The work in general product and business analytics is mostly deciding what a number should mean and then defending that decision. A typical week contains a metric that moved and nobody can explain, an experiment readout where the headline is flat but three segments look interesting, a request to define success for a feature that ships next month, and a forecast or sizing input for a planning cycle. Very little of it arrives as a well-posed question; the first deliverable is usually a restatement of the question in terms that have a numerator, a denominator and a window. The output is a decision about shipping, pricing, spending or stopping, and it has to survive somebody else recomputing it from the same tables.
What makes it hard is the absence of a physical constraint to anchor definitions. A supply chain has units that either arrived or did not; a product funnel has whatever the tracking plan happened to record, sessionised by a rule somebody chose, joined on an identity that resets when a browser clears its cookies. Two competent analysts can produce different conversion rates from the same warehouse and both be right, which means the defensible answer is the one whose assumptions are written down. On top of that, the effects being measured are small: a genuine improvement to a mature funnel is often a fraction of a percentage point in absolute terms, comfortably inside the noise of a week, so most of the skill is in variance control and sizing rather than in modelling.
The skills that carry the most weight are SQL across mismatched grains, experiment design, and the judgement to say what a result does not support. Event, session, subscription-period and exposure data all live at different grains, and the standard failure is a join that fans revenue across rows or an inner join that deletes exactly the population the question was about. Experiment work is judged less on whether a test statistic was computed correctly than on whether the randomisation unit matched the interference structure, whether the horizon was fixed in advance, and whether the analysis population was the exposed set rather than the assigned set. Above all of this sits communication: a correct analysis delivered as a table of numbers with no stated decision is treated as unfinished.
Metric definition and metric-tree construction
editorialPreparation area covering the translation of a loosely worded goal into a metric with a stated numerator, denominator, window and exclusion rule, and the assembly of those metrics into a tree where each layer explains the one above it.
What to demonstrate
- Whether a proposed metric is actually computable from the available tables, and whether the candidate says so when it is not
- Whether the candidate names the window, the lag before publication and the excluded populations rather than leaving them implied
- Ability to explain how a metric would be gamed and to name the specific guardrail that catches that behaviour
- Judgement about the grain a metric belongs at, particularly the distinction between a per-user and a per-account question
How to prepare
- Write out each metric in the tree above from memory, including its lag rule, until the definitions are recall rather than reconstruction
- Take three vague goals such as 'improve engagement' and produce two defensible metrics for each, with the argument for choosing between them
- Practise stating the failure mode of a ratio metric whose denominator is the thing that moved, and how you would detect that in the data
- Rehearse the difference between a count, a rate and a rate-of-rates, and which of the three survives being rolled up across periods
Warehouse SQL across event, session, subscription and exposure grains
editorialPreparation area for queries that span an append-only event log, derived sessions, billing periods and experiment exposures, where a naive join fans out revenue and an inner join removes exactly the rows that carry the answer.
What to demonstrate
- Correct handling of fan-out: pre-aggregating one side in a CTE before joining, and being able to demonstrate what the unaggregated join would have done to the total
- Deliberate treatment of NULL foreign keys, including signed-out events with no user_id, sessions with consent_state = 'denied' and accounts with no subscription row
- Fluency with window functions for first-event identification, cohort indexing, running counts and deduplicating overlapping billing periods
- Whether rates are rolled up by re-summing numerator and denominator rather than by averaging daily or weekly rates
How to prepare
- Build the full visitor-to-signup-to-activation funnel as one query using left joins forward, so that lost stages stay visible as NULLs instead of disappearing
- Write MRR at the start and end of a month from fct_subscription_period, handling mid-period plan changes without double-counting the account
- Practise a retention triangle from dim_user and fct_event with both window bounds enforced, and verify the row count at each grain before aggregating
- Reconstruct a per-attempt funnel from flow_instance_id, and be able to say what breaks when that id is missing
Experiment design, sizing and readout discipline
editorialPreparation area for choosing a randomisation unit, powering a test before it launches, and reading it out in a way that survives scrutiny, including the cases where the honest answer is that the test could not have detected the effect in question.
