As a Data Scientist at Mathematica, you play a pivotal role in transforming data into actionable insights that guide decision-making and influence public policy. Your work directly impacts a variety of projects aimed at improving outcomes in sectors such as health, education, and social policy. With a strong emphasis on data-driven solutions, you will be involved in high-stakes analyses that not only shape Mathematica's products but also contribute to the broader mission of enhancing societal well-being.
Your contributions as a Data Scientist will be critical in advancing Mathematica's reputation as a leader in data analysis and policy evaluation. You will engage with diverse teams to tackle complex problems, utilizing advanced statistical techniques and machine learning algorithms. This role offers a stimulating environment where you can leverage your skills to solve real-world issues, collaborate with passionate professionals, and see the tangible impact of your work.
Phone Screen
reportedMost 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
Technical Assessment
reportedA handful of shapes account for most of what gets asked in this format: a ranking or deduplication inside groups, a running or rolling total, a period-over-period comparison, and a cohort tracked forward over time. Recognising the shape quickly is most of the speed here; deriving it from scratch while a clock runs is where the time goes. Know that a window function keeps every row while a GROUP BY collapses them, and know which one the question needs. If the exercise is in Python instead of SQL, the same shapes arrive as groupby with transform, shift and merge, and the same grain mistakes are available.
What to demonstrate
- Whether you reach the right construct without a detour, such as ROW_NUMBER over a partition to deduplicate instead of a self-join against a MAX subquery
- Whether you know what your window frame actually is, since adding ORDER BY inside OVER changes the default frame and silently changes a running total
- Whether the thing runs. A near-miss that throws an error scores below a plainer query that returns the right rows.
How to prepare
- Write each of the four shapes once from memory against a small schema and keep the working version somewhere you will reread it: dedupe with ROW_NUMBER, a running total, a month-over-month change with LAG, and a retention table
- Compute one running total twice on data with tied timestamps, once on the default frame and once with ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW, and look at where the two disagree
- If Python is on the table, rebuild the dedupe and the running total with groupby and cumsum, then assert the two implementations return identical rows
Multiple Interviews
reportedAn extra round usually exists because something is still open after the standard loop: a skill the earlier interviews did not sample, a level decision, or two interviewers who disagreed. It is rarely a rerun of what you already did well. Ask the recruiter who you are meeting, what function they sit in, and how long the session runs. That is an ordinary scheduling question, and the answer changes what you should prepare. What separates a strong candidate here is treating the round as a fresh evaluation with its own bar, rather than assuming earlier performance carries you through or sinks you.
What to demonstrate
- Whether you can answer well on ground the earlier rounds did not cover, without leaning on what you already said to someone else
- Consistency of the facts in your stories: the same sample size, timeframe, team size and scope of your own role as in earlier conversations
- How you handle an unfamiliar format live, including whether you ask what kind of answer is wanted before producing one
How to prepare
- Ask the recruiter for the interviewer's function, the length, and whether to expect a coding surface, a discussion, or a presentation. Preparing for a 30 minute conversation with a partner team is not the same work as preparing for a 60 minute technical block.
- Write out what each earlier round actually covered, then list the two or three areas nobody probed. That gap is the most likely subject of the extra round.
- Re-read the numbers in the project stories you have already told, so a second telling does not quietly contradict the first.
PracHub editorial advice for the preparation topics above.
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.
Comparing cohort retention curves of different maturities, or building the curve from users who are still present
A cohort four weeks old has no week-8 value, so an average taken across cohorts silently drops young cohorts from the later columns and keeps them in the earlier ones. The curve then bends upward at the tail, and the reading that 'retention is improving over time' is an artefact of which cohorts survived to be measured. The same error appears in the denominator when retention is computed over users active in the current period rather than over the full original cohort, which conditions on survival and guarantees a flattering number. The fix is a triangle: fix the cohort at signup, bound every window on both sides, and only compare cells where every cohort has had the full elapsed time, publishing the rest as blank rather than as a partial average.
