Interview guides · American Institutes for Research

American Institutes for Research Data Scientist Interview Questions & Guide 2026

SQL practice for American Institutes for Research data scientist candidates: window functions, funnel and retention queries, joins that quietly drop rows.

The 60-second brief

At the American Institutes for Research (AIR), a Data Scientist (often titled Quantitative Researcher) is a cornerstone of the organization’s mission to apply evidence-based, data-driven solutions to society’s most pressing challenges. You will not be working in a vacuum; you will collaborate with an interdisciplinary team of economists, sociologists, public health experts, and policy analysts to unravel complex issues regarding health care quality, costs, and access.

Most of the loop measures decision-making under uncertainty rather than recall. You are scored on whether you state your assumptions, commit to an estimate you can defend, and say explicitly what evidence would change it.

Focus areas

Separate novelty effects from durable behaviour change
Turn a vague request into a measurable question
Pick a randomisation unit that respects interference

Overview

Your work directly influences federal, state, and local policy. Whether you are analyzing Medicare claims data or designing rigorous evaluations for health innovations, your technical outputs are translated into actionable insights for stakeholders. This role is inherently impactful, requiring you to bridge the gap between high-level statistical rigor and clear, persuasive communication that informs real-world decision-making.

The role at AIR is highly mission-driven. When preparing, emphasize how your technical skills can serve the public good, as this is a key differentiator in their evaluation process.

The American Institutes for Research interview process

American Institutes for Research candidates report 4 rounds · ≈ 3-5 weeks. The stages below are what candidates describe, not a published process.

Application Review

Whoever runs this call is usually not a practitioner. They take notes, and a hiring manager skims those notes later, so the real question is whether your work survives being written down by someone outside the field. Test every project sentence against that: could a non-specialist repeat it correctly without knowing what a propensity score is? Carry a plain-language version of each project and one reason you want this particular role that you could not copy onto another application. Vagueness at this stage reads as inexperience, even when the underlying work was genuinely deep.

What to demonstrate

Whether a non-specialist can restate your projects accurately, since their paraphrase is what reaches the hiring manager
Whether your reason for wanting the role points at the work itself rather than the company's reputation
Whether your language signals the level being screened for: what you decided yourself versus what you were handed

How to prepare

Write a two-sentence, jargon-free version of each major project: the question nobody could answer, and the decision your work changed. Read it to someone outside data and have them repeat it back
Point your 'why this role' answer at something concrete in the job description or the product surface you would be working on, and keep it to two sentences
Have two questions ready about measurement: which metric the team is held to, and who acts on an analysis once it lands

Take-Home Coding Test

The clock is part of the test. Three to six hours is not enough to do everything the dataset supports, so the submission mostly reveals how you spend a fixed budget against an open question. A reviewer sees which paths you took and, by absence, which you abandoned. Work that runs out of time inside the analysis ships a thin conclusion, while work that cuts scope early protects the last hour for writing. The most reliable way to lose here is to leave the scoping decision implicit, so it reads as something you missed rather than something you chose.

What to demonstrate

Whether the scope you settled on is presented as a decision with a reason, rather than left for the reader to infer from what is missing
Whether the depth of the work is consistent with the stated time budget, instead of several half-finished directions left open
Whether the closing section reads as something written on purpose rather than assembled from whichever cells survived

How to prepare

Run a timed rehearsal on a public dataset with a hard stop, holding the final sixty minutes for writing no matter where the analysis has got to
Before opening the data, list the questions it could plausibly answer, pick one, and keep the discarded ones as a short note on what you did not attempt and why
Commit a one-line finding after each analysis step so the writeup is assembled from recorded results rather than from memory at midnight

Panel Interviews

Where a loop ends with a senior leader, that conversation is rarely another skills test. The technical signal already exists by then, so the questions tend to open up: what you would look at first, where a metric you have heard about could mislead, what you would push back on. The decision being made is scope, which in practice means level and how much you would be trusted to own unsupervised. Treating it as a formality is the usual mistake. An open question late in the day is still being scored, and a vague answer reads as someone who has not run anything themselves.