What to demonstrate
- Whether the randomisation unit matches the interference structure, and whether the standard error is computed on that unit rather than on the row
- Ability to size a test from first principles: for a proportion, roughly 16 p(1-p) divided by the squared absolute lift per arm, at 5% two-sided alpha and 80% power with equal arms
- Recognition that the analysis population is the exposed set, that assignment without exposure dilutes the estimate toward zero, and that a sample-ratio mismatch invalidates the readout rather than being a footnote
- Whether novelty and primacy effects are addressed, and whether the candidate distinguishes a metric that recovered from one that was never affected
How to prepare
- Memorise the proportion sizing shortcut and practise computing a minimum detectable effect from a realistic weekly traffic figure in under a minute
- Be able to state the design effect for clustered randomisation, variance inflated by 1 + (m-1) rho with m the mean cluster size and rho the intraclass correlation, and what it does to required sample size
- Practise explaining why a per-session metric randomised on users needs a delta-method or bootstrap standard error rather than a naive one
- Prepare a short account of variance reduction with a pre-period covariate, including the fact that it removes a share of variance equal to the squared correlation between covariate and outcome
Causal inference when randomisation is unavailable
editorialPreparation area for questions where an experiment is impossible, illegal or already too late, covering the quasi-experimental designs, the assumption each one rests on, and how to argue that assumption is plausible in the case at hand.
What to demonstrate
- Whether the candidate names the identifying assumption rather than the method, for instance parallel counterfactual trends rather than 'difference-in-differences'
- Ability to choose between difference-in-differences, a geo or time-based holdout, regression discontinuity and matching on the basis of what the data actually supports
- Awareness of what matching cannot fix, namely selection on anything unobserved, and willingness to say so instead of presenting a balanced covariate table as proof
- Whether a placebo or pre-trend check is proposed before the estimate is believed
How to prepare
- Practise writing the parallel-trends check you would run before a difference-in-differences estimate, and what you would conclude if the pre-period trends diverge
- Prepare one worked case where a launch was staggered across regions and explain how the staggered timing itself provides the comparison
- Rehearse the argument for a geo holdout as the cheapest credible read on channel incrementality, including how you would size it on total conversions
- Be able to state in two sentences why observational channel comparisons overstate the channels closest to conversion
Diagnosing a metric movement and landing the decision
editorialPreparation area for the open-ended case where a number moved and the task is to find out why and say what to do, working from a decomposition rather than from a list of guesses.
What to demonstrate
- Whether the first move is to verify the metric itself, covering instrumentation changes, a late-arriving data partition, a client release and a definition edit, before any product hypothesis
- Whether the decomposition is systematic, splitting the metric into its factors and then across segment, platform, geography, tenure and channel rather than sampling hypotheses at random
- Ability to size the contribution of each candidate cause, so that a segment moving sharply but carrying two percent of volume is correctly set aside
- Whether the answer ends in a recommendation with its uncertainty stated, and whether the candidate says plainly when the data cannot yet support one
How to prepare
- Rehearse a fixed opening sequence: confirm the movement is real and outside normal weekly variation, confirm the pipeline and tracking plan did not change, then decompose
- Practise the multiplicative decomposition of a funnel metric so that a drop can be attributed to a specific stage rather than to the funnel in general
- Build the habit of quantifying every candidate cause in the units of the headline metric, so contributions can be ranked and the remainder made explicit
- Practise delivering the finding in three lines, the movement, the cause with its share, and the decision, before any supporting detail
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After a recruiter call involving the hiring manager, I had a technical screen that mostly covered my projects, the role, and resume alignment. A couple more technical conversations followed, mixing coding-style problem-solving and debugging with JavaScript, Java, and SQL. The feeling was practical: they were testing reasoning, not memorization. My background stayed central throughout. I repeatedl…
Read full experiencePracHub editorial advice for the preparation topics above.
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.
