Monadic pricing: compare one-price reactions and the commercial tradeoff

Monadic pricing shows each eligible person one price for the same complete offer, then compares responses across independently assigned groups. For Lumen’s illustrative sparkling-tea six-pack, that means a buyer sees $12, $15 or $18, never all three before answering. The comparison preserves a first reaction to each price; the commercial decision still needs the response distribution, valid base and economics.

The card and outcome stay fixed

Lumen’s grocery team needs candidate prices for a market pilot. The three cells below keep the six-pack and purchase setting fixed while the displayed price changes.

Ask likelihood of buying at the displayed price with a fixed timeframe and a fully labeled scale. Define the summary before looking at results. For example, top-two-box can mean definitely or probably would buy, while the full distribution remains available.

Use the exact card: “Lumen sparkling tea: six 250 ml cans, one-off purchase at your usual grocery store. The displayed price is the total for the six-pack, including applicable tax. No delivery charge applies.” Replace only the price with $12, $15 or $18.

Ask: “At this displayed total price, how likely would you be to buy this six-pack at your usual grocery store within the next four weeks?” Options are definitely would; probably would; might or might not; probably would not; definitely would not; not applicable. The example allocation is 300 eligible people randomized 100 per cell, one card each, 100 valid answers per cell, with no exclusions or missing answers. In an actual study, show each of those flow counts rather than assuming they match.

The cell dataset contains these counts:

The A–B difference is 10 percentage points; B–C is 15. These comparisons describe the example’s responses. They do not establish a causal sales effect, and small differences should not be declared reliable without appropriate design and uncertainty analysis.

The timeframe and channel turn a general liking question into a specific stated-intent outcome. Keep the full category distribution even if the decision uses top-two-box. A person moving from “definitely” to “probably” would leave that binary summary unchanged while weakening conviction.

Do not redefine positive intent after seeing which scale cut favors a price. The measure should connect to the progression decision named in the brief. Comprehension and objections explain the result, while remaining distinct from the primary intent outcome.

Random assignment protects the price comparison

The offer description, channel and instrument remain identical across cells.

The original allocation is 300 eligible people, 100 per price, one card each. This allocation is not a minimum requirement. Use recorded random assignment and plan any essential audience balance before collection. A staff-selected price based on apparent enthusiasm would change who enters each cell.

Keep exposure clean. A participant who saw another tested amount through a screenshot, repeat entry or later comparison has a different information history. Record the event under a declared rule. A follow-up after the primary block may be useful; it cannot become another independent first reaction.

The planned cell and the final valid cell are separate. Random assignment balances in expectation, while selective missingness can change the achieved composition. Inspect the actual audience and reason for loss before assuming the design remained comparable.

Interest and contribution can point to different prices

In these cells, positive intent falls from 60% at $12 to 50% at $15 and 35% at $18. The $12 option leads on that share. The question is whether more stated interest is the objective or one input to a commercial choice.

Multiplying displayed price by the stated share gives arithmetic indices of $7.20, $7.50 and $6.30. Thus $15 leads on this price-times-intent calculation even while $12 leads on intent. The index is not observed revenue: it treats stated intent as if it were volume and omits costs. Its role is to reveal why “most positive answers” and “best commercial candidate” need not be the same choice.

For contribution, the team needs applicable costs and an appropriate behavioral volume measure. For penetration, it may value trial and reach. For a premium positioning objective, it needs evidence that the offer communicates and delivers the premium. State which objective the analyst should optimize before interpreting a score.

If the result points to two viable candidates, a useful recommendation can take both into a market pilot with a defined conversion and repeat outcome. The study does not fail merely because it leaves that final behavior question open.

The interval depends on the sampling model

Under an illustrative independent random human-sampling model, an approximate 95% interval for a difference is pA−pB ± 1.96 × sqrt(pA(1−pA)/nA + pB(1−pB)/nB). NIST’s two-proportion guidance describes this large-sample comparison. It does not account for nonresponse, coverage bias or dependence; choose an appropriate interval for the actual design.

Uncertainty around the intent gaps

Each cell has 100 valid answers. These unadjusted large-sample intervals concern stated intent under the independent human-sampling model, not sales or generated-response error.

