Business Analytics Quiz: Difference In Differences
10 questions · exam conditions
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Difference In DifferencesQuestion 1 of 10

A subscription company tests a retention program. The monthly churn rate for participating customers falls from 1212% to 88%. During the same period, churn among comparable nonparticipants falls from 1010% to 99%.

Which statement correctly interprets the difference-in-differences estimate?

The program reduced churn by 44 percentage points because participant churn fell from 1212% to 88%.
The program reduced churn by 33 percentage points beyond the decline observed among nonparticipants.
The program reduced churn by 22 percentage points because post-period churn was 88% versus 99%.
The program reduced churn by 55 percentage points after combining the declines in both customer groups.
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Business Analytics Quiz

Business Analytics Quiz: Difference In Differences

Practice Difference In Differences in Business Analytics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Difference In Differences, giving you a quick way to practice the rules, question types, and explanations that matter most for Business Analytics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A subscription company tests a retention program. The monthly churn rate for participating customers falls from 1212% to 88%. During the same period, churn among comparable nonparticipants falls from 1010% to 99%.

Which statement correctly interprets the difference-in-differences estimate?

  1. The program reduced churn by 44 percentage points because participant churn fell from 1212% to 88%.
  2. The program reduced churn by 33 percentage points beyond the decline observed among nonparticipants. (correct answer)
  3. The program reduced churn by 22 percentage points because post-period churn was 88% versus 99%.
  4. The program reduced churn by 55 percentage points after combining the declines in both customer groups.
Explanation: Whenever you see a difference-in-differences (DiD) question, your goal is to isolate the program's true causal effect by stripping out trends that would have happened anyway. The core formula is: (Changeparticipants)−(Changenonparticipants)(Change_{participants}) - (Change_{nonparticipants}). Here, participants fell from 12%12\% to 8%8\%, a decline of 44 percentage points. But nonparticipants also improved — from 10%10\% to 9%9\%, a decline of 11 percentage point. That 11 pp decline reflects a background trend unrelated to the program (perhaps seasonal behavior or a market-wide shift). To find the program's net effect, you subtract the background trend: 4−1=34 - 1 = 3 percentage points. This confirms B is correct — the program reduced churn by 33 pp beyond what would have occurred naturally. A is tempting because 44 pp is a real number from the data, but it ignores the counterfactual. Without subtracting the background trend, you're giving the program credit for changes it didn't cause. C compares post-period churn levels between the two groups (8%8\% vs. 9%9\%), which is a simple cross-sectional comparison — it ignores where each group started and conflates pre-existing differences with program effects. D adds the two declines (4+1=54 + 1 = 5), which has no logical basis in DiD methodology; you subtract the control group's change, you don't add it. Your study tip: always draw a quick two-by-two table (Before/After × Treatment/Control) and compute the DiD manually. The control group's change is your "would have happened anyway" baseline — never ignore it.

Question 2

A restaurant chain evaluates a delivery initiative by comparing participating regions with nonparticipating regions before and after launch. At the same time as the launch, a major competitor closes all of its locations in the participating regions but none in the comparison regions. Sales rise more in participating regions.

What is the most important consequence of the competitor closures for the difference-in-differences analysis?

  1. They are harmless because difference-in-differences automatically removes every event occurring during the post period.
  2. They matter only if participating and comparison regions had identical sales levels before the initiative.
  3. They improve identification because the closures create a larger post-period difference between the two groups.
  4. They undermine identification because their sales effect cannot be separated from the initiative's differential effect. (correct answer)
Explanation: Whenever you see a difference-in-differences (DiD) question, your central concern should be the parallel trends assumption: in the absence of the treatment, both groups would have followed the same trajectory. DiD estimates the treatment effect by calculating (Yˉtreated,post−Yˉtreated,pre)−(Yˉcontrol,post−Yˉcontrol,pre)(\bar{Y}_{treated,post} - \bar{Y}_{treated,pre}) - (\bar{Y}_{control,post} - \bar{Y}_{control,pre}). This math only isolates the initiative's impact if no other differential shock hits one group but not the other during the study window. That's exactly what the competitor closures represent — a differential shock. They affect participating regions but not comparison regions, so any sales bump they generate gets folded into the post-period difference. You can't tell whether the sales increase came from the delivery initiative, the reduced competition, or some combination. D is correct because the closures' effect and the initiative's effect are perfectly confounded; they cannot be disentangled from the DiD estimate alone. A is wrong because DiD does not automatically purge every concurrent event — it only removes shocks that affect both groups equally. A region-specific event is precisely what breaks the design. B is wrong because the parallel trends assumption is about trends (equal slopes over time), not identical pre-period levels; different baseline sales are perfectly acceptable. C is wrong and represents a tempting trap: a larger post-period gap makes the initiative look more effective, but that's the problem, not a benefit — inflated differences produce biased, not improved, estimates. When reviewing quasi-experimental designs on your exam, always ask: Did anything else change for one group but not the other? If yes, identification is threatened.