Treating a non-significant result as proof of no effect
Say whether the confidence interval excludes the effect sizes you would have cared about. If it does not, the honest reading is that the test was underpowered, so report the minimum detectable effect the design could have found and what sample size would resolve it.
Explaining an aggregate move without decomposing the mix shift
Split the change in the aggregate into within-segment movement and movement in segment weights before you explain it. Every segment's rate can fall while the overall rate rises, purely because volume shifted toward segments that already had higher rates.
Choose a category, try a prompt, then open its approach, worked solution or follow-up when you need it.
What metrics do you use to evaluate the performance of a model?
What metrics do you use to evaluate the performance of a model?
Approach
- Say how the offline result would be validated online before it is trusted.
- Frame the prediction: the label, the moment of prediction, and the action it triggers.
- 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?
Implement seven-day activation from its written definition
Implement the seven-day activation rate. Inputs: dim_user with user_id, account_created_at_utc and is_internal; fct_event with user_id, occurred_at_utc and is_core_action. A user activates when core-action events carrying a non-NULL user_id fall on at least two distinct UTC dates inside [account_created_at_utc, account_created_at_utc + 7 days). The denominator is every non-internal user whose account_created_at_utc lands in the cohort week, including users with no events at all. Return one row per cohort week with numerator, denominator and rate, publishing only weeks whose last signup is at least eight days old.
Approach
- Build the denominator first, from dim_user alone, filtered on is_internal = False. Deriving it from the join is the standard way to lose every user who never fired an event, which is exactly the population the metric is about.
- Join events to users on user_id with a left join from the user side, then apply the window as a half-open interval: occurred_at >= created AND occurred_at < created + 7 days. The right bound is exclusive, so an event at exactly created + 7 days does not count.
- Count distinct UTC dates per user, not distinct events. Floor occurred_at_utc to date before the nunique, and do it in UTC rather than local time so the threshold does not move with the user's country.
- Apply the >= 2 threshold, aggregate to cohort week, and compute the rate by re-summing numerator and denominator per week rather than averaging any per-user or per-day rate. Fix the week anchor explicitly: cohort_week is the Monday of the signup week in UTC, which is what Postgres DATE_TRUNC('week') returns and what any SQL version of this metric will produce. In pandas, subtract dt.weekday days from the floored timestamp. If you reach for periods instead, the anchor that matches is to_period('W') (equivalently 'W-SUN'), whose weeks end Sunday and therefore start Monday; to_period('W-MON') labels weeks that end on Monday, so it runs Tuesday through Monday and its start_time is a Tuesday. Mixing the two shifts every cohort label by one day and silently moves Mondays into the previous week.
- Suppress immature weeks: drop any cohort week whose maximum account_created_at_utc is within 8 days of the data cut, and return them as absent rather than as a partial number.
Follow-up
- The threshold is 2 distinct days. What changes in the reported history if someone moves it to 3, and how would you publish that change?
- Invited seats and SSO-provisioned users have no pre-signup session. Should they be in this denominator at all, and what does including them do to the rate for sales-assisted accounts?
- How would you produce the same metric at account grain, and which of the two would you put on the dashboard?
Sessionise an event stream with gap and midnight rules
Sessionise a raw event stream. Input: a DataFrame with visitor_id, user_id (often NULL), occurred_at_utc and event_name, unsorted, up to 5 million rows. A session breaks when the gap from that visitor's previous event exceeds 30 minutes, and is force-closed at UTC midnight so no session spans two calendar dates. A gap of exactly 30 minutes does not break. Emit one row per session with session_id, visitor_id, the user_id as of the last event in the session, started_at_utc, ended_at_utc, session_date, duration_seconds and event_count. Vectorise; do not loop per visitor.
Approach
- Sort by ['visitor_id', 'occurred_at_utc', 'event_id'] once, then express the whole problem as one boolean vector: a row starts a new session when the visitor changed, or the gap exceeds 30 minutes, or the UTC date differs from the previous row's UTC date. Cumsum that vector and you have the session key.