What to demonstrate

Whether your view of the business has anything specific behind it, given that you are working only from what is public and are expected to say so
Whether the scope of work you describe owning matches the scope of the role, instead of sitting a level below it
Whether you can disagree with something concrete and stay useful about it, rather than agreeing with everything said in the room
Whether your questions are ones only this person could answer, as opposed to ones the recruiter already covered

How to prepare

Build one view you could defend for two minutes using only public information: what the funnel probably looks like, which metric likely drives decisions, and where that metric could mislead. Being wrong for a stated reason survives this round; having no view does not
Write down the largest piece of work you have owned from question to decision, who else touched it, and what you decided alone, then check that it reads at the level you are interviewing for
Prepare one thing you would want changed if you joined and phrase it as a question rather than a verdict, so it opens a conversation instead of closing one

Research Talk Presentation

Rounds outside the standard loop often open with something deliberately under-specified: a loose business problem, an open question about a product area, a dataset described in one sentence. The common failure is surveying, listing six plausible approaches and committing to none of them. The thing that separates a strong answer is scoping out loud. State what you are treating as the goal, name the metric you would move, say what you are choosing not to do and why, then take one path through to an actual answer. An interviewer can follow you down a narrow path. Nobody can grade a menu.

What to demonstrate

Whether you turn an ambiguous prompt into a stated question with a measurable outcome before doing any work
The judgement visible in what you cut, and whether you say why you cut it rather than silently dropping it
Whether you land on a concrete recommendation with its caveat attached, rather than an unranked set of options

How to prepare

Take three vague prompts, such as 'is this feature working', 'why did retention drop', and 'should we expand into a new segment'. For each, write one sentence of goal, one primary metric with its window, and two things you are explicitly not doing.
Practise giving the recommendation first and the reasoning second, in five minutes. Loosely defined rounds are usually time-boxed, and an answer that arrives last often does not arrive.
Keep a running assumption list as you talk, on paper or in the shared doc, so the interviewer can challenge one assumption instead of your whole answer.

Where candidates lose points

Watching an experiment daily and stopping when it crosses significance

A fixed-sample test controls type I error at one pre-declared look. Checking repeatedly and stopping at the first p < 0.05 inflates the false positive rate to roughly 0.15 to 0.20 for ten looks, and it rises further with more frequent checks, because the p-value takes a random walk that will eventually dip below the threshold under the null. The usual defences are a fixed horizon declared before launch, group-sequential boundaries such as O'Brien-Fleming that spend alpha across a planned number of looks, or always-valid confidence sequences that are correct under continuous monitoring. Compounding it, the effect size reported conditional on having crossed the threshold is biased away from zero, and the bias is larger the lower the power was, so an underpowered test that 'won' typically overstates the lift it found.

Reading a pooled rate that moved because the mix moved, not because any behaviour changed

A pooled conversion rate is a weighted average, and a shift in the weights can move it in the opposite direction to every one of its parts. A paid campaign that brings low-converting traffic drops overall signup conversion even if desktop, mobile web and app conversion each rose that week, which is Simpson's paradox and it is the single most common cause of an inexplicable dashboard move. The discipline is to decompose before explaining: recompute the rate holding last period's segment weights fixed, and compare that counterfactual to the actual, so the mix effect and the rate effect are separated numerically rather than argued about. Segment on the dimensions that actually reweight, which in this domain are almost always device_type, referrer_channel, country and new versus returning.

Dropping rows with missing values without naming the mechanism

Say whether the values are missing at random, missing by a known process, or missing in a way that depends on the outcome, and handle them accordingly. Deleting incomplete rows silently redefines the population whenever missingness correlates with what you are measuring.

Never asking what decision the analysis will inform

Open with who makes the decision, what the options are, and by when. The answer determines the precision you need, the segments worth cutting, and whether an observational read suffices or an experiment is required.