Slicing a flat experiment until a segment reaches significance
Testing one metric across twenty segments at a nominal 5% level produces a significant result about two thirds of the time when nothing is happening anywhere, and the segment that surfaces is by construction the one with the most favourable noise. The reported effect in that slice is then badly overstated, because selection on significance conditions the estimate on being large. What makes it dangerous rather than merely wrong is that a post-hoc segment always has a plausible story attached, so it survives the meeting. The controls are declaring the small number of segments of interest before launch, correcting across the ones tested, and treating anything discovered afterwards as a hypothesis that needs its own adequately-powered test rather than a finding.
Building features from data that postdates the prediction time
Check every feature against the timestamp at which the model would actually score, and drop anything computed from a window that includes or follows the label event. For a forecasting use case, split train and test by time rather than at random, and split by entity when the same entity recurs.
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.
Choose a category, try a prompt, then open its approach, worked solution or follow-up when you need it.
Cluster bootstrap for a per-session rate randomised on users
An experiment randomised on user_id reports a per-session conversion rate, so sessions inside a user are correlated. Input: one row per session with user_id, variant in {control, treatment} and converted in {0,1}. Write a cluster bootstrap from scratch: resample users with replacement within each arm, keep every session of a drawn user, recompute each arm's ratio of converted sessions to sessions, and take the difference. Return the point estimate, a 95 percent percentile interval from at least 2,000 resamples, the naive session-level interval that ignores clustering, and the ratio of their widths.
Approach
- Name the estimand precisely: it is a ratio of sums, sum(converted) over sum(sessions) within an arm, not the mean of per-user rates. Those differ whenever session counts vary across users, and the ratio is what the reported metric is.
- Resample the cluster, not the row. Draw n_users user ids with replacement inside each arm and take every session belonging to each draw, including duplicate draws of the same user. Keeping the user count fixed per arm rather than the session count is what preserves the sampling design.
- Precompute per-user (converted_sum, session_count) once, so each resample is two vector lookups and a division rather than a repeated filter over the session frame. That turns 2,000 resamples from minutes into under a second.
- Take the 2.5th and 97.5th percentiles of the 2,000 differences for the interval, and report the point estimate from the full data rather than from the bootstrap mean, since the bootstrap mean carries the resampling bias.
- Compute the naive interval from the session-level binomial standard error and compare widths. The expected inflation is roughly sqrt(1 + (m-1)*rho), with m the mean sessions per user and rho the intraclass correlation of converted within users, so a computed ratio far from that value points at a bug in one of the two intervals.
Follow-up
- Users average 3.4 sessions and the intraclass correlation is 0.12. What width ratio do you predict before running it, and does your bootstrap land there?
- Give the delta-method standard error for this ratio and say when you would prefer it to the bootstrap.
- Half the users in the treatment arm have exactly one session. What does that do to the cluster bootstrap's coverage, and how would you check it?
Permutation test for a difference in conversion rates
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.
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?
Split a pooled conversion drop into rate and mix
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.
Worked solution 25 min
- Aggregate to one row per (week, segment tuple) with summed visitors and signups, then split into w0 and w1 frames and align with an outer join, filling missing visitors and signups with 0.
- Compute w_s = visitors / visitors.sum() within each week, and r_s = signups / visitors only where visitors > 0. Where a week's visitors are 0, set that week's r_s to that week's pooled rate, the stated convention; never leave it NaN.
- rate_effect = (w0 * (r1 - r0)).sum(); mix_effect = ((w1 - w0) * r0).sum(); interaction = ((w1 - w0) * (r1 - r0)).sum().
- contribution = w0*(r1-r0) + (w1-w0)r0 + (w1-w0)(r1-r0) per segment, which reduces to w1r1 - w0r0; sort by abs and return the head.
- assert abs(rate + mix + interaction - (pooled1 - pooled0)) < 1e-12.
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?