Question 3

A marketplace launches a seller-training program in April. An analyst conducts placebo difference-in-differences calculations using only earlier months and obtains treated-minus-control changes of 11 unit in January, 88 units in February, and 1515 units in March. The estimated April effect is 2020 units.

Which conclusion is most defensible from these results?

  1. The April effect is credible because the placebo estimates are all smaller than the post-launch estimate.
  2. The April effect is exactly 55 units because the latest placebo estimate should be subtracted mechanically.
  3. The rising placebo estimates suggest a preexisting differential trend that weakens the causal interpretation. (correct answer)
  4. The parallel-trends condition is confirmed because none of the placebo estimates equals the April estimate.
Explanation: Whenever you see a difference-in-differences question involving placebo tests, your focus should be on whether the parallel-trends assumption holds — meaning treated and control groups were moving together before any intervention. Placebo estimates let you check this by running fake "treatments" in pre-intervention periods where the true effect should be zero. Here, the placebo treated-minus-control changes are 11, 88, and 1515 units across January, February, and March — a steadily climbing sequence. This pattern tells you the treated group was already pulling away from the control group before April, which is exactly what a preexisting differential trend looks like. If parallel trends held, these placebo estimates should hover near zero with no systematic direction. Because they don't, the April estimate of 2020 units cannot be cleanly attributed to the training program — some or all of it may simply be the continuation of that pre-existing gap. Answer C is therefore the most defensible conclusion. Answer A is tempting but logically flawed: placebo estimates being smaller than the April estimate doesn't validate anything. What matters is whether pre-period estimates are near zero, not merely smaller than the post-period number. Answer B invents a mechanical subtraction rule (20−15=520 - 15 = 5) that has no basis in DiD methodology — you don't adjust by the last placebo figure alone. Answer D misreads what "parallel trends confirmed" would actually require; the placebo estimates not equaling the April figure is irrelevant — they need to be close to zero. As a study tip: when evaluating DiD validity, always ask "are the pre-treatment placebo estimates near zero and stable?" A rising or falling trend in pre-period gaps is a red flag, regardless of the post-treatment estimate's magnitude.

Question 4

A promotional campaign officially begins in July, but customers in treated markets learn about it in June and begin purchasing early. Relative to what would have occurred without the campaign, treated-market sales are already 44 units higher in June and are 1010 units higher in July. Control-market sales follow their usual trend. The analyst treats June as the pre period and July as the post period.

What effect will the basic difference-in-differences calculation estimate under these conditions?

  1. An effect of 66 units, understating the July effect because June is already affected (correct answer)
  2. An effect of 1010 units, correctly capturing the full July effect despite anticipation
  3. An effect of 1414 units, overstating the July effect by adding the anticipation response
  4. An effect of 44 units, measuring only the purchases shifted into the pre period
Explanation: Whenever you see a difference-in-differences (DiD) question, your job is to track what the estimator actually measures — not what the researcher intended to measure. DiD computes: (Ytreated,post−Ytreated,pre)−(Ycontrol,post−Ycontrol,pre)(Y_{treated,post} - Y_{treated,pre}) - (Y_{control,post} - Y_{control,pre}). The pre-period is supposed to be "clean," but here it isn't. Because customers anticipate the campaign, treated-market sales are already elevated by 44 units in June (the pre period). In July, they're elevated by 1010 units. The DiD estimator sees a treated-market increase of 10−4=610 - 4 = 6 units from pre to post, and subtracts zero from the control side (controls are unaffected in both periods). So DiD estimates 66 units — which is answer A. This understates the true July effect of 1010 units because the baseline (June) is already contaminated by anticipatory purchasing. Answer B is wrong because DiD cannot "see through" the corrupted pre-period; it mechanically differences whatever values exist in pre and post. Answer C would only be correct if DiD added the anticipation effect rather than subtracted it — but since June's elevation reduces the measured pre-to-post jump, the estimate goes down, not up. Answer D confuses the estimator's output with the size of the anticipation effect itself; 44 units is what leaked into June, not what DiD reports. Study tip: Always ask whether the pre-period is truly unaffected. Anticipation effects, leakage, or pre-treatment contamination all bias DiD downward by inflating the baseline — a classic trap on business-analytics exams.