- Get the comparison direction right on the gap: the rule is strictly greater than 1800 seconds, so an event at exactly 1800 seconds continues the session. Write it as gap > pd.Timedelta(minutes=30), and make the tie a test case rather than an assumption.
- Derive the midnight break from the date change, not from inserting synthetic boundary rows. A date change implies a break even when the gap is two seconds, which is precisely the force-close rule and is why the two conditions are ORed rather than one subsuming the other.
- Aggregate with a single groupby on the session key: min and max of occurred_at_utc, size for event_count, and last for user_id, which is correct because the frame is already sorted so 'last' is the final event in the session. That is the identity-as-of-session-end rule.
- Compute duration_seconds as (max - min).dt.total_seconds(), which makes a single-event session 0 seconds. Say so explicitly, because a downstream mean session duration is sensitive to whether single-event sessions are 0 or excluded.
Worked solution 35 min
- df = df.sort_values(['visitor_id','occurred_at_utc','event_id']).reset_index(drop=True).
- new_visitor = df.visitor_id.ne(df.visitor_id.shift()); gap = df.occurred_at_utc.diff(); new_day = df.occurred_at_utc.dt.date.ne(df.occurred_at_utc.dt.date.shift()).
- is_start = new_visitor | (gap > Timedelta(minutes=30)) | new_day; df['session_key'] = is_start.cumsum().
- g = df.groupby('session_key'); out = g.agg(visitor_id=('visitor_id','first'), user_id=('user_id','last'), started_at_utc=('occurred_at_utc','min'), ended_at_utc=('occurred_at_utc','max'), event_count=('event_id','size')).
- out['session_date'] = out.started_at_utc.dt.date; out['duration_seconds'] = (out.ended_at_utc - out.started_at_utc).dt.total_seconds(); assign session_id from the sorted index.
Follow-up
- Sessions are used as the denominator of a conversion rate. How does moving the inactivity gap from 30 to 45 minutes move that rate, and in which direction?
- A visitor's clock is 40 minutes ahead, so their events arrive with future occurred_at values. What does your sessioniser do, and what would you rather it did?
- The same person signs up mid-session on mobile and continues on desktop. How many sessions and how many users does your output show, and is that the right answer?
How would you optimize a slow-running SQL query?
How would you optimize a slow-running SQL query?
Approach
- State the window function and its partition and ordering out loud before writing it.
- Handle the rows that do not match: a LEFT JOIN with a NULL check is usually the question.
- Check whether any join is one-to-many before aggregating, or the sums inflate.
Follow-up
- How would you verify this result without re-running the same query?
- What breaks if events arrive late or out of order?
Given a dataset, demonstrate how to perform a time series analysis.
Given a dataset, demonstrate how to perform a time series analysis.
Approach
- Say which table is the grain you start from, and join outward from it.
- Compute rates by summing numerator and denominator separately, never by averaging rates.
- State the window function and its partition and ordering out loud before writing it.
Follow-up
- How would you verify this result without re-running the same query?
- What breaks if events arrive late or out of order?
Attribute account MRR to first-touch channel without seat fan-out
dim_user holds user_id, account_id, first_touch_channel, account_created_at_utc. dim_account holds account_id, lifecycle_status. fct_subscription_period holds account_id, period_start_utc, period_end_utc, period_status, mrr_cents_constant_fx. For a given as-of date, report active MRR by the first-touch channel of the account's earliest-created user. An account has many users and many periods. The channel totals must sum exactly to total active MRR on that date, and accounts whose label is NULL must appear as their own bucket.
Approach
- Reduce the label side to one row per account before any join: ROW_NUMBER() OVER (PARTITION BY account_id ORDER BY account_created_at_utc, user_id) = 1 over dim_user, carrying first_touch_channel. Joining dim_user to the period table directly repeats each revenue row once per seat.