Read an experiment from first exposure, not assignment
fct_experiment_exposure holds experiment_id, unit_type, unit_id, variant, user_id, assigned_at_utc, first_exposed_at_utc, is_in_analysis_population and planned_end_utc. fct_event holds user_id, occurred_at_utc, is_core_action, and carries events up to a known data cut, :data_cut_utc. For one experiment randomised on unit_type = 'user', return per variant: exposed units, units with at least one core action in the seven days after that unit's own first exposure, the rate, and the variant share of exposed units. Only units whose seven-day window has fully elapsed as of the data cut belong in the readout. Units appearing under more than one variant are excluded from both arms and counted separately.
Approach
- Run the contamination pass as an aggregate, not a window: SELECT unit_id FROM fct_experiment_exposure WHERE experiment_id = :exp GROUP BY unit_id HAVING COUNT(DISTINCT variant) > 1, then anti-join it away. PostgreSQL rejects COUNT(DISTINCT variant) OVER (PARTITION BY unit_id) outright, since DISTINCT is not implemented for window functions; if you want the test inline, MIN(variant) OVER (PARTITION BY unit_id) <> MAX(variant) OVER (PARTITION BY unit_id) is the equivalent that does run.
- Do not resolve contamination by keeping the earliest variant. A unit that saw both arms carries treatment from both, so assigning it to either one biases that arm.
- Define the population as is_in_analysis_population = TRUE AND unit_type = 'user' AND first_exposed_at_utc < planned_end_utc AND first_exposed_at_utc + interval '7 days' <= :data_cut_utc. The horizon filter is what makes the readout reproducible next week instead of drifting with every re-run; the data-cut filter is the one that actually buys seven days of follow-up, since a unit exposed an hour before the horizon otherwise contributes an hour of observation to a seven-day rate.
- Measure the outcome on a per-unit relative window: LEFT JOIN fct_event on user_id with is_core_action = TRUE and occurred_at_utc in [first_exposed_at_utc, first_exposed_at_utc + interval '7 days'). LEFT JOIN so units with no outcome stay in the denominator at zero rather than being deleted by an inner join.
- Check the sample ratio before reading the effect: variant share of exposed units against the intended split, tested as a binomial. Run it on the truncated population as well as on the full exposed set, because if one arm exposes later on average the data-cut filter removes more of that arm and can manufacture a ratio mismatch the randomisation did not have. A mismatch on the full set means the exposure data is not a valid randomisation and invalidates the readout rather than being a footnote under it.
- Report the per-variant rate, the absolute difference, and the fact that the variance unit is unit_id. That is straightforward here only because the grain is already one row per user; a per-session outcome under user randomisation would need a delta-method or bootstrap standard error instead.
Follow-up
- Some units were assigned days before they were exposed. What does analysing the assigned set instead do to the estimated effect, and in which direction?
- The split is 51/49 on 400,000 exposed units. Do you read the result?
- The treatment arm exposes on average two days later than control. What does that do to a fixed calendar outcome window, and which arm does it favour?
Seven-day activation rate by weekly signup cohort
dim_user holds user_id, account_created_at_utc, is_internal. fct_event holds user_id, occurred_at_utc, is_core_action. A user is activated when core-action events fall on at least two distinct UTC dates inside [account_created_at_utc, account_created_at_utc + 7 days). Return, for the last twelve complete weekly signup cohorts, the cohort week, cohort size, activated users and the activation rate. Exclude is_internal users. Every signup in the cohort week stays in the denominator, including users who never returned.
Approach
- Start from dim_user as the denominator spine with is_internal = FALSE and DATE_TRUNC('week', account_created_at_utc) as the cohort key. Driving the query from the event table instead would silently condition on having events and delete the entire non-activating population.
- Join fct_event on user_id with is_core_action = TRUE and a per-user bound, occurred_at_utc >= u.account_created_at_utc AND occurred_at_utc < u.account_created_at_utc + interval '7 days'. The bound is correlated to each user's own signup timestamp, not a single global date range.
- Aggregate per user with COUNT(DISTINCT occurred_at_utc::date) >= 2, then LEFT JOIN that back onto the spine and COALESCE the flag to FALSE so non-activators contribute a zero rather than vanishing.