Questions & practice

What are the advantages and limitations of the statistical model you chose for your recent project?

Medium · machine learning and modelling

Approach

Pick an evaluation metric that matches the cost of each error type, not a default.
Say how the offline result would be validated online before it is trusted.
Check what information would not exist at prediction time, and exclude it.

Follow-up

How would you choose the decision threshold, and who owns that choice?
Where could label leakage enter this setup?

Split a pooled conversion drop into rate and mix

Medium · mix shift · decomposition · pandas

You have weekly visit-to-signup counts by segment: a DataFrame with week, device_type, referrer_channel, visitors and signups. The pooled rate fell 0.84 percentage points between two consecutive weeks while several individual segments rose. Write a function that, for a caller-supplied list of segment columns, splits the pooled change into a rate effect, a mix effect and an interaction term that sum exactly to the observed change. Return those three scalars plus a per-segment contribution table sorted by absolute contribution, so the largest single driver can be named.

Approach

State the algebra before coding: the pooled rate is r = sum over segments of w_s * r_s, with w_s the segment's share of the denominator. Then r1 - r0 decomposes exactly into sum(w_s0 * (r_s1 - r_s0)) for rate, sum((w_s1 - w_s0) * r_s0) for mix, and sum((w_s1 - w_s0) * (r_s1 - r_s0)) for interaction. The identity is per-segment, so it holds for any numbers you put in the four slots.
Pivot both weeks onto a common segment index with an outer join so a segment that appeared or vanished is kept rather than dropped, then decide what rate to give a segment with no visitors in one of the weeks, and document the choice. The identity stays exact either way because the missing week's weight is 0, but the attribution does not. Filling the missing rate with 0 sends an appearing segment's entire w_s1 * r_s1 into the interaction term, since w_s0 = 0 makes both the rate term and the mix term (w_s1 - w_s0) * r_s0 identically zero; a vanishing segment then splits as -w_s0 * r_s0 in rate, -w_s0 * r_s0 in mix and +w_s0 * r_s0 in interaction.
The convention used below instead imputes the missing week's rate as that week's pooled rate. A vanishing segment then lands wholly in mix at -w_s0 * r_s0, with rate and interaction cancelling; an appearing segment puts w_s1 * r_pooled0 in mix (volume arriving at the average rate) and only w_s1 * (r_s1 - r_pooled0) in interaction (its rate differing from that average). Impute by which week the segment is missing from, never by argument order, or the swap identities below stop holding.
Guard the division where visitors is 0 so no NaN enters the vectors, because a single NaN poisons every sum. A segment with zero visitors in both weeks contributes exactly 0 and can be dropped; a segment missing from only one week does not contribute 0, and where its contribution lands is settled by the convention above, not by the guard.
Compute the three components as vectors over segments, then sum. Keep the vectors, because the per-segment contribution table is what turns the decomposition into an explanation.
Assert that the three components sum to the observed pooled change within floating-point tolerance. This identity is exact, so a mismatch means an implementation bug, not a modelling judgement.

Follow-up

The mix effect accounts for 0.71 of the 0.84 point drop, driven by paid_social volume. What is your recommendation, and what would change it?
Why is a two-way split into a counterfactual rate and a residual also exact, and when would you prefer it to the three-way version?
Segmenting on device and channel leaves a large interaction term. What does that tell you about the choice of segments?

Permutation test for a difference in conversion rates

Medium · permutation test · resampling · inference

Write a two-sided permutation test from scratch for a difference in conversion rates, using no scipy hypothesis function. Input: a DataFrame with unit_id, variant in {control, treatment} and converted in {0,1}, one row per randomisation unit. Compute the observed difference in proportions, then build the null distribution by reshuffling the variant labels while holding each arm's size fixed. Report the p-value as (1 + the count of permuted statistics at least as extreme in absolute value) / (B + 1) with B at least 10,000, and return the permutation distribution.

