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Johns Hopkins Applied Physics Laboratory Data Scientist Interview Questions & Guide 2026

Data scientist prep for Johns Hopkins Applied Physics Laboratory candidates: drill A/B design, power and minimum detectable effect on original exercises.

The 60-second brief

A Data Scientist at the Johns Hopkins Applied Physics Laboratory (APL) occupies a unique and highly impactful role at the intersection of advanced research and national security. Unlike typical corporate data science roles focused on commercial metrics, data scientists at APL solve complex, high-stakes problems for government sponsors, including the Department of Defense, NASA, and federal health agencies. You will work on diverse applications ranging from satellite telemetry analysis and predictive healthcare modeling to custom machine learning pipelines for autonomous systems.

Nearly every loop contains a round whose deliverable is a recommendation to someone non-technical. Practise stating a conclusion, the confidence attached to it, and the cost of being wrong in each direction, because that triple is the artifact being graded.

Focus areas

  • Size an experiment before anyone launches it
  • Pick a randomisation unit that respects interference
  • Turn a vague request into a measurable question

Overview

The impact of your work at APL is measured by its contribution to critical national challenges and scientific discovery. You will be tasked with extracting actionable insights from massive, often unstructured, and highly noisy datasets that represent real-world physical systems. This requires not only deep technical expertise in statistical modeling and machine learning but also a strong collaborative spirit to work alongside aerospace engineers, physicists, and military analysts.

What makes this role exceptionally rewarding is the scale of the infrastructure and the intellectual freedom to innovate. You will have access to high-performance computing (HPC) clusters and state-of-the-art laboratory facilities. APL fosters an environment where academic rigor meets practical execution, making it an ideal place for researchers who want to see their theoretical models deployed in defense of the nation and the advancement of science.

The Johns Hopkins Applied Physics Laboratory interview process

Johns Hopkins Applied Physics Laboratory candidates report 4 rounds · ≈ 3-5 weeks. The stages below are what candidates describe, not a published process.

Recruiter Phone Screen

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

Technical Phone Screen

Most candidates lose this call inside the first two minutes, during the walkthrough of their own background. The account runs chronologically, sits at the level of tools and titles, and never arrives at a decision anyone could have disagreed with. Anchor on a problem instead of a timeline: what the team could not answer, what you did about it, what happened next. Ninety seconds is enough, and stopping on time leaves room for the half of the call that belongs to you. What you ask about how work gets prioritised signals your level more reliably than the walkthrough does.

What to demonstrate

  • Whether your background summary has a shape (problem, decision, consequence) or is a chronological list of tools and employers
  • Whether you can account for gaps, short stints and the reason you are looking, unprompted and without hedging
  • The substance of the questions you ask back, which an experienced screener reads as a level signal

How to prepare

  • Time your opening walkthrough against a clock. If it runs past two minutes, compress the earliest role into a single clause and spend the recovered time on the most recent one
  • Write one honest sentence for every gap or short stint visible on your resume and offer it before being asked about it
  • Prepare questions about how work arrives and gets prioritised: who writes the request, how often priorities change, and what happens to an analysis after it is delivered

Research Presentation

Because the format is not fixed, prepare the reasoning rather than the ritual. Nearly every version of this round draws on the same underlying material: a design you can defend, a metric you can define exactly, an analysis whose assumptions you can state out loud. Only the wrapper changes, whether that is a take-home, a live case, a deep dive on past work, or a rough estimate on a whiteboard. Answers rehearsed to fit one shape stall the moment the shape differs. Practise naming the assumption behind a number, then saying how much the conclusion moves if that assumption is wrong.

What to demonstrate

  • Whether your justification for a method survives the question 'why not the simpler thing', including when the simpler thing would have worked
  • Precision under pressure: what exactly counts as an active user, a conversion or a success, over what window, with what exclusions
  • Whether you carry an argument through to a recommendation instead of stopping at a list of tradeoffs

How to prepare

  • For each project you plan to mention, write the metric definition in one sentence: numerator, denominator, time window, exclusions. Say it out loud once, because vagueness shows up in speech before it shows up on paper.
  • Rehearse the same project at three lengths: two minutes, ten minutes, and a deep dive on one technical decision. Cutting live is harder than it sounds.
  • For your headline result, write down what would have had to be true for it to be wrong, and how you ruled that out.