- Reduce the money side to one row per account too: the period where period_start_utc <= :as_of AND period_end_utc > :as_of AND period_status IN ('active','past_due'). If more than one row survives that filter the account holds overlapping subscriptions, which must be deduped or deliberately summed, and either way the choice is stated rather than left to the join.
- Join the two one-row-per-account CTEs and SUM(mrr_cents_constant_fx). Use the constant-FX column, since the same query run in two quarters otherwise reports currency moves as channel performance.
- Bucket NULL first_touch_channel as 'unattributed' with COALESCE instead of letting it drop. Roughly the share of users with no observed touch is not small, and dropping it understates the total and inflates every named channel's share.
- Reconcile: the SUM over the joined result must equal the SUM over the period CTE alone. That single equality check catches fan-out immediately, which is why it is worth writing before presenting the number.
Worked solution 30 min
- Compute total active MRR on the as-of date from the period table alone and write the number down as the target.
- Build the label CTE and assert COUNT(*) = COUNT(DISTINCT account_id).
- Build the as-of period CTE and assert the same, investigating any account with more than one surviving row.
- Join, COALESCE the channel, aggregate, and compare the total to the target.
- Deliberately run the naive dim_user join and record the inflation factor, which is the MRR-weighted mean seat count.
Follow-up
- Which user should own the account's label: earliest created, the 'owner' role, or the one who converted? What does each choice systematically favour?
- What does this table entitle you to say about the value of a channel, and what does it not?
- Some accounts have a parent_account_id. How does rolling those up change both the numerator and the channel mix?
If given a new dataset, what steps would you take to explore and analy…
If given a new dataset, what steps would you take to explore and analyze it?
Approach
- Restate the decision this analysis has to support, and who acts on the answer.
- Fix the population and the time window before naming any metric.
- Decompose the metric into the rates that drive it, and say which one you would check first.
Follow-up
- How would you detect that the metric is being gamed rather than genuinely improving?
- What would you do if the primary metric and the guardrail moved in opposite directions?
How do you prioritize tasks when managing multiple projects?
How do you prioritize tasks when managing multiple projects?
Approach
- State what result would change your recommendation, so the answer is falsifiable.
- Restate the decision this analysis has to support, and who acts on the answer.
- Fix the population and the time window before naming any metric.
Follow-up
- Which segment would you cut first, and what would that rule out?
- What would you do if the primary metric and the guardrail moved in opposite directions?
How would you approach a dataset with numerous outliers?
How would you approach a dataset with numerous outliers?
Approach
- State what result would change your recommendation, so the answer is falsifiable.
- Fix the population and the time window before naming any metric.
- Name one primary metric, then the guardrail that stops it being gamed.
Follow-up
- How would you detect that the metric is being gamed rather than genuinely improving?
- What would you do if the primary metric and the guardrail moved in opposite directions?
Walk me through a project where you had to make trade-offs between acc…
Walk me through a project where you had to make trade-offs between accuracy and interpretability.
Approach
- Decompose the metric into the rates that drive it, and say which one you would check first.
- Fix the population and the time window before naming any metric.
- Name one primary metric, then the guardrail that stops it being gamed.
Follow-up
- How would you detect that the metric is being gamed rather than genuinely improving?
- What would you do if the primary metric and the guardrail moved in opposite directions?
Explain how you would design an experiment to test a hypothesis.
Explain how you would design an experiment to test a hypothesis.
Approach
- Say whether units interfere with each other, and switch design if they do.
- Decide the analysis before seeing data, including how long it runs and when you look.
- Name the guardrails that would stop a launch even on a positive primary result.
Follow-up
- What would you do if you could not randomise at all?
- How would you handle interference between treated and control units?
Explain the difference between supervised and unsupervised learning.
Explain the difference between supervised and unsupervised learning.
Approach
- Work from the decision backwards to the evidence you would need.
- Clarify what is being asked and what a complete answer would contain.
- State your assumptions explicitly before working the problem.
Follow-up
- What assumption would you test first?