Approach

Name the null being tested: the sharp null that each unit's outcome is the same under either label. That is what licenses permuting labels, and it is stronger than the null of equal means, which matters when someone asks whether the test is valid under unequal variances.
Extract converted to a single numpy array of 0s and 1s and record n_treatment. Every permutation is then just a reshuffle of one array, and the treatment mean is the mean of the first n_treatment entries of the shuffled array.
Vectorise the B permutations with rng.permuted on a tiled 2-D array, or with argsort of a (B, n) random matrix. A Python loop calling np.random.shuffle B times is correct but roughly an order of magnitude slower and often runs past the time limit.
Use the +1 correction in both numerator and denominator. Without it a p-value of exactly 0 is reportable, which is false: the observed labelling is itself one of the permutations, so the smallest attainable p-value is 1/(B+1).
Compare the resulting p-value against a two-proportion z-test as a sanity check. At these sample sizes they should agree closely; a large divergence means the statistic or the shuffle is wrong, not that the permutation test found something subtle.

Worked solution (25 min)

y = df['converted'].to_numpy(); n_t = (df['variant'] == 'treatment').sum(); obs = y[treat_mask].mean() - y[~treat_mask].mean().
Build the null: for B draws, shuffle y and take the mean of the first n_t entries minus the mean of the rest.
p = (1 + (np.abs(null) >= abs(obs) - 1e-12).sum()) / (B + 1), with the small tolerance so exact ties count as at least as extreme.
Return obs, p and the null array; plot or describe the null to confirm it is centred at 0.

Expected result: The observed difference, a p-value in [1/(B+1), 1], and a null distribution whose mean is approximately 0 and whose standard deviation approximately matches the analytic pooled standard error sqrt(p_pool*(1-p_pool)*(1/n1 + 1/n2)).

Verify it yourself

The null distribution's mean is within a few Monte Carlo standard errors of 0; if it is centred on the observed difference, the code bootstrapped instead of permuted.
The null's standard deviation agrees with the analytic pooled standard error to within a couple of percent.
The p-value agrees with a hand-computed two-proportion z-test p-value to within about 0.01 at these sample sizes.
Setting converted identical in both arms by construction yields a p-value near 1, and a planted large effect yields the floor of 1/(B+1).

Follow-up

The arms are 200 and 20,000 units. Does the permutation test stay valid, and what happens to its resolution at B = 10,000?
Give a 95 percent confidence interval for the difference. Can you get it from this permutation distribution, and if not, what would you run instead?
The randomisation unit is user_id but the outcome is per session. What breaks, and what is the fix?

Paying accounts with no active seat in 28 days

Medium · anti-join · null-semantics · retention-risk

dim_account holds account_id, account_type, lifecycle_status, seats_licensed. fct_event holds account_id, user_id, occurred_at_utc, is_core_action, and its account_id is NULL for every signed-out and pre-signup event. Find accounts with lifecycle_status = 'active' and account_type <> 'internal' that had no distinct user complete a core action in the trailing 28 days. Return account_id, seats_licensed and days since that account's most recent core action, with NULL where the account has never emitted one. Order by seats_licensed descending.

Approach

Build the recent-activity set first: fct_event rows with is_core_action = TRUE, occurred_at_utc >= now() - interval '28 days', and an explicit account_id IS NOT NULL. Making the NULL exclusion explicit in the CTE is what lets you reason about the anti-join afterwards.
Express the exclusion with NOT EXISTS (correlated on account_id) or a LEFT JOIN with an IS NULL guard. Do not use NOT IN against this column: it is nullable, and SQL's three-valued logic turns the whole predicate UNKNOWN, returning zero rows.
Compute last-seen separately as MAX(occurred_at_utc) per account over all history, LEFT JOINed on, so an account that has never emitted a core action (NULL) is distinguishable from one that went quiet six weeks ago. Those two cases have different causes and different owners.
Rank by seats_licensed, or better by the account's current mrr_cents_constant_fx if you are allowed the subscription table, because a silent fifty-seat account is a renewal conversation and a silent one-seat account is noise.
Before shipping, check whether the never-seen group is a cluster by signup date or surface. A block of accounts with no events at all is usually an instrumentation gap, not a set of customers who stopped using the product.