These are unadjusted pairwise illustrations, not collected findings. The first includes zero; the second’s lower bound is close to zero and could change with the planned comparison adjustment. Predeclare the primary comparison rather than inspecting all pairs and declaring the best-looking result reliable.

For a planning example, detecting 60% versus 50% with equal independent groups, two-sided 5% significance and 80% power requires approximately 388 completed eligible people per cell using the usual normal approximation without continuity correction. With pbar=.55, the calculation is n=[1.96×sqrt(2×.55×.45)+.8416×sqrt(.60×.40+.50×.50)]²/.10²=387.34, rounded up. This is power for that one stated-intent difference, not a universal minimum or precision target. Different tests, multiple comparisons, clustering, exclusion allowances and smaller segment differences change the requirement; see PASS’s two-proportion design guide.

Plan for the smallest difference that would change the price recommendation, rather than using the illustrative 10-point gap by default.

The 388-per-cell plan is prospective: it assumes a specified 10-point difference, two independent equal groups and the named normal approximation. It does not retrospectively certify the 100-per-cell example. Use our sample size worksheet to examine the planned effect before collection.

The primary contrast determines the plan

A three-cell test has three possible pairs, while a four-segment analysis creates up to twelve cell-segment combinations. Decide which comparison changes the price recommendation and how secondary views will be interpreted. A whole-study total cannot guarantee precision in every small cut.

If the central decision is $12 versus $15 for the current target, plan that contrast. Include $18 only when it is a credible option with a defined role, not because an extra price makes the chart look complete. Smaller meaningful gaps require more evidence than larger ones under the same model.

Subgroup reasons can generate a useful follow-up hypothesis. A segment with a high stated share at $18 may value an occasion differently, or may have too few valid records for a strong inference. Show the base and context before converting every cut into a separate price strategy.

Assignment and valid answers need separate counts

These stages identify what an exclusion means. A loading failure creates absent exposure; an inapplicable answer is a valid response state; a valid negative answer stays in the intended outcome base. Dropping those negative answers would make the price look better than it is.

Reconstruct positive counts and denominators from saved records. Keep assigned price, displayed version and outcome linked. If those disagree, solve the exposure problem before accepting the dashboard summary. An attractive aggregate cannot reveal which card a person actually saw.

Later comparisons have their own exposure history

After the independent block, the team may ask about competing offers, reasons or direct preference. Label those results by the later exposure. Someone choosing $12 after seeing all three amounts has answered a different question from their first response at $15.

Declare exclusions and any sensitivity analysis before reading the result. Show how many records each rule affects and whether the price recommendation changes. A response-quality rule should improve the relevance of the evidence, rather than remove unfavorable answers.

For modeled cells, inspect grounding and validation and preserve the dependence of the generated responses. The human interval and sample-size arithmetic cannot be transferred by giving generated records the same A/B labels.

Two feasible prices can progress to a pilot

For this example, the next action is to compare the feasible $12/$15 tradeoff with the economics owner and plan a primary behavioral pilot. The intent shares and wide interval explain why it would be premature to declare one price universally superior. $18 can remain a secondary candidate if the objective and audience justify it.

A finished report retains the exact card, valid bases, full intent categories, uncertainty assumptions and reason codes. It names the candidate price, the objective that favors it and the remaining fact that could change the choice. Those details let a buyer challenge the recommendation constructively.

Use the sample size worksheet for the planned independent comparison and our repeated-ladder guide if tracing brackets is the better task. Confirm the named design and analysis with any provider, including a Vensia modeled study.

Complete cell records

The records preserve assigned eligible people, positive intent and all other valid answers for each price. Copy them as monadic-pricing.csv to reuse the worked counts. In each cell, positive_intent + other_valid_answers = assigned_eligible = 100; the share is positive_intent / 100.

All three price cells

cell,price,assigned_eligible,positive_intent,other_valid_answers,evidence_type
A,12,100,60,40,fictional_teaching_data
B,15,100,50,50,fictional_teaching_data
C,18,100,35,65,fictional_teaching_data

Further reading

• our pricing research guide
• our pricing method selector

For a scoped Vensia study discussion, identify which price contrast would change the recommendation and which evidence the proposed study would return. That gives the proposal a specific comparison and outcome to address.