- How would you know your answer was wrong?
Size an activation test before anyone writes code
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.
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
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?
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.
Prepare, practise & reflect
One practical outcome each day. Spend longer where you need it.
0 / 7 done01Design 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.
Practice prompt ↗Practice prompt ↗Practice prompt ↗Worked solution ↗02Power 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.
Practice prompt ↗Practice prompt ↗Practice prompt ↗03Variance 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.
Practice prompt ↗Practice prompt ↗Practice prompt ↗04Validity 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.
Practice prompt ↗Practice prompt ↗Worked solution ↗05When 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.
Practice prompt ↗Practice prompt ↗06The 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.
Practice prompt ↗Practice prompt ↗07Present 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.
Practice prompt ↗Practice prompt ↗Worked solution ↗Expand any day for tasks and deliverables. Your progress is saved on this device.
Interviewers here are not checking whether you can describe a project. They want the decision you made, why you made it under the information you had, and what changed afterwards that someone else could measure. A story that ends at 'I built a model' has no ending. Say what the model caused, or what you stopped doing because of it.
Tell me about a time you had to work with a difficult team member.
Tell me about a time you had to work with a difficult team member.
Approach
- Quantify the outcome, including what you would not claim credit for.
- Pick a story where you drove the decision, not one where you observed it.
- State the situation in two sentences and spend the rest on your reasoning.
Follow-up
- What would you do differently if you ran that project again?
- How did you know the outcome was caused by your change?
Handle a request for numbers supporting a decision already made
A senior leader has already decided to sunset a plan tier and asks you for the analysis showing it is the right call. Accounts on that tier carry 6% of MRR at constant FX and have the highest licensed-seat utilisation in the book. The leader's support matters to your next review cycle, and the decision is being presented in four days. Deliver what you produce, what you decline to produce, and the exact sentence you will say in the meeting where the number appears on a slide.
Approach
- Recognise what is being probed: whether you can find the legitimate request inside an illegitimate framing instead of either complying or refusing on principle. The generic answer promises to push back; the strong one produces something genuinely useful and states its limits in the room, without ambushing anybody.
- Separate the decision from the justification. Sunsetting the tier may be correct for reasons the data does not hold, such as support cost, roadmap surface area or sales motion. What you decline is a one-sided document. What you produce is the case read both ways, which also happens to be more useful to the leader.
- Build the symmetric analysis: MRR at risk at constant FX, the share of affected accounts with a plausible migration path given seats_licensed and billing_term, the recovery rate assumed for that migration and where it came from, and the downside case in which high-utilisation accounts treat the sunset as a reason to re-evaluate the vendor entirely.
- Surface the inconvenient fact privately and early. The highest seat utilisation in the book is a retention signal, and the leader should hold it before the room does, so they can incorporate it rather than be caught by it.
- Agree the meeting sentence in advance with the leader, so that nobody is surprised. Something to the effect that the tier is 6% of MRR and its accounts are the most heavily used in the book, and that the case for sunsetting rests on cost and focus rather than on revenue. That is true, it supports the decision on its real grounds, and it stops the deck claiming the numbers endorse it.
- Decide your own line before you need it: what you will not put your name to, and that the route if asked anyway is your own manager rather than a confrontation in the meeting.
Follow-up
- The deck circulates with your analysis included and the downside case removed. What do you do, and by when?
- What changes if the honest analysis says the sunset is clearly the wrong call?
- How do you write the same memo when the leader is your skip-level and the meeting is tomorrow?
Explain a wide interval to a non-technical executive
A pricing change is under consideration. Your best estimate of its effect on trial-to-paid conversion is a 1.8pp drop, with a 95% interval from a 4.6pp drop to a 1.0pp rise, read from a geo holdout rather than a randomised test. An executive preparing a board slide asks you for 'the number'. You have ninety seconds and one slide, and the words confidence interval, p-value and significance are not usable with this audience. Deliver the slide headline, the single supporting line, and what you say aloud.
