market-size pairs have two-sided p-values below 0.05 in the documented pooled weekly tests, both overall and within each promotion. These are unadjusted comparisons and share the repeated-record limitation. Sales-based market categories also make the sales differences partly expected.
05 / A useful reality checkOlder doesn't
Older doesn't
mean higher sales.
Store age has almost no overall linear correlation with weekly sales: r = −0.029. In the two-variable regression, its coefficient is also uncertain (p = 0.221).
Age is not a reliable shortcut
Promotion 1Promotion 2Promotion 3
The regression, without the overpromise
Descriptive model
Only 20.9% of sales variation is explained.
The fitted model uses market size and store age. It does not include promotion, and it has no held-out forecast validation.
It encodes Small = 1, Medium = 2, Large = 3, forcing equal steps. That misses the dip in medium-market sales. Treat these fitted values as an illustration of the model, not a sales forecast.
Fitted weekly sales, thousands
Age coefficient: +0.119 thousand per year, with a 95% interval from −0.072 to +0.311.
Sales = 24.768 + 12.599 × market code + 0.119 × age
06 / The decisionShortlist two.
Shortlist two.
Don't crown one.
Promotion 1 has the best average.
Promotion 3 is still a credible contender.
Promotion 2 is the weaker option.
Analysis notes
Data, methods & limitations
This educational fast-food case study contains 548 observations from 137 stores across four weeks. The three-way promotion comparison is an A/B/n test. Store labels in the charts are anonymous sequential labels.
The documented promotion comparisons use two-sided, equal-variance pooled t-tests at a 5% significance threshold. The additional store-average sensitivity check uses Welch's t-test on 43, 47 and 47 store means. Optional Holm correction covers the three promotion comparisons within the selected analysis. The displayed 95% confidence intervals are individual, not simultaneous, intervals.
Sales means, totals, market profiles and regression coefficients were recalculated from the dataset. Rounded display values may differ slightly from intermediate spreadsheet values. Missing promotion-cost data prevents a profit comparison; four weeks alone does not establish a lasting effect. There is no no-promotion control, so these comparisons do not estimate lift against doing nothing.
The case brief documents randomly selected markets, not the promotion-assignment procedure. Shared market conditions and the sales-based market-size definition limit causal interpretation. The original ordinal-coded regression is retained as a descriptive model, with its assumptions made explicit.