- Restrict the published cohorts to those whose week ended at least eight days ago. A cohort younger than that has not finished its seven-day window, so its rate is mechanically low and reads as a decline.
- Roll up by summing the numerator and denominator per cohort week, and state the two-distinct-days threshold next to the number since it is a choice that re-bases the whole history if changed.
Worked solution 20 min
- Write the cohort spine and confirm its total equals the count of non-internal signups in the date range.
- Write the per-user distinct-active-days CTE with both interval bounds and inspect a handful of users manually.
- LEFT JOIN, COALESCE the flag, aggregate to cohort week.
- Apply the eight-day publication lag and drop the incomplete cohort.
- Re-run with a closed upper bound (<= +7 days) and note how many users change state, to show the boundary is doing work.
Follow-up
- Why two distinct days rather than one event? What happens to the published history if someone changes it to three?
- Invited seats and SSO-provisioned users get an account_created_at_utc at provisioning and may never sign in. Should they be in this denominator?
- The rate rose 3 points this week. What do you check before believing it?
Diagnose a 50.5 to 49.5 split before reading the result
An experiment randomised on visitor_id ran for 11 days. fct_experiment_exposure holds 104,320 control rows and 102,180 treatment rows for the experiment_id, all with is_in_analysis_population = TRUE, against a configured 50/50 split. The treatment arm shows a 3.1% relative lift in visit-to-signup conversion at p = 0.004, and the team wants to ship. Decide whether that lift can be reported, show the arithmetic behind your decision, and name the three checks you would run first on the exposure logging.
Approach
- Test the split instead of eyeballing it. Chi-square goodness of fit against 103,250 expected per arm gives 2 x 1070^2 / 103,250 = 22.2 on 1 degree of freedom, p about 2.5e-6. The conventional alarm threshold is p < 0.001, so this is a sample ratio mismatch.
- Treat the mismatch as invalidating, not as a caveat. The arms are no longer exchangeable, so the 3.1% lift has no causal reading and rebalancing on covariates afterwards does not restore it.
- Walk the logging path in the order units flow through it: assignment service, then the exposure event fired on the treated surface, then the filters that build the analysis population. Each stage can drop one arm preferentially.
- Name the three suspects this stack actually has. Exposure emitted by client code the treatment arm reaches later or not at all when its bundle errors; an extra redirect or render in one arm that loses slow connections; and a post-assignment filter (is_bot_flagged, is_internal, consent_state) that correlates with variant.
- Check whether the imbalance is uniform by splitting counts on session_date, surface, app_version and device_type. A mismatch confined to one client build or to day one points at a deployment fault that can be fixed and re-run, not at a design fault.
Follow-up
- The imbalance is entirely in one app_version on android. Can you salvage the other surfaces, and under what argument?
- How would you monitor this across every running experiment without drowning in false alarms from a daily chi-square at alpha 0.05?
- The missing rows turn out to be disproportionately visitors with consent_state = 'unknown'. What does that do to the estimate even after the logging bug is fixed?
Halve the runtime of a flat test with pre-period data
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
- 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.
- 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.
- 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.
- 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%.
- 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.
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?
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?
Gross revenue churn doubled with no cancellations behind it
Gross monthly revenue churn computed from fct_subscription_period doubled from 1.8% to 3.6% in one month. The support queue shows no rise in cancellations and renewals look normal. You have fct_subscription_period with subscription_id, account_id, period_start_utc, period_end_utc, mrr_cents, mrr_cents_constant_fx, seats_billed, period_status, change_reason and canceled_at_utc, plus dim_account. Decompose the 1.8-point rise into named mechanisms, size each in points of the headline, and state the remainder you cannot explain.
Approach
- Reconstruct the numerator row by row and group it by change_reason before arguing about causes. A mid-period plan or seat change closes the current period row and opens a new one, so any implementation that treats a closed row as lost revenue books upgrades, downgrades and seat changes as churn; the change_reason breakdown of the numerator makes that visible in one query.
