What you will be able to do
- Specify and estimate contribution per eligible offer in a price experiment.
- Distinguish demand response, elasticity and uncertainty about profit.
- Design a reproducible pricing decision with guardrails and segment discipline.
Before you begin: Comfort with percentages, averages, contribution and basic confidence intervals.
Define the outcome before collecting data
Choose the quantity you want to estimate before choosing a questionnaire. Here it is average contribution per eligible offer, including zero for customers who do not purchase. That denominator matters: looking only at buyers ignores the customers a higher price drives away. Define eligibility, the product, delivery terms and the time allowed to purchase. Contribution is realised revenue less costs that change because the purchase occurs, with refunds and payment fees treated consistently. If each customer can buy multiple units, measure the full customer outcome rather than forcing the data into a one-purchase model. State whether acquisition costs differ by price and whether they belong in the decision. An explicit outcome definition prevents attractive but irrelevant statistics from replacing the commercial objective.
Randomise at the unit that receives the price
Suppose one thousand eligible customers are randomly assigned to two prices, with five hundred in each arm. Keep product quality, marketing copy and fulfilment conditions comparable. Save the allocation procedure and assigned price before outcomes arrive. If one customer visits repeatedly, preserve that customer's assignment; treating each visit as independent can mix exposure and understate uncertainty. If customers share prices or purchase for each other, consider a suitable group assignment and analyse at that level. Random assignment supports causal interpretation because the offer groups are comparable in expectation, not because every characteristic will match exactly. Monitor missing records, price overrides and stockouts. Report assignment-based results so excluding inconvenient customers after randomisation does not undo the protection provided by the design.
Demand certainty is not profit certainty
We first quantify uncertainty about conversion. The higher-price purchase rate minus the lower-price rate is minus ten percentage points. For two independent samples of five hundred, add the estimated binomial variances: thirty percent times seventy percent over five hundred, plus forty percent times sixty percent over five hundred. The square root is three percentage points. Multiplying by one point nine six gives an approximate ninety-five percent margin of five point eight eight points. The interval excludes zero, so the data provide evidence of lower conversion at the higher price under this design. This does not yet establish a contribution gain. That outcome weights purchases by different margins and has a different variance, which we must calculate separately.
Connect evidence to an implementable price decision
Prepare a pricing memorandum that begins with the decision, the population and the primary outcome. Show conversion, revenue and contribution together so the reader can see why their rankings differ. Include uncertainty around the contribution effect and disclose the assumptions behind it. Then address repeat use, customer fairness, channel agreements, capacity and any cost that changes at scale. Name the person responsible for implementation and define a review date with a reversal trigger. If prices are personalised or regulated, obtain the relevant commercial and legal review before deployment. A well-designed experiment answers a defined causal question; it does not automatically resolve every policy constraint. Preserve the allocation data and reproducible calculations so later analysts can distinguish market change from measurement error.
Apply the method
Work through each task before opening the model answer. Compare your reasoning with the review criteria. Written answers stay on this page and clear when you leave or reload it.
Applied task 1
Show model answer and review criteria
Conversion difference = −0.10, SE = sqrt(0.3×0.7/500 + 0.4×0.6/500) = 0.03, interval [−0.1588, −0.0412]. Contribution difference = 1, variance = 30²×0.3×0.7/500 + 20²×0.4×0.6/500 = 0.57, interval about [−0.48, 2.48]. Different outcomes and monetary weights produce different uncertainty.
- Shows both formulas and correct intervals with units.
- States independent-customer and normal-approximation assumptions.
- Does not confuse conversion evidence with established profit improvement.
Applied task 2
Show model answer and review criteria
Define contribution over a fixed customer follow-up window including refunds and repeat purchases; randomise stable customer IDs or justified clusters. Prespecify the minimum useful gain, sample plan, one primary analysis and retention/service guardrails. Define how the estimate and uncertainty lead to adopt, continue testing or reject.
- Defines complete customer outcomes and denominator.
- Aligns assignment and analysis with repeat exposure and spillovers.
- Links uncertainty and guardrails to prospective decision rules.
Method references
- J-PAL — Randomization
Methodological basis for random assignment and choosing an assignment unit. Original IDER hypothetical price experiment and arithmetic. / Fondements de la randomisation ; expérience et calculs hypothétiques originaux IDER.
- NIST — Confidence limits for a proportion
Background on uncertainty for proportions. The two independent-arm normal approximations and contribution calculations are explicitly derived in this clinic, not presented as NIST Wilson intervals. / Repères sur les proportions ; calculs à deux groupes explicités dans la formation.