Interview guides · Brillio

Brillio Data Scientist Interview Questions & Guide 2026

A two-week prep plan for Brillio data scientist candidates: write your answer before reading the solution, revisit misses three days later.

The 60-second brief

As a Data Scientist at Brillio, you operate at the intersection of advanced analytics, enterprise digital transformation, and business strategy. You are responsible for transforming complex, ambiguous business challenges into structured data science problems, designing robust predictive models, and building scalable artificial intelligence solutions for Fortune 1000 clients. Your work directly influences enterprise product metrics, operational forecasting, and decision-making frameworks across global industries.

Allocate prep to your weakest link rather than your favourite topic. Of the three things that usually gate the outcome (SQL that is correct under messy joins, sound reasoning about experiments, and structured framing of an open-ended problem), candidates tend to over-invest in modelling theory and under-invest in framing.

Focus areas

Analyse at the account grain, cluster errors
Read NRR on a fixed account cohort
Power experiments for heavy-tailed account revenue

Overview

This role is critical to Brillio because clients look to the firm to turn market disruption into competitive advantage through innovative digital adoption. Whether you are architecting multi-agent generative AI systems, developing time-series forecasting models for supply chain optimization, or designing rigorous experimentation frameworks, your contributions drive measurable commercial performance. You will collaborate closely with cross-functional teams of engineers, product managers, and business stakeholders to deliver high-impact digital products.

Succeeding in this role requires a unique blend of technical depth, product intuition, and business acumen. You must be comfortable working with both structured and unstructured data, validating objectives against statistical measures, and communicating complex technical narratives to executive audiences. Expect an inspiring, fast-paced environment where your analytical rigor and design thinking skills shape the next generation of enterprise AI solutions.

The Brillio interview process

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

HR Screening

A screening call is a matching exercise run by someone who will not evaluate your statistics. They are checking that the work described on your resume is work you personally did, and that its scope matches the level the role is written for. Logistics get settled in the same half hour so nobody spends an interviewer's afternoon on a mismatch. The answer that fails is the one narrated in the plural. If every sentence is 'we built' and 'the team decided', there is nothing specific to write down about you. Name the piece that was yours, the decision you made inside it, and what changed after.

What to demonstrate

Whether the ownership implied by your resume survives one round of follow-up about who actually did which part
Whether your described scope (data size, stakeholders, what shipped) matches the seniority the role is written at
Whether timeline, location and compensation expectations make the rest of the loop worth scheduling

How to prepare

Rewrite your top three resume bullets in the first person singular, each with the decision you made and what moved afterwards, then say them out loud once so the 'we' does not return under pressure
Attach one number to each project: the baseline, the change, and the window it was measured over. Where impact was never measured, say that plainly rather than inventing a figure
Settle your compensation range before the call and give it as a range with a reason behind it, such as current total comp or a competing timeline, instead of deflecting the question twice

Online Technical Assessment

Before anything else, this round is a reading test. You are given a small schema and a question phrased in business language, and most of the difficulty sits in the gap between them. Who counts as an active user, does a refunded order still count as an order, is that date column an event time or a load time. Weak answers start typing immediately and compute something precise about the wrong population. Strong ones pin the definition in one sentence, name the column that encodes it, then write the query. On a timed assessment with nobody to tell, write the definition in a comment anyway.

What to demonstrate

Whether an ambiguous term becomes a specific column and filter before any computation happens
Whether you read the schema for keys and cardinality rather than only for column names
Whether the result answers the question at the grain it was asked at, per user or per session or per day

How to prepare

Take three metrics you already use and write down the exact filter and exact grain behind each, then practise stating one of them in a single sentence out loud
On a schema you have never seen, spend the first minute writing what one row of each table means and which key it is unique on, then predict which joins can duplicate rows
Rehearse a version where the definition changes halfway through, and edit the query you have instead of starting over

Technical Evaluations

Much of what gets scored here happens out loud while you type. Nobody can see your reasoning inside a half-written query, so five silent minutes read as being stuck even when they are not. State the plan in plain language first: which tables, what grain you are aggregating to, and the one filter that defines the population. Then write it. The narration doubles as insurance, because a wrong plan gets caught early and cheaply while a wrong query gets caught at the end with no time left to redo it. A timed statistics section, where one exists, is a separate test with its own clock.