1-on-1 Interviews

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

Counting on an identity key that changes underneath the metric

visitor_id is per browser and per device, and it resets on cookie clearance, private browsing and platform privacy changes, so the distinct-visitor count drifts upward for reasons unrelated to reach. Any rate with visitors in the denominator therefore decays over time even when behaviour is constant, and any rate with visitors in the numerator inflates. The stitching at signup makes it worse in both directions: a user who signed up on mobile and returns on desktop is two visitors and one user, while a shared device is one visitor and several users. Decide which key each metric is counted on, write it into the definition, and when comparing a period before and after a platform privacy change, expect a level shift in every visitor-keyed metric and do not attribute it to the product.

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.

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.

Reading an observational correlation as a causal effect

Name the confounder you are most worried about and the design that would remove it: an experiment, a difference-in-differences with a checked pre-period trend, an instrument, or a regression discontinuity. When none is available, state which direction the bias likely runs and bound the claim accordingly.

Questions & practice

How did you validate your model's performance, particularly when dealing with limited or noisy experimental data?

Medium · machine learning and modelling

Approach

  1. Frame the prediction: the label, the moment of prediction, and the action it triggers.
  2. Set a baseline first, so any model has something honest to beat.
  3. Say how the offline result would be validated online before it is trusted.

Follow-up

  • What would you monitor after launch to know the model is still valid?
  • How would you choose the decision threshold, and who owns that choice?

Have you ever had to scale a machine learning model to run on resource-constrained edge devices? How did you approach it?

Medium · machine learning and modelling

Approach

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

Follow-up

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

How would you explain the underlying mathematics of your machine learning model to a sponsor who does not have a technical background?

Medium · machine learning and modelling

Approach

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

Follow-up

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

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

  1. 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.
  2. 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.
  3. 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.
  4. 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).
  5. 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)

  1. y = df['converted'].to_numpy(); n_t = (df['variant'] == 'treatment').sum(); obs = y[treat_mask].mean() - y[~treat_mask].mean().
  2. Build the null: for B draws, shuffle y and take the mean of the first n_t entries minus the mean of the rest.
  3. 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.
  4. 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?

What software engineering best practices (such as version control, unit testing, and containerization) do you integrate into your research workflow?

Medium · sql and data manipulation

Approach

  1. Say which table is the grain you start from, and join outward from it.
  2. Check whether any join is one-to-many before aggregating, or the sums inflate.
  3. Compute rates by summing numerator and denominator separately, never by averaging rates.

Follow-up

  • How does the query change if the join becomes one-to-many?
  • How would you verify this result without re-running the same query?

Weekly visit-to-signup conversion split by acquisition channel

Easy · funnel · conversion · aggregation

From fct_session (session_id, visitor_id, started_at_utc, referrer_channel, is_bot_flagged, consent_state) and fct_event (visitor_id, occurred_at_utc, event_name), compute visit-to-signup conversion for one ISO week, split by channel. session_id is the unique key of fct_session. Denominator: distinct visitor_id with a session starting in the week, is_bot_flagged = FALSE and consent_state <> 'denied'. Numerator: those visitors with a 'signup_completed' event in the same week. Label each visitor with the referrer_channel of their first session in the window. Return channel, visitors, signups and rate, plus one all-channel total row.