Worked solution (25 min)

Count NULL account_id rows in fct_event over the window so you know the trap is live in this data rather than hypothetical.
Write the active-account spine and the 28-day activity CTE.
Write the anti-join with NOT EXISTS, then deliberately run the NOT IN version and record that it returns zero rows.
Add the all-time MAX(occurred_at_utc) LEFT JOIN and derive days_since as a date difference.
Split the output into 'quiet' and 'never seen' and eyeball the never-seen group for a shared signup window or surface.

Expected result: One row per silent active account with seats_licensed and days_since_last_core_action, ordered by seats_licensed descending. Accounts that never emitted a core action show NULL and are reported as a separate group rather than as the worst churn risks.

Verify it yourself

Silent accounts plus accounts with at least one active user equals the total count of active non-internal accounts.
The NOT IN variant returns zero rows, which is the demonstration that a NULL is present.
No account_id appears twice in the output.
Every days_since_last_core_action is either NULL or greater than 28.

Follow-up

How would you distinguish a genuinely idle account from one whose events lost their account_id after an instrumentation change?
Would you count on fct_event.account_id or resolve user_id through dim_user instead, and what does each choice miss?
Licensed-seat utilisation is the continuous version of this. How would you turn this boolean into that ratio?

Pair flow starts to completions within a thirty-minute bound

Medium · event-streams · conditional-aggregation · flow-funnel

fct_event holds event_id, flow_id, flow_instance_id, event_name, occurred_at_utc, surface, app_version. Using only rows where event_name is 'flow_started', 'flow_completed' or 'error_shown', compute the daily core-flow completion rate by surface and app_version. Numerator: distinct flow_instance_id whose flow_completed occurs within 30 minutes of its flow_started with no error_shown for the same instance in between. Denominator: distinct flow_instance_id with a flow_started that day. Report rows with a NULL flow_instance_id as a separate coverage count, not inside either side.

Approach

Collapse the stream to one row per flow_instance_id using conditional aggregation: MIN(occurred_at_utc) FILTER (WHERE event_name = 'flow_started') AS started, MIN(...) FILTER (WHERE event_name = 'flow_completed') AS completed, MIN(...) FILTER (WHERE event_name = 'error_shown') AS first_error. This makes the 'first' semantics explicit and avoids a self-join entirely.
Apply the predicates on that single row: completed IS NOT NULL AND completed <= started + interval '30 minutes' AND (first_error IS NULL OR first_error > completed). Note the last clause encodes 'in between' literally, so an error surfaced after a successful completion does not disqualify the attempt.
Bucket by started::date, surface and app_version. Splitting by app_version is not decoration: a completion-rate regression is nearly always confined to one client build, and a pooled daily rate hides it behind the installed base.
Count NULL flow_instance_id rows as a separate coverage figure. They cannot be attributed to an attempt at all, so they belong in neither numerator nor denominator, and their share tells you how much of the rate is unmeasurable.
For any roll-up to week or to all surfaces, re-sum the numerator and denominator rather than averaging the daily rates.

Follow-up

occurred_at_utc is client-supplied. What do you do with an instance whose completion timestamp precedes its start?
flow_instance_id is missing on 4 percent of starts for one app_version. What can and cannot you conclude about that build?
An instance starts at 23:55 and completes at 00:04. Which day owns it, and what does the alternative do to the daily series?

Can you explain a time you had to pivot your analytical approach due to data quality issues?

Medium

Approach

Say what you would check first and why it is the highest-information step.
State your assumptions explicitly before working the problem.
Clarify what is being asked and what a complete answer would contain.

Follow-up

How would you know your answer was wrong?
What assumption would you test first?

How do you ensure the reproducibility of your research and data cleaning pipelines?