- Check the recognition timestamp. Churn belongs at period_end_utc, because revenue continues until the period ends, not at canceled_at_utc when the button was pressed. Then count period_end_utc rows per month across thirteen months: annual cohorts concentrate their period ends in the month twelve months after they were signed, so a spike that repeats in the same month last year is seasonality in the book, not an event this month.
- Recompute the whole numerator and denominator on mrr_cents_constant_fx. If the constant-currency figure is materially flatter, the move is an exchange-rate translation and belongs nowhere in a churn narrative.
- Check period_status handling. Rows with period_status = 'past_due' are dunning, not cancellation; a status-based rule counts them as loss while a period-end rule does not, and a dunning backlog can move the number by itself.
- Express every mechanism in points of the headline, sum them, and print the residual explicitly next to the month-to-month standard deviation of the prior twelve months. A decomposition without a stated remainder is a story, not an accounting.
Follow-up
- Which of these mechanisms should be fixed in the metric definition and which should be reported as a genuine business fact?
- How would you present a month whose churn is dominated by an annual cohort anniversary without the audience concluding the business is deteriorating?
- What would you change so that an upgrade can never enter the churn numerator again, and how would you test that it worked?
Roughly 90 minutes a night on weekdays with one longer weekend block. The plan deliberately cuts scope rather than compressing everything, on the assumption that finishing one thing a night beats half-starting four.
Prepare, practise & reflect
One practical outcome each day. Spend longer where you need it.
0 / 7 done01Fix the scope and set a baseline
- Read the role description and write the three things the loop will almost certainly test, then write an explicit not-doing list for everything else and keep it visible all week.
- Take one 20-minute SQL prompt and one 10-minute metric question cold, and write the single sentence that says what blocked each attempt, since that sentence is what decides which two topics get the most evenings.
- Set the week's one rule: one problem finished to completion every night, including the night you only have 40 minutes.
Deliverable: A one-page scope with an explicit not-doing list and two cold attempts, each carrying one sentence on what blocked it.
Practice prompt ↗Practice prompt ↗Worked solution ↗02One query pattern, written three times
- Choose the single pattern most likely to appear (a cohort retention grid, or a funnel counted by user) and write it three times from a blank file rather than editing the previous attempt.
- On the third attempt, write the grain of every CTE as a comment before writing its body.
- Stop at 90 minutes even if the third version is imperfect, and write the one thing you would fix with another hour.
Deliverable: Three independent versions of the same query plus a note on what changed between them.
Practice prompt ↗Practice prompt ↗03Only the statistics you will be asked to defend
- Write, in under 200 words, how you would decide whether a difference between two groups is real: the test, its assumptions, and what you would switch to when an assumption fails.
- Compute a 95 percent confidence interval for a difference in proportions by hand on realistic numbers, then write in one sentence what changes if the two samples are paired rather than independent.
- Write your answer to "what does a p-value mean", check it against a definition, and delete the version that describes it as the probability the hypothesis is true.
Deliverable: A 200-word written answer and one hand-computed interval you can reproduce under pressure.
Practice prompt ↗Practice prompt ↗Worked solution ↗04One case, and the assumptions holding it up
- Answer one product case aloud in 20 minutes with a recording running, then listen back with a pen and mark every claim you asserted without saying what it rested on: an assumed user behaviour, an assumed data source, an assumed baseline rate, an assumed grain.
- Pick the three assumptions the recommendation actually depends on, write how you would check each one against data, and say which one being wrong would flip the recommendation rather than merely weaken it.
- Write the four-step structure you used onto a card small enough to hold in working memory when you are nervous.
Deliverable: One recording, three load-bearing assumptions each with a written check, and a four-step structure card.
Practice prompt ↗Practice prompt ↗05Your own work, timed
- Write a 90-second version and a four-minute version of your main project, and time both out loud rather than reading them.
- Prepare answers to the two follow-ups that always come: what you would do differently, and how you knew it worked.
- Put one number in the first sentence and be able to say exactly where that number came from and what it excludes.
Deliverable: Two timed narratives with one defensible number in the opening line.