Approach

  1. Build a visitor spine that is one row per visitor: filter sessions to the week, drop is_bot_flagged and consent_state = 'denied', then take the first session per visitor with ROW_NUMBER() OVER (PARTITION BY visitor_id ORDER BY started_at_utc, session_id) = 1 to carry the channel label. Collapsing to one row here is what makes the channel buckets mutually exclusive and the totals additive.
  2. session_id is the unique key, so that ordering is total and the label is reproducible. If the table carried no unique key you would have to write an explicit tie rule instead, because two sessions on different channels at the identical timestamp would otherwise label the visitor differently between runs.
  3. Attach the outcome as a semi-join (EXISTS on a signup_completed event for that visitor inside the same week) rather than a join to the event table, so a visitor who fires the event twice does not count twice and inflate the numerator past the denominator.
  4. Aggregate with COUNT() as visitors and COUNT() FILTER (WHERE signed_up) as signups, and compute the rate as signups::numeric / NULLIF(visitors, 0) so an empty channel returns NULL rather than a division error.
  5. Produce the total with GROUP BY GROUPING SETS ((channel), ()), which re-sums numerator and denominator for the total row. Averaging the channel rates gives a different and wrong number whenever channel volumes differ, which they always do.
  6. Verify the spine before trusting the output: COUNT(*) must equal COUNT(DISTINCT visitor_id), and the per-channel visitor counts must sum to the total row.

Worked solution (20 min)

  1. Write the filtered session CTE and check its row count against an unfiltered count, so you know how much volume the bot and consent filters removed.
  2. Add the ROW_NUMBER first-session pick and assert one row per visitor.
  3. Add the EXISTS outcome flag and aggregate with FILTER.
  4. Add GROUPING SETS for the total and format the rate to four decimal places.
  5. Spot-check one channel by hand: pull its visitor list, count signups directly, compare.

Expected result: One row per referrer_channel plus a total row, with visitors, signups and a decimal rate. Channels with zero signups appear with rate 0, not missing. The total rate lies strictly between the minimum and maximum channel rate unless one channel holds all the volume.

Verify it yourself

  • Per-channel visitor counts sum exactly to the total row's visitor count.
  • COUNT(*) equals COUNT(DISTINCT visitor_id) on the spine CTE.
  • Replacing the EXISTS with a plain inner join changes the signup count only if duplicate signup_completed events exist; if it does change, say by how much.
  • Every rate is between 0 and 1.
  • Re-running the first-session pick with session_id removed from the ORDER BY returns the same labels; if it does not, visitors hold same-timestamp sessions on different channels and the tie rule is doing real work.

Follow-up

  • The denominator is distinct visitors. If a browser release shortens cookie lifetime, what happens to this rate, and how would you tell that apart from a genuine drop?
  • A visitor's first session is direct and their signup session is paid search. Your label says direct. When is that the wrong answer for the decision being made?
  • How do you roll four weeks into a month, and why is averaging the four weekly rates wrong?

Describe a situation where you had to manage a heavy workload across multiple projects. How did you prioritize your tasks?

Medium · product sense and metrics

Approach

  1. Fix the population and the time window before naming any metric.
  2. Restate the decision this analysis has to support, and who acts on the answer.
  3. Decompose the metric into the rates that drive it, and say which one you would check first.

Follow-up

  • What would you do if the primary metric and the guardrail moved in opposite directions?
  • Which segment would you cut first, and what would that rule out?

How do you optimize your data pipelines when processing large-scale, multi-dimensional datasets?

Medium · product sense and metrics

Approach

  1. Fix the population and the time window before naming any metric.
  2. Name one primary metric, then the guardrail that stops it being gamed.
  3. Restate the decision this analysis has to support, and who acts on the answer.

Follow-up

  • How would you detect that the metric is being gamed rather than genuinely improving?
  • Which segment would you cut first, and what would that rule out?

Walk us through your graduate research or a major technical project. Why did you choose this specific modeling approach over alternatives?

Medium

Approach

  1. Clarify what is being asked and what a complete answer would contain.
  2. State your assumptions explicitly before working the problem.
  3. Work from the decision backwards to the evidence you would need.

Follow-up

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

Halve the runtime of a flat test with pre-period data

Medium · cuped · variance reduction · stratification

A test on 28-day core actions per user is powered for six weeks and the team will not wait. You have fct_event (user_id, occurred_at_utc, is_core_action) covering the period before each unit's first_exposed_at_utc in fct_experiment_exposure, and the pre-period count correlates with the in-experiment count at r = 0.6. Apply CUPED, state precisely how much runtime it buys, and handle the units with no pre-period because they signed up after the experiment started.