Question 5

Before a marketing intervention, treated-region revenue is 100100 and comparison-region revenue is 5050. Afterward, treated-region revenue is 120120 and comparison-region revenue is 6060. Thus, both regions grow by 2020%, although their absolute increases differ.

Which statement best describes the difference-in-differences conclusion?

  1. Both level and percentage specifications estimate an effect of zero, because identical growth rates eliminate any estimated difference under either modeling approach.
  2. Both level and percentage specifications estimate an effect of 1010, because absolute dollar changes are the only valid basis for a difference-in-differences comparison.
  3. A level specification estimates 1010, while a proportional-growth specification estimates zero, because each embeds a different counterfactual assumption about how trends should be measured. (correct answer)
  4. A level specification estimates zero, while a proportional-growth specification estimates 1010, because the differing baseline revenues produce a larger absolute gain in the treated region.
Explanation: Whenever you see a difference-in-differences question involving regions with different baseline values, your first instinct should be to ask: what does "parallel trends" actually mean here — parallel in levels or parallel in growth rates? That assumption is everything. Under a level specification, you assume the two regions would have grown by the same absolute dollar amount. The treated region gained 120−100=20120 - 100 = 20, while the comparison region gained 60−50=1060 - 50 = 10. The estimated treatment effect is 20−10=1020 - 10 = 10. Under a proportional-growth specification, you assume both regions would have grown by the same percentage. Both actually grew by 20%20\%, so the counterfactual is perfectly matched — the estimated effect is 00. Answer C captures this exactly: two different counterfactual assumptions produce two different numerical conclusions, neither of which is inherently "correct" without external justification. Answer A is wrong because the two specifications do not agree — identical percentage growth only eliminates the effect under the proportional model, not the level model. Answer B is wrong on two counts: the level estimate is 1010, not the same under both models, and claiming absolute dollars are the "only valid" basis is an unjustified assertion — proportional specifications are entirely legitimate in many contexts. Answer D reverses the results entirely — the level specification yields 1010 (not zero), and the proportional specification yields 00 (not 1010). The key study tip: always identify which parallel-trends assumption a DiD model embeds. A level model assumes equal absolute trends; a log or proportional model assumes equal percentage trends. The same data can tell completely different causal stories depending on that choice.

Question 6

A grocery chain introduces rapid delivery at selected stores. Sales at treated stores rise by 55 units. Nearby comparison stores lose customers to the treated stores, causing their sales to fall by 33 units; absent this spillover, their sales would have remained unchanged.

How does the spillover affect the basic difference-in-differences estimate of the treated stores' sales effect?

  1. It produces an estimate of 22 units and therefore understates the effect by 33 units.
  2. It produces an estimate of 88 units and therefore overstates the effect by 33 units. (correct answer)
  3. It produces an estimate of 55 units because comparison-group spillovers cancel in the calculation.
  4. It produces an estimate of 33 units because only the comparison-group decline identifies the effect.
Explanation: Whenever you see a difference-in-differences (DiD) question involving spillovers, your job is to trace exactly what the comparison group's trend looks like — because DiD uses that trend as a stand-in for what would have happened to treated stores absent the treatment. The DiD estimator works by taking the treated group's change minus the comparison group's change: τ^=ΔYtreated−ΔYcomparison\hat{\tau} = \Delta Y_{\text{treated}} - \Delta Y_{\text{comparison}}. In this scenario, treated stores rise by +5+5 units. The comparison stores, however, lose 33 units due to customer spillover — customers migrating to the convenient rapid-delivery stores. Their "true" counterfactual change was 00, but DiD observes −3-3. Plugging in: τ^=5−(−3)=8\hat{\tau} = 5 - (-3) = 8. The method thus overstates the true effect of 55 by 33 units, making B correct. The key intuition: spillover artificially depresses the comparison group, making the treated group look even better by comparison than it truly is. A gets the arithmetic backwards — subtracting 33 from 55 gives 22, which would only apply if the comparison group rose by 33, not fell. C is wrong because spillovers do not cancel — they corrupt the comparison group's trend, which is precisely what DiD relies on. D misunderstands the estimator entirely; DiD uses the difference between both groups' changes, not the comparison group's change alone. Study tip: When spillovers push the comparison group down, DiD overstates the effect; when they push it up, DiD understates it. Sketch the formula and plug in the direction of the spillover every time.

Question 7

An analyst estimates the regression Y=40+8T+5P−6(TxP)Y = 40 + 8T + 5P - 6(T x P), where TT equals one for treated branches and PP equals one in the post-implementation period.

What are the model's predicted post-period outcome for a treated branch and its difference-in-differences estimate, respectively?

  1. A predicted outcome of 5353 and an estimated treatment effect of 88
  2. A predicted outcome of 4747 and an estimated treatment effect of −6-6 (correct answer)
  3. A predicted outcome of 4545 and an estimated treatment effect of 55
  4. A predicted outcome of 3939 and an estimated treatment effect of −14-14
Explanation: Whenever you see a Difference-in-Differences (DiD) regression, recognize that the model uses indicator variables and their interaction to isolate a treatment effect. The standard setup is Y=β0+β1T+β2P+β3(T×P)Y = \beta_0 + \beta_1 T + \beta_2 P + \beta_3(T \times P), where β3\beta_3 is the DiD estimate — it captures the effect unique to treated units in the post-period, beyond any general time trend or baseline group difference. Here, the model is Y=40+8T+5P−6(T×P)Y = 40 + 8T + 5P - 6(T \times P). For a treated branch (T=1T = 1) in the post-period (P=1P = 1), plug in directly: Y=40+8(1)+5(1)−6(1×1)=40+8+5−6=47Y = 40 + 8(1) + 5(1) - 6(1 \times 1) = 40 + 8 + 5 - 6 = 47. The DiD estimate is simply the coefficient on the interaction term, which is −6-6. That makes B correct — a predicted outcome of 4747 and a treatment effect of −6-6. Choice A reports 5353, which ignores the interaction term entirely (40+8+5=5340 + 8 + 5 = 53), and incorrectly labels β1=8\beta_1 = 8 as the treatment effect. Choice C uses 4545 and attributes the time trend coefficient β2=5\beta_2 = 5 as the treatment effect — both errors. Choice D produces 3939 by misapplying signs and mistakes −14-14 as the effect, likely by incorrectly combining multiple coefficients. Your key takeaway: in a DiD regression, always look at the interaction term coefficient — that alone is the causal treatment estimate. Never confuse β1\beta_1 (treated vs. control baseline gap) or β2\beta_2 (pre-to-post time trend) with the actual treatment effect.

Question 8

A retailer measures the effect of redesigned stores on average monthly spending among loyalty-program members. After redesign, treated stores enroll many new low-spending members, while comparison stores experience no similar enrollment change. The analyst compares average member spending before and after redesign in both groups.

Why should the analyst be cautious when interpreting the difference-in-differences estimate as a change in individual customer spending?

  1. Average spending cannot be used in difference-in-differences unless every store begins with the same number of members.
  2. The design becomes invalid whenever treatment changes an outcome by enrolling additional customers in the post period.
  3. The comparison group must also redesign its stores so that membership counts remain balanced across the two groups.
  4. The treated sample's composition changed, so lower average spending may reflect new members rather than customer-level changes. (correct answer)
Explanation: Whenever you see a difference-in-differences (DiD) question, ask yourself: are we comparing apples to apples? DiD estimates a treatment effect by assuming that any change in the treated group's average outcome — beyond what the control group experienced — reflects the treatment itself. This assumption breaks down when the composition of the treated group changes between periods. Here, the store redesign attracted many new, low-spending members in the post-period. If average spending falls (or rises less than expected) in treated stores, that shift could simply reflect this influx of budget-conscious newcomers — not any change in how existing customers behave. The DiD estimate is picking up a compositional change, not a causal effect on individual spending. That's exactly why D is correct: the treated sample's composition changed, so you cannot confidently attribute differences in average spending to customer-level behavioral changes. A is wrong because DiD does not require equal store sizes or equal member counts at baseline — it requires parallel trends, not identical scales. Misreading the parallel-trends assumption as a size-balance requirement is a common trap. B overstates the problem. Enrollment changes don't automatically invalidate DiD — they introduce a specific interpretation hazard. The design can still be executed; the analyst just needs to be careful about what the estimate actually measures. C describes a made-up requirement. There is no rule that the comparison group must mirror treatment-group operational changes to maintain validity. Enforcing that would defeat the purpose of a control group. Study tip: On any DiD question, always check whether the who being measured stays consistent across periods. If group membership changes, averages shift for compositional reasons — and your estimate no longer cleanly isolates the treatment effect.

Question 9

A retailer introduces a new inventory system in selected stores. Average weekly sales in the treated stores increase from 200200 units before implementation to 250250 units afterward. In untreated stores, average weekly sales increase from 180180 units to 210210 units over the same period.

Assuming the parallel-trends condition is appropriate, what is the difference-in-differences estimate of the system's effect on weekly sales?

  1. An increase of 3030 units, based on the change in untreated stores
  2. An increase of 5050 units, based on the change in treated stores
  3. An increase of 2020 units, after removing the untreated-store change (correct answer)
  4. An increase of 7070 units, based on the difference between both changes
Explanation: Whenever you see a question involving a treated group and an untreated group measured before and after some intervention, you're dealing with difference-in-differences (DiD) — a method designed to isolate a true causal effect by stripping away trends that would have happened anyway. The core formula is: DiD=(Yˉtreated,post−Yˉtreated,pre)−(Yˉuntreated,post−Yˉuntreated,pre)\text{DiD} = (\bar{Y}_{treated,post} - \bar{Y}_{treated,pre}) - (\bar{Y}_{untreated,post} - \bar{Y}_{untreated,pre}) Plugging in the numbers: the treated stores changed by 250−200=50250 - 200 = 50 units, and the untreated stores changed by 210−180=30210 - 180 = 30 units. The DiD estimate is 50−30=2050 - 30 = 20 units — making C correct. Those 30 units of growth in untreated stores represent background trends (seasonality, market conditions, etc.) that also affected treated stores. Removing them isolates the system's true effect. A is wrong because it reports only the untreated-store change (+30+30), which captures the background trend — not the treatment effect at all. B is wrong because it reports only the raw before-after change in treated stores (+50+50) without subtracting the counterfactual trend; this overstates the effect by conflating natural growth with the system's impact. D is wrong because it adds the two changes (50+30=8050 + 30 = 80... or perhaps misreads as 7070) rather than subtracting them — a fundamental misapplication of the DiD logic. A useful memory anchor: DiD is always a subtraction of two changes, not an addition or a single change in isolation. If you find yourself reporting just one group's movement, you haven't finished the calculation.

Question 10

A company plans to evaluate a pricing tool in one division. In the two quarters before implementation, revenue in the treated division rises from 100100 to 110110. Revenue in potential comparison division A rises from 8080 to 9090, while revenue in potential comparison division B rises from 100100 to 103103. No other pre-implementation information is available.

Based only on these pre-implementation revenue patterns, which comparison division is more supportive of a difference-in-differences design?

  1. Division A, because its revenue change matches the treated division's change despite different starting levels (correct answer)
  2. Division B, because its initial revenue matches the treated division's level despite a different change
  3. Division A, because lower initial revenue guarantees that post-period growth will remain comparable
  4. Division B, because equal initial levels are sufficient to establish the required counterfactual trend
Explanation: Whenever you see a question about difference-in-differences (DiD), the critical concept to evaluate is parallel trends — the assumption that the treated and control groups would have followed the same trajectory (not necessarily the same levels) in the absence of treatment. DiD does not require equal starting points; it requires equal changes over time. Look at the pre-period revenue changes: the treated division rises by $10\$10 (from 100100 to 110110). Division A also rises by $10\$10 (from 8080 to 9090), matching that trend exactly despite starting at a different level. Division B rises by only $3\$3 (from 100100 to 103103), showing a clearly different trajectory even though its starting level matches the treated division. This makes A the correct answer. Division A exhibits the same pre-period change as the treated group, which is precisely the evidence you need to support the parallel trends assumption underlying a valid DiD design. Answer B is tempting but wrong — it confuses level matching with trend matching. Equal starting levels tell you nothing about whether two groups move in parallel. Answer C compounds this error by claiming that lower initial revenue "guarantees" comparable future growth, which is economically unfounded; initial levels don't determine trajectory. Answer D makes the same fundamental mistake as B, asserting that equal initial levels are sufficient for the counterfactual trend — they are not. Study tip: On DiD questions, always ask "do the changes match?" not "do the levels match?" Parallel trends is about slopes, not intercepts.