Practice prompt ↗Practice prompt ↗Worked solution ↗06The one full rehearsal, in a longer weekend block
- Run a 60-minute mock covering query work, a case and a behavioural question in a single sitting with no breaks, because sustained attention is the thing evenings have not trained.
- Immediately afterwards, and before hearing any feedback, write the three moments you lost the thread.
- Spend the rest of the block only on those three moments, and on nothing you merely feel shaky about.
Deliverable: Mock notes naming three failure moments with a specific fix written under each.
Practice prompt ↗07Taper
- Write the 20-minute warm-up you will actually do on the morning of the interview: one query you can already write from a blank file, one metric you can define out loud, and nothing you have never seen before.
- Re-read only your own notes from this week, and open no new material.
- Write down the logistics: the tool you will be asked to work in, whether lookups are allowed, and the sentence you will use when you do not know something.
Deliverable: A one-page card holding the case structure, the project numbers, and the logistics.
Practice prompt ↗Worked solution ↗Expand any day for tasks and deliverables. Your progress is saved on this device.
An answer without a quantity is hard to interrogate, so interviewers keep probing until they find one. Come with the baseline, the change, the window it was measured over, and how confident you were. If the effect never got measured, say so and say what you would have measured. Fabricated precision is worse than an honest gap.
Disagree with a product manager's roadmap claim using data
A product manager proposes building a feature on the argument that accounts connecting an integration in week one retain three times better at week four. The figure is correctly computed from dim_user and fct_event, and it has already been shown to leadership. You have one scheduled 1:1 before the roadmap locks. Deliver the specific analysis you would run to test whether the relationship is causal, the result that would change your own mind, and how you open the conversation so that the PM is not put in the position of defending the number in public.
Approach
- Recognise what is being probed: whether you can separate a number being right from an inference being wrong, and do it without costing the PM face. The generic answer recites that correlation is not causation; the strong one names the specific confound and proposes the cheapest design that could distinguish the explanations.
- State the alternative concretely. Accounts that connect an integration in week one are accounts that already have a workflow and a technical owner, so week-one intent plausibly drives both the connection and week-four retention. The selection is on intent, which no amount of post-hoc adjustment observes.
- Order the discriminating analyses by cost. First, condition on pre-connection activity by comparing retention within strata of week-one core-action count, which removes the crude version of the confound but not unobserved intent. Second, look for variation in integration availability that was unrelated to intent, such as a staggered release or an outage window. Third, an encouragement design that randomises a prompt to connect and reads the intent-to-treat effect on week-four retention, which is the only version that identifies an effect.
- Run the timing check, because it is nearly free and it is the most persuasive single piece of evidence. If the retention advantage among connectors is already visible before any of them connected, the causal story is largely finished.
- Pre-commit to what would change your mind and say it before you show anything: if the gap survives stratification and the encouragement arm moves week-four retention at all, the feature has a case and you will say so.
- Open the 1:1 by agreeing with the true part, that the correlation is real and worth chasing, then ask what effect size the roadmap plan assumes. That makes the size of the claim the topic instead of its authorship.
Follow-up
- The encouragement test needs six weeks and the roadmap locks in two. What do you recommend in the interim?
- Stratifying on week-one activity closes half the gap. What do you conclude, and what do you still not know?
- How would you word this in the roadmap document so the PM's original number is reframed rather than deleted?
Turn an ambiguous onboarding question into a measurable metric
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
- 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.
- 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.
- 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.
- 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.
- 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?
Choose between three teams' requests with one analyst-week
You have one analyst-week. Three requests land the same morning. A growth team wants a paid-channel readout before a Friday spend decision. A billing team wants gross monthly revenue churn rebuilt, because the current figure recognises cancellation at canceled_at_utc rather than period_end_utc and is therefore wrong. A product team wants a dashboard for a feature launching in six weeks. All three sponsors are peers of your manager. Deliver your ranking, the explicit rule that produced it, and the message you send to the two teams you defer.