Approach

  1. Define the adjusted outcome: Y_cuped = Y - theta (X - Xbar), with theta = Cov(Y, X) / Var(X) estimated on the pooled sample so theta itself carries no treatment effect. It is unbiased because X is pre-exposure and therefore has equal expectation in both arms.
  2. Quantify the gain exactly: Var(Y_cuped) = Var(Y)(1 - r^2) = Var(Y) x 0.64, so 36% of the variance is removed. Required sample scales with variance, so six weeks becomes 3.8 weeks, and at the original sample the MDE shrinks by sqrt(0.64) = 0.8.
  3. State the precondition that actually bites: X must be measured strictly before first_exposed_at_utc, not before assigned_at_utc and not before the calendar start of the experiment. Any post-exposure information in the covariate lets the treatment effect leak in and biases the estimate rather than merely failing to help.
  4. Handle missing pre-periods as a stratum, never by dropping rows. Dropping changes the population; setting X to the pooled mean leaves those units' adjustment at zero, which is unbiased but buys them no reduction, so report the covered share and expect the blended reduction to fall short of 36%.
  5. Note that stratification is the same mechanism with a categorical covariate. Post-stratifying on device_type and referrer_channel removes the variance those stratum means explain, and it composes with CUPED provided the strata are also fixed before exposure.

Worked solution (30 min)

  1. Build the covariate: for each unit_id in fct_experiment_exposure, count fct_event rows with is_core_action = TRUE and occurred_at_utc in [first_exposed_at_utc - 28 days, first_exposed_at_utc).
  2. Estimate theta on the pooled sample as Cov(Y, X) / Var(X), and confirm Xbar is statistically indistinguishable between arms before using it.
  3. Form Y_cuped = Y - theta (X - Xbar) and run exactly the test you would have run on Y.
  4. For units with no pre-period, set X to the pooled mean so their adjustment is zero, and report what share of the sample that is.
  5. Report unadjusted and adjusted estimates side by side, with the interval narrower on the adjusted one.

Expected result: 1 - 0.6^2 = 0.36 of the outcome variance is removed, so the required sample falls to 64% of the original and the six-week plan becomes about 3.8 weeks. At the original sample the MDE shrinks by a factor of 0.8. The blended reduction is smaller in proportion to the share of units with no pre-period, and that share is stated alongside the result.

Verify it yourself

  • Adjusted and unadjusted point estimates should be close. CUPED reduces variance, it does not move the effect, so a large shift means X was imbalanced at baseline and needs investigating rather than celebrating.
  • The realised standard error ratio should be near sqrt(1 - r^2) using the r observed in this experiment, not the historical r.
  • Var(Y_cuped) must be no larger than Var(Y) for the fitted theta. A larger value means theta has the wrong sign or was estimated on the wrong window.

Follow-up

  • Here the covariate is the same metric as the outcome. When would you deliberately pick a different one, and what is the risk if that covariate is itself affected by treatment?
  • The point estimate moves by 0.4 standard errors when CUPED is applied. Is that reassuring or alarming, and what would you check?
  • How does CUPED combine with cluster randomisation on account_id, and at which grain is the covariate built?

A conversion rate that fell in one regulatory region

Medium · consent · identity-keys · denominator · geography

Visit-to-signup conversion fell 1.3 points over six weeks. Signups cut by dim_user.country_code put the fall in one regulatory region where a consent banner shipped in week one, but absolute signups from that region are flat. fct_session carries consent_state, visitor_id, is_bot_flagged and session_date and no country column, so the denominator cannot be cut the same way. Using fct_session and fct_event, decide whether behaviour changed or the denominator did, state what these tables cannot settle, and name the one column that would settle it.

Approach

  1. Name the asymmetry before computing anything. The numerator is user-keyed and therefore cuttable by country; the denominator is visitor-keyed and is not. Dividing a region-filtered numerator by an unfiltered denominator produces a quantity that is not a rate, and presenting it as a regional conversion rate is the first mistake available here.
  2. Attack the denominator on the dimension you do have. Compute distinct visitor_id per week and sessions per distinct visitor_id per week: a consent banner that blocks or shortens the identity cookie raises the distinct-visitor count and lowers sessions per visitor, which depresses any visitor-keyed rate with no behaviour behind it.
  3. Split on consent_state. Sessions with consent_state = 'denied' can enter the denominator but can never be joined forward to a signup, so a rising denied share mechanically drives the pooled rate down by roughly its own share. Report the granted-only rate and the denied share as two separate numbers rather than one blended figure.
  4. Cross-check with measures that do not depend on the visitor key at all: absolute weekly signups, which are given as flat, and signups per session rather than per visitor.
  5. State the limit honestly. Without country on the session or on its entry event, the regional attribution rests on the numerator alone, and the correct request is that one column, not a more elaborate model on top of the data you have.

Follow-up

  • If granted-only conversion is the metric going forward, what selection bias have you accepted, and in which direction does it point?
  • How would you handle the six weeks of already-published history once the new definition is adopted?
  • What is the smallest instrumentation change that restores a cuttable denominator without collecting more personal data than before?

Suggested practice checklist

For someone who can already write the query and train the model but stalls when asked what to measure or whether a change is worth making. Metric definition and case structure come first; the technical work is kept as maintenance rather than the centre of the week.

Day 1 — Metric anatomy

  • For three products you use daily, write one primary metric, two input metrics that plausibly move it, and one guardrail that would catch a cheap way of moving the primary at the cost of the product.
  • For one of them, specify the metric precisely enough that two analysts would return the same number: numerator, denominator, unit of observation, time window, and how returning and deleted accounts are treated.
  • Pick a ratio metric and write what happens to it when the denominator shrinks for reasons unrelated to the numerator, with a concrete example of that happening.

Deliverable: A one-page metric tree for one product, with the primary metric written as an unambiguous spec.

Day 2 — Diagnosing a drop without guessing

  • Take the prompt "weekly active users fell 8 percent week over week" and write the segmentation plan before proposing any cause: platform, region, tenure cohort, acquisition channel, and whether the movement sits in the numerator or in a changed denominator.
  • List the instrumentation failures that manufacture fake drops (a client release that stopped firing an event, a bot filter change, a shifted date boundary or timezone) and write the query that rules out each one.
  • Rehearse stating the boring explanations first, seasonality and day-of-week composition, before reaching for a product cause.

Deliverable: A drop-diagnosis checklist short enough to recite from memory in under a minute.

Day 3 — Should we build it

  • Take a feature idea and write it as a bet: what you believe is true, what would have to be true for it to pay off, the metric that would confirm it, and the effect size that would justify the engineering cost.
  • Size the opportunity top-down and bottom-up, then reconcile the two numbers in writing instead of quoting whichever is friendlier.
  • Write the counter-metric that would make you kill the feature even if it wins on the primary metric.

Deliverable: A one-page product memo ending in a decision rather than a list of considerations.

Day 4 — The places aggregate numbers lie

  • Construct a Simpson's paradox numerically: two segments where the treatment wins within each segment yet loses overall, and identify the shift in segment weights that causes it.
  • Take a heavy right-tailed quantity such as revenue per user and write why the mean is the wrong summary, which percentile you would report instead, and what a moving mean with a stable median tells you.
  • Write your definition of a session for the product from day one, then name two real behaviours it misclassifies.

Deliverable: One page holding a worked Simpson's paradox table and a session definition with its two known failure cases.

Day 5 — Technical maintenance, aimed at metrics

  • Solve four timed SQL prompts that all end in a ratio metric, so the question of grain stays live in every answer.
  • Compute a 95 percent confidence interval for a proportion on a small sample, and state why the normal approximation is unreliable when either np or n(1 minus p) falls below roughly 10, along with which interval you would use instead.
  • Take one metric from your day-one tree, write the query that computes it correctly, then write the query that computes it wrong in the most plausible way and explain how you would notice.

Deliverable: Four solved prompts plus a matched correct and plausible-wrong query for one metric.

Day 6 — Turning engineering work into data science stories

  • Write three project stories as situation, decision, trade-off, outcome, each carrying one number and one thing you got wrong.
  • For the story you will lead with, prepare an answer to "what would you do differently" that names a decision you made, not a constraint you were handed.
  • Practise the sentence that reframes a systems project as a question project: the question the work answered, ahead of the pipeline it shipped.

Deliverable: Three written stories with the lead story delivered aloud and timed under four minutes.

Day 7 — Mock case and gap list

  • Run a 40-minute mock case with someone playing a product manager who pushes back on your metric choice, and record it.
  • Listen back and mark every moment you proposed a solution before the success metric existed.
  • Rewrite those moments as the question you should have asked, and rehearse the first 90 seconds of the case until scoping comes before solving.

Deliverable: A recorded case plus a rewritten opening 90 seconds.

Stories where someone disagreed with you

Have two ready. In one, the data was on your side and you had to move someone who outranked you. In the other, the pushback was correct and you changed position. The second is the harder story and it lands better, because it shows you separate being right from being attached to an answer. Name the person's actual objection.

How do you handle project ambiguity when sponsor requirements change mid-way through a development cycle?

Medium · behavioural and stakeholder questions

Approach

  1. Quantify the outcome, including what you would not claim credit for.
  2. Name the disagreement or constraint, and how you resolved it with evidence.
  3. Pick a story where you drove the decision, not one where you observed it.

Follow-up

  • What did you decide not to do, and why?
  • What would you do differently if you ran that project again?

Describe a time when your research methodology failed. How did you diagnose the issue, and what steps did you take to pivot?

Medium · behavioural and stakeholder questions

Approach

  1. State the situation in two sentences and spend the rest on your reasoning.
  2. Name the disagreement or constraint, and how you resolved it with evidence.
  3. Pick a story where you drove the decision, not one where you observed it.

Follow-up

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

Turn an ambiguous onboarding question into a measurable metric

Easy · scoping · metric definition · stakeholder

Two days before a planning review, a director asks whether onboarding is working. You have dim_user (account_created_at_utc, signup_surface, is_internal), fct_event (is_core_action, flow_id, flow_instance_id, event_name, occurred_at_utc, received_at_utc) and fct_session. No further meeting with the director is possible before you start work. Deliver three clarifying questions you would send in writing, the metric you will compute in the meantime with its numerator, denominator, window and exclusions, and one sentence naming the question you are deliberately not answering.

Approach

  1. Recognise what is being probed: whether you convert a goal into a computable predicate without stalling for requirements or guessing in silence. Listing clarifying questions is the generic answer; shipping a defensible default alongside them is the strong one, because the review is in two days and it will happen with or without you.
  2. Infer the decision behind the request. A question about whether onboarding works, arriving before a planning cycle, usually means whether to staff it next quarter. That points at a rate with visible headroom over several cohorts, not at a descriptive dashboard.
  3. Write the three questions so that each one changes the SQL. Which population, all signups or only self-serve from dim_user.signup_surface. What counts as working, reaching a core action or completing the onboarding flow_id. Against what bar, last quarter's cohorts or a stated target.
  4. Propose the default explicitly: seven-day activation on weekly signup cohorts. Numerator, users with is_core_action = TRUE events on at least two distinct UTC dates inside [account_created_at_utc, account_created_at_utc + 7 days). Denominator, the signup cohort with is_internal = FALSE. Publish with an eight-day lag, and state that the two-distinct-days threshold is a frozen choice rather than a discovery.
  5. Name the exclusion in the same breath as the number. The series shows whether users activate; it does not establish that onboarding caused the level, which needs a staged rollout or an experiment.

Follow-up

  • The director replies that they meant the onboarding flow specifically, not activation. What changes in the query and in the caveats?
  • Your cohort metric needs an eight-day lag and the review is in two days. What do you present, and how do you label it?
  • Two of your three questions come back unanswered. Which one do you refuse to proceed without?