What to demonstrate

Whether the query you write matches the plan you just described
What you do with a hint, meaning whether the correction gets absorbed or the first approach gets defended
Whether you can debug your own wrong output by reading the result set and naming which part of the query produced the anomaly

How to prepare

Solve three problems while screen-sharing into a recording, then watch it back and mark every stretch longer than thirty seconds where you said nothing
Practise compressing the plan into one sentence before typing, then check afterwards whether the finished query actually matched it
Time yourself on statistics questions that carry a business reading, such as what a confidence interval does and does not claim, rather than re-reading notes without a clock

Final Discussion

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

What to demonstrate

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

How to prepare

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

Where candidates lose points

Treating raw request or usage volume as engagement

Most traffic in this domain is emitted by machines. Continuous-integration pipelines, scheduled batch jobs, synthetic monitors, backfills and client retries can all grow by an order of magnitude from one configuration change made by one engineer, and none of it represents a new decision to use the product. The inversion is what makes it dangerous: when the platform degrades, clients retry, so error-driven retry volume rises at the exact moment the customer is most likely to leave, and an engagement dashboard built on raw counts shows growth immediately before a churn. Filter on traffic_class and on successful status before anything else, and keep failed-request volume as its own separate series.

Comparing accounts that received a sales or customer-success touch against those that did not

Assignment of coverage is deliberate and pulls in both directions at once: the largest accounts get a named owner because they are valuable, and the accounts showing distress get one because they are at risk. The comparison therefore mixes a strong positive selection with a strong negative one, and the naive estimate can come out with either sign depending on which assignment rule dominated during the period examined. Nothing about matching on observed size fixes this, because the risk signal that triggered coverage is usually the same signal that predicts the outcome. It needs either an actual randomised or staggered rollout of coverage, or a design built on a capacity constraint or territory boundary that assigns coverage for reasons unrelated to account health.

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.

Ending an analysis without a recommendation or next step

Close with what you would do and what would change your mind, stated as a condition you can check later. If the evidence is genuinely inconclusive, recommend the specific next measurement and say what it costs in time or exposure.

Questions & practice

Explain the internal mathematical mechanics and optimization differences between gradient boosting machines and random forests.

Medium · machine learning and modelling

Approach

Check what information would not exist at prediction time, and exclude it.
Pick an evaluation metric that matches the cost of each error type, not a default.
Set a baseline first, so any model has something honest to beat.

Follow-up

Where could label leakage enter this setup?
What would you monitor after launch to know the model is still valid?

Permutation-test a consumption experiment randomised at account level

Hard · permutation-test · heavy-tails · cuped · experiment-readout

An experiment randomised 900 accounts into two arms. You have one row per account: account_id, arm, consumption_28d (billable units after launch) and consumption_pre (the 28 days before). Consumption is heavy-tailed and the largest account is several percent of the total. Write a permutation test from scratch: winsorise at the pooled 99th percentile as a pre-registered rule, use the difference in arm means of the winsorised outcome as the statistic, and obtain a two-sided p-value from 20,000 relabellings of the account-level arm vector. Report the observed effect, the p-value, and the same test on a CUPED-adjusted outcome.

Approach

Be precise about what the permutation test needs. Under the sharp null of no effect for any account, the outcomes are exchangeable across arm labels, and the test is valid for ANY statistic T(outcomes, labels) provided the identical function is applied to the observed labels and to all 20,000 relabellings. The pooled 99th percentile is a function of the outcome vector alone, so recomputing it inside the loop returns the same number 20,000 times: that is wasted CPU, not a bias, and hoisting it out is an optimisation rather than a correctness fix. Say plainly that capping at all changes the estimand from mean consumption to mean capped consumption; it is not a neutral cleaning step.
The mistake that does invalidate the test is an asymmetry between the observed statistic and the permuted ones, and the easiest way to create it is to derive the cleaning rule from the observed arm labels and then freeze it — winsorise each arm at its own observed 99th percentile, hold those two caps fixed, and permute. The observed value is then computed with caps matched to its own partition while every relabelling is scored with caps belonging to a different one, so the null distribution no longer answers the question the p-value claims to answer. A per-arm cap recomputed consistently inside every permutation is a valid test, but it estimates a contrast whose two sides are capped at different thresholds, so prefer the pooled cap on estimand grounds and pre-register it.
Permute the account-level arm vector, because the account is the randomisation unit. Relabelling anything finer — users, workspaces, requests — generates a null distribution narrower than the design actually supports and returns p-values that are anti-conservative.
Vectorise the null: tile the treatment indicator into a (B, n) matrix and permute along axis 1 with rng.permuted(..., out=...). The statistic is a difference of means, so the treated sum alone determines it and the whole null is one matrix-vector product. Use the two-sided p-value (1 + count(|stat_perm| >= |stat_obs|)) / (B + 1); the plus-one on each side is not cosmetic, it keeps the p-value away from exactly zero and keeps the test valid at finite B.
For CUPED, fit theta = cov(y, x) / var(x) on the pooled data and use that same theta for the observed statistic and every relabelling. Pooled theta, like the pooled cap, carries no label information, so where in the loop you compute it is again only a performance question; fitting theta within arms is what goes wrong, because the adjusted outcome then depends on the labels and an observed-label fit frozen across all 20,000 relabellings breaks the match between observed and permuted statistics. x must be measured entirely before launch, which consumption_pre is. Expected variance reduction is about 1 - corr(y, x)^2; measure the achieved reduction from the two null distributions rather than asserting it.