Approach
- Recognise what is being probed: whether you prioritise on decision value and reversibility or on who asked most recently and most loudly. The generic answer sorts by importance; the strong one states a rule, applies it, and accepts the ranking it produces even where that is uncomfortable.
- Score each request on three statable things: the decision it unblocks and the date that decision is made, the cost of being wrong in the meantime, and whether the work is one-off or compounding. A wrong published churn figure compounds, because it is quoted downstream and enters forecasts; the channel readout has a fixed date that cannot move; the dashboard has six weeks of slack.
- Notice the tension between value and urgency rather than resolving it by feel. The churn defect is the most valuable item and the least urgent one, which is exactly the shape of work that never gets done.
- Break the churn item in two. A one-hour severity check, sizing the gap between the two recognition points in MRR, is cheap enough to do before ranking anything and may promote the item outright. Do that first, then rank.
- Make the deferrals concrete. Each deferred team gets a date, a reason expressed as another team's decision deadline rather than as relative importance, and the smallest thing you can hand them immediately.
Follow-up
- The dashboard team escalates to your manager. What do you say in that conversation?
- Your severity check shows churn is overstated by 15%. Does the ranking change, and does anybody need to be told today regardless of the ranking?
- A fourth request arrives Wednesday with a Thursday deadline. What comes off the list, and who do you tell first?
- 01
A product manager proposes building a feature on the argument that accounts connecting an integration in week one retain three times better at week four. The figure is correctly computed from dim_user and fct_event, and it has already been shown to leadership. You have one scheduled 1:1 before the roadmap locks. Deliver the specific analysis you would run to test whether the relationship is causal, the result that would change your own mind, and how you open the conversation so that the PM is not put in the position of defending the number in public.
- 02
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.
- 03
You have one analyst-week. Three requests land the same morning. A growth team wants a paid-channel readout before a Friday spend decision. A billing team wants gross monthly revenue churn rebuilt, because the current figure recognises cancellation at canceled_at_utc rather than period_end_utc and is therefore wrong. A product team wants a dashboard for a feature launching in six weeks. All three sponsors are peers of your manager. Deliver your ranking, the explicit rule that produced it, and the message you send to the two teams you defer.
Are these confirmed ZoomInfo interview questions?
No. Every prompt here is an original PracHub practice exercise written for the Data Scientist role and for product and business analytics data problems. This guide does not claim to reproduce ZoomInfo's interview questions, rounds or hiring timeline. Confirm the actual format, team and scope with your recruiter.
PracHub Data Scientist practice ↗How should I approach a take-home assignment?
Respect the stated time budget, then make your choices legible. Write down what you did not do and why you cut it. A clean, reproducible analysis that answers the question asked beats a sprawling notebook with six models. Put a short summary at the top for a hiring manager: the question, the answer, your confidence, the caveats. These are graded mostly on judgment and communication; the modelling rarely separates candidates.
PracHub Data Scientist practice ↗Do I need experiment design beyond a straightforward A/B test?
Know why you would not run one. Interference between units in marketplaces and social graphs, long feedback cycles, populations too small to power, and cases where randomisation is not permissible. Be ready with one alternative for each: switchback or cluster randomisation, difference-in-differences where you can argue parallel trends, regression discontinuity at a threshold that already exists. This is where mid-level and senior answers separate quickly.
PracHub Data Scientist practice ↗What should I ask the interviewer?
Ask things whose answers would change whether you accept the job. How decisions get made when the data is ambiguous. What happened the last time an experiment contradicted a senior person's intuition. What share of the team's work is ad hoc versus owned. How the previous person in this role was evaluated. Skip anything the careers page answers. You are also being read on what you thought was worth asking about.
PracHub Data Scientist practice ↗Sources & methodology 2 sources ↗
Official role evidence, timestamped platform data and clearly labeled preparation advice.
- 01PracHub Data Scientist practice ↗
Cross-company practice questions for this role. Not an employer question record.
platform · Accessed 2026-09-22 - 02PracHub interview preparation framework ↗
The shared preparation framework these checkpoints and the seven-day plan follow.
platform · Accessed 2026-09-22
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