Approach
- Recognise what is being probed: whether you can carry uncertainty into a decision instead of either hiding it or hiding behind it. The generic answer promises to explain the interval in plain English; the strong one replaces the question 'what is the number' with 'across this range, where does the decision change'.
- Find the threshold before you draft anything. Ask what the pricing case assumes, then compute the conversion drop at which the higher price stops adding revenue: price uplift on the conversions kept against the revenue lost from conversions forgone. That single figure is what makes the range legible.
- Restate the estimate and both bounds in the unit the audience already reasons in. Convert percentage points into monthly first-paid conversions at current trial volume, then into mrr_cents_constant_fx, so the slide reads as money per month rather than as statistics.
- Place the range against the break-even and say which part of it sits on each side. If most of the range clears the threshold, that is a recommendation to proceed with a monitoring plan; if the range straddles it, that is a recommendation to narrow the range first.
- Name what would narrow it and what that costs in weeks, then give one recommendation with an explicit condition for revisiting it. Uncertainty stated without a next step is read as indecision and the midpoint gets used anyway.
Follow-up
- The executive says to give the midpoint and they will manage the risk. What do you do?
- How does the slide change if the interval were a 4.6pp to 0.2pp drop, with no positive outcomes in range?
- Why is a geo holdout the credible read here rather than the attributed channel numbers you already have?
- 01
Tell me about a time you had to work with a difficult team member.
- 02
A senior leader has already decided to sunset a plan tier and asks you for the analysis showing it is the right call. Accounts on that tier carry 6% of MRR at constant FX and have the highest licensed-seat utilisation in the book. The leader's support matters to your next review cycle, and the decision is being presented in four days. Deliver what you produce, what you decline to produce, and the exact sentence you will say in the meeting where the number appears on a slide.
- 03
A pricing change is under consideration. Your best estimate of its effect on trial-to-paid conversion is a 1.8pp drop, with a 95% interval from a 4.6pp drop to a 1.0pp rise, read from a geo holdout rather than a randomised test. An executive preparing a board slide asks you for 'the number'. You have ninety seconds and one slide, and the words confidence interval, p-value and significance are not usable with this audience. Deliver the slide headline, the single supporting line, and what you say aloud.
Is this an official Mathematica interview guide?
No. It is PracHub's own research and practice material for the Data Scientist role at Mathematica. Rounds and questions reflect what candidates have reported, not a process Mathematica has published, and they change over time. Confirm the current format and scope with your recruiter.
PracHub interview research ↗What is the typical interview difficulty level for the Data Scientist position?
The interview process is known to be rigorous, with a mix of technical, behavioral, and situational questions. Candidates often report that preparation should focus on both technical skills and collaborative problem-solving abilities.
PracHub interview research ↗How long does the interview process usually take?
Candidates have experienced timelines ranging from 5-8 weeks from application to offer, reflecting the thoroughness of the evaluation process.
PracHub interview research ↗What differentiates successful candidates?
Successful candidates demonstrate a strong technical foundation, effective communication skills, and a clear alignment with Mathematica's mission and values. They also showcase a collaborative mindset and an ability to influence decisions through data-driven insights.
PracHub interview research ↗How does Mathematica support remote work?
Mathematica has adapted to hybrid work models, allowing flexibility while encouraging collaboration and connection among team members.
PracHub interview research ↗Sources & methodology 3 sources ↗
No official company page is cited. Rounds and questions come from candidate reports and PracHub editorial material; each source shows the date it was read.
- 01PracHub interview research ↗
PracHub editorial research into this company and role, maintained with this guide. Candidate-reported, not an employer publication.
PracHub page · Accessed 2026-09-22 - 02PracHub Data Scientist practice ↗
Cross-company practice questions for this role.
PracHub page · Accessed 2026-09-22 - 03PracHub interview preparation framework ↗
The framework the preparation plan follows.
PracHub page · Accessed 2026-09-22
Explore related engineering environments and compare the preparation focus.
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