Worked solution (45 min)

cap_y = np.quantile(df.consumption_28d, 0.99); y = np.minimum(df.consumption_28d.to_numpy(float), cap_y); cap_x = np.quantile(df.consumption_pre, 0.99); x = np.minimum(df.consumption_pre.to_numpy(float), cap_x)
t = (df.arm == 'treatment').to_numpy(); n1 = int(t.sum()); n0 = len(t) - n1; obs = y[t].mean() - y[~t].mean()
rng = np.random.default_rng(11); L = np.tile(t.astype(np.int8), (20_000, 1)); rng.permuted(L, axis=1, out=L); s1 = L @ y; stats = s1/n1 - (y.sum() - s1)/n0
p = (1 + int(np.sum(np.abs(stats) >= abs(obs)))) / (20_000 + 1)
theta = np.cov(y, x, ddof=1)[0,1] / np.var(x, ddof=1); y_adj = y - theta*(x - x.mean()); repeat steps 2 to 4 on y_adj and compare stats.std(ddof=1) between the two runs.

Expected result: A two-sided p-value strictly between 1/20001 and 1, an observed effect expressed in capped billable units per account, and a CUPED null whose standard deviation is smaller than the unadjusted one by roughly sqrt(1 - corr(y, x)^2). The CUPED point estimate stays close to the unadjusted one, since the adjustment removes variance rather than shifting the effect.

Verify it yourself

The permutation null is centred near zero: |mean(stats)| is a small fraction of std(stats).
An A/A run, relabelling arm at random before the test and repeating over seeds, gives roughly uniform p-values with about 5% below 0.05.
std(stats_cuped) < std(stats) whenever corr(y, x) is materially non-zero, and the ratio matches sqrt(1 - r^2) to within simulation noise.
Moving the pooled cap computation inside the permutation loop reproduces the same p-value bit for bit at the same seed — the direct demonstration that a pooled cap carries no label information — while setting the cap to infinity reproduces the uncapped test exactly, so the winsorisation switch is independently verifiable.

Follow-up

The p-value is 0.04 with the cap and 0.31 without it. What do you report, and what did you pre-register?
Colleagues in a shared workspace can see the treated behaviour. How does that change the design and the estimate?
How many accounts would you need to detect a 5% lift given this outcome's distribution?

Bootstrap a confidence interval for net revenue retention

Medium · bootstrap · retention · resampling

You have one row per account with arr_start_cents (ARR twelve months ago) and arr_end_cents (ARR today, zero if churned), covering the fixed cohort of accounts that had ARR twelve months ago. Net revenue retention is sum(arr_end_cents) / sum(arr_start_cents). Write a nonparametric bootstrap from scratch, without scipy.stats.bootstrap: resample accounts with replacement, recompute the ratio of sums on each resample, and return the point estimate with a 95% percentile interval from 10,000 resamples. Also report the interval you would get from the mean of per-account ratios, and explain the difference.

Approach

Resample the account, because the account is the unit the estimand is defined over. One bootstrap draw is a vector of account indices and both numerator and denominator are recomputed from that same draw; resampling the two sides independently destroys the within-account correlation that makes a ratio estimator stable.
Vectorise