Interpreting a Flat Growth Curve After Process Change
A regional bakery chain with 40 outlets has tracked weekly croissant sales for three years. Sales were flat at roughly 12,000 units per week for 18 months. Six months ago the operations team replaced the laminated-dough proofing schedule, moving proof time from 90 to 120 minutes and lowering proof temperature by 3°C. Over the following 26 weeks, weekly sales averaged 12,180 units with a standard deviation of 640, versus a prior standard deviation of 610. Two outlets in a tourist district show a 9% rise; the other 38 show changes between -2% and +2%. The finance director says the change is working because average sales rose. The production manager says the change failed because most stores did not move. Both cite the same dataset.
1. Evaluate both claims. Which interpretation is better supported by the data, and what additional analysis would sharpen the conclusion?
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The finance director's claim rests on a mean difference of about 180 units, which is roughly 0.3 of the prior standard deviation. With 26 post-change weeks and a weekly SD near 620, the standard error of the post-period mean is about 122 units. The observed shift is therefore small relative to normal week-to-week noise, and the two claims are not equally defensible.
The production manager's observation is more informative because it describes the distribution, not just the mean. If 38 of 40 outlets moved by -2% to +2%, the aggregate lift is concentrated in two locations. A pooled average can rise while the typical outlet is unchanged, and the tourist outlets may be responding to seasonality or foot traffic rather than proofing.
Sharpen the conclusion by:
- Comparing each outlet to its own prior 18-month baseline rather than to the chain mean.
- Checking whether the two tourist outlets had a concurrent demand shock.
- Running a paired test across outlets, since outlet-level pairing removes between-store variance.
- Reviewing whether 26 weeks spans a seasonal cycle; a year-over-year comparison would control for that.
The honest conclusion is that the evidence does not yet show a chain-wide effect. The change may be neutral, which is itself a finding worth acting on.
2. The finance director proposes extending the new schedule to all products and declaring success. What decision rule would you recommend before scaling?
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Scaling on a 180-unit mean shift that is within noise would convert an ambiguous result into an irreversible commitment. A defensible rule has three parts.
First, define the effect size that matters commercially. If a 3% lift in croissant sales is the threshold for justifying the labor cost of longer proofing, state that before looking at more data. A pre-specified threshold prevents post hoc rationalization.
Second, require the effect to appear at the outlet level, not only in the pooled mean. A reasonable bar is that a majority of comparable outlets show a directional change consistent with the mechanism, and that the change survives outlet-level pairing.
Third, run a limited pilot on one additional product line with a matched control group of outlets. Compare pilot and control over at least 12 weeks, ideally spanning a seasonal transition.
If the pilot shows a lift below the commercial threshold, stop. If it shows a lift above threshold in most outlets, scale. If it is ambiguous again, the process change is probably not the lever and the team should look elsewhere, such as display placement or pricing.