Medium

Approach

Say what you would check first and why it is the highest-information step.
Work from the decision backwards to the evidence you would need.
Clarify what is being asked and what a complete answer would contain.

Follow-up

What assumption would you test first?
How would you know your answer was wrong?

Size an activation test before anyone writes code

Easy · power · minimum detectable effect · proportions

A team wants to test a new onboarding checklist against the seven-day activation rate: users with is_core_action = TRUE events on at least two distinct UTC dates inside the first seven days, counted from dim_user.account_created_at_utc with is_internal = FALSE. Baseline is 22%. Weekly non-internal signups are 9,000, split evenly between two arms. State the minimum detectable effect after two weeks of enrolment, the enrolment needed to detect a 1.5 percentage point absolute lift, and the earliest date a readout would be honest.

Approach

Use the two-proportion sizing shortcut n = 16 p(1-p) / d^2 per arm, where d is the absolute lift. The 16 is 2(1.96 + 0.84)^2 = 15.7 rounded, i.e. two-sided alpha 0.05, 80% power, equal arms.
Invert it for the MDE at fixed n: d = sqrt(16 p(1-p) / n). Two weeks gives 9,000 per arm, so d = sqrt(2.746 / 9000) = 0.0175, which is 1.75 percentage points absolute or 7.9% relative on a 22% base.
Run it forward for d = 0.015: n = 2.746 / 0.000225 = 12,202 per arm, 24,404 total, about 2.7 weeks of enrolment. Round up to three whole weeks so the enrolment window contains no partial week, since signups are not uniform across weekdays.
Add the metric's own lag rather than reporting the enrolment end date. Activation is unobservable until seven days after the last enrolled signup, and the definition publishes on an eight-day lag, so the readout lands 29 days after launch.
Close by testing whether the ask is realistic. If the team's honest prior is a 0.5pp lift, the requirement is about 110,000 per arm and roughly 24 weeks of enrolment, and saying so before launch is the deliverable.

Worked solution (20 min)

Compute p(1-p) = 0.22 x 0.78 = 0.1716 and 16 x 0.1716 = 2.746.
MDE at two weeks: n = 4,500 per arm per week x 2 = 9,000; d = sqrt(2.746 / 9000) = 0.0175.
Sample for d = 0.015: n = 2.746 / 0.000225 = 12,202 per arm, which is 2.71 weeks of enrolment, so enrol three whole weeks.
Readout date = 21 days of enrolment + 8 days of follow-up and publication lag = 29 days from launch.
State the boundary of what this quarter can answer: below roughly 0.7pp the requirement passes 56,000 per arm and more than a full quarter of enrolment.

Expected result: MDE after two weeks is 1.75 percentage points absolute, 7.9% relative. Detecting 1.5pp needs 12,202 users per arm, so three weeks of enrolment and a readout 29 days after launch. Detecting 0.5pp needs about 110,000 per arm, roughly 24 weeks, which is the answer the team needs to hear before the code is written.

Verify it yourself

MDE must fall as 1 / sqrt(n). Doubling enrolment from two weeks to four should move 1.75pp to 1.24pp, not to 0.88pp.
Substituting d = 0.0175 back into 16 p(1-p) / d^2 must return about 9,000 per arm.
An exact two-proportion calculator at alpha 0.05 two-sided, power 0.80, p1 = 0.22, p2 = 0.235 returns about 12,260 per arm, within half a percent of the shortcut.

Follow-up

The team also wants trial-to-paid read from the same test. What does a second primary metric do to your alpha, and what would you actually do about it?
Signups are heavier on weekdays. What goes wrong if enrolment runs 17 days instead of 14?
The activation definition uses a two-distinct-days threshold. If that were loosened to one day, what happens to the baseline rate and to the sample you need?

Attribute a flow-completion drop to one client build

Medium · release-regression · instrumentation · staged-rollout

Core-flow completion rate on surface = 'ios', defined as distinct flow_instance_id reaching 'flow_completed' within 30 minutes of 'flow_started' with no 'error_shown' on the same id in between, fell from 78% to 71% over four days. A new iOS build began a staged rollout on day one. Using fct_event columns flow_id, flow_instance_id, app_version, event_name, user_id and occurred_at_utc, produce the completion rate per build per day, size the loss in absolute completions, and say whether the fix is a rollback. Treat the possibility that the instrumentation changed rather than the flow.

Approach

Cut the rate by app_version and day, each build against its own denominator. A pooled series during a staged rollout is a weighted average whose weights move daily, so it declines in proportion to the rollout share even when the old build is perfectly flat; confirming that proportionality is itself the evidence the regression is build-specific rather than environmental.
Test the denominator before believing the rate. Compute flow_started events per distinct user_id on each build: if the new build re-mints flow_instance_id on retry, or fails to carry the id from start to completion, the denominator inflates and the numerator falls with nothing changing for the user.
Normalise to a user-level outcome that is immune to the id question, namely completions per distinct user_id per day on each build. This is the number that says whether anyone actually failed to finish.
Check the error path: pull error_shown counts and their properties for flow_instance_id values on the new build. A genuine regression produces errors; an instrumentation break produces missing completions with no corresponding error volume, and the two prescribe different fixes.
Size the real loss as the per-user completion gap multiplied by daily users on the new build, and give the rollback recommendation conditional on the error evidence rather than on the rate.

Follow-up

The rollout is at 45% and product wants to go to 100% tomorrow. What do you say, and what would you need by when?
If the flow_instance_id is genuinely being re-minted, what is the correct historical treatment of the four affected days?
How would you have caught this on day one instead of day four?

Suggested practice checklist

For a candidate whose interviews will centre on A/B testing, metric movement and causal claims. Design comes before arithmetic, arithmetic before analysis, and the week ends by rehearsing the readout rather than the derivation.

Day 1 — Design one test end to end on paper

Take a single feature change and write the full design: randomization unit, the exact point of exposure, the primary metric with its grain, guardrails, allocation, planned duration, and the decision rule committed before any data exists.
Write why the randomization unit must sit at or above the level where treatment can spill over, and give one case where user-level randomization is still contaminated (shared accounts or devices, or two participants in the same marketplace).
State in advance what you will do if the primary metric is flat while a secondary metric is significant.

Deliverable: A one-page test design with a decision rule written before launch.

Day 2 — Power arithmetic until it is automatic

Compute required sample size per arm for a binary metric with the normal approximation, n is approximately 2 times (z for alpha/2 plus z for power) squared times p(1 minus p) divided by delta squared, for baselines of 2, 10 and 40 percent at a 5 percent relative lift, and note that for a fixed relative lift the requirement falls as the baseline rises because delta grows proportionally with p.
Redo the calculation for a continuous metric using variance in place of p(1 minus p), and show why a heavy-tailed quantity such as revenue per user needs either far more traffic or a capped version with a stated cap.
Convert one of the results into weeks given a weekly eligible traffic figure, then list the two honest ways to shorten it (accept a larger detectable effect, or reduce variance) and write why quietly lowering the power target is a decision to miss more real wins, not a speedup.

Deliverable: A small script or sheet that maps baseline, minimum detectable effect, alpha and power to sample size and weeks, cross-checked against a published calculator.

Day 3 — Variance and the unit-of-analysis problem

Take a ratio metric whose denominator is not the randomization unit (clicks per session, randomized by user) and compute the standard error twice, once naively at session level and once by the delta method or a user-level bootstrap, then record how much the naive version understates it.
Implement CUPED on simulated data: choose a pre-period covariate X measured before assignment, estimate theta as Cov(Y, X) divided by Var(X), and analyse Y minus theta times (X minus its mean) in place of Y. Confirm the variance of the adjusted outcome equals the raw variance multiplied by one minus the squared correlation between Y and X, so a correlation of 0.45 removes about 20 percent of the variance and not 80.
Now run that simulation a few hundred times and confirm the adjusted effect estimate is unbiased for the same effect rather than numerically identical to the raw one. Within any single run the two differ, sometimes by a large fraction of the true effect, because the two arms' pre-period covariate means never coincide exactly in a finite sample; they agree in expectation, which is the property that matters and the one to state out loud.

Deliverable: A notebook showing the adjusted estimator with a measurably smaller variance than the raw one, plus a repeated-simulation table showing the two estimators agreeing on average while differing run by run.

Day 4 — Validity threats you can actually test for

Run a sample ratio mismatch check as a chi-square goodness-of-fit test against the intended allocation, and write the three causes you would chase first (assignment logged before exposure, an arm-specific redirect or load failure, bot filtering applied asymmetrically).
Simulate peeking: generate A/A data, test daily at alpha 0.05 across 14 looks, record the inflated false positive rate, then apply an alpha-spending boundary or commit to a fixed horizon and confirm the rate returns to nominal.
Write how you would separate a novelty effect from a durable lift using the treatment effect plotted against days since first exposure, and what shape would change your recommendation.

Deliverable: One table showing the peeking false positive rate before and after correction, plus a written SRM triage list.

Day 5 — When randomization is not available

Write the identifying assumption for difference-in-differences (parallel trends in the absence of treatment), then plot pre-period trends for two candidate control groups and justify rejecting one of them.
Design a switchback test for a change where user-level randomization would leak across participants, choosing a time-block length against the carryover you expect and saying how you would detect carryover in the data.
List what an interrupted time series or a synthetic control buys you and the one thing neither can rule out: an unobserved shock that coincides with the launch.

Deliverable: A one-page memo recommending a single quasi-experimental design and naming its weakest assumption explicitly.

Day 6 — The readout query

Write the assignment-to-exposure join that returns exactly one row per unit per experiment, and handle units appearing in both arms by excluding and counting them rather than silently keeping one.
Compute the per-arm metric, its variance and the relative lift with a confidence interval in SQL, then reproduce the identical numbers in a notebook as a cross-check.
Add a segment breakdown and write the sentence that keeps it from being p-hacking: segments declared in advance, everything else reported as exploratory and corrected for multiplicity.

Deliverable: A single query that outputs the full readout table, matched to a notebook recomputation.

Day 7 — Present it to someone who will not read the appendix

Give a 10-minute readout of a real or simulated experiment in the order decision, number, uncertainty, caveat.
Have your listener ask "can we ship it" in the case where the primary is flat and a guardrail moved, and answer with a recommendation rather than a request for more data.
Rewrite your opening line so the recommendation lands before any methodology.

Deliverable: A one-page readout whose first line is the recommendation.

Ownership when the result is inconvenient

Sometimes the honest read is that the initiative did not work, and the person who commissioned the analysis was hoping otherwise. Interviewers want to know whether you softened it. Prepare the case where you delivered an unwelcome result, how you presented the uncertainty without hiding behind it, and what the team did next.

Describe a situation where you had to manage multiple competing deadlines.

Medium · behavioural and stakeholder questions

Approach

Pick a story where you drove the decision, not one where you observed it.
Quantify the outcome, including what you would not claim credit for.
Close with what you would do differently, concretely.

Follow-up

What would you do differently if you ran that project again?
How did you know the outcome was caused by your change?

Tell me about a time you had to explain a complex technical finding to a non-technical stakeholder or client.

Medium · behavioural and stakeholder questions

Approach

Pick a story where you drove the decision, not one where you observed it.
Name the disagreement or constraint, and how you resolved it with evidence.
Close with what you would do differently, concretely.

Follow-up

How did you know the outcome was caused by your change?
What would you do differently if you ran that project again?

Describe your experience working with Medicare or Medicaid claims data.

Medium · behavioural and stakeholder questions

Approach

State the situation in two sentences and spend the rest on your reasoning.
Close with what you would do differently, concretely.
Quantify the outcome, including what you would not claim credit for.

Follow-up

How did you know the outcome was caused by your change?
What did you decide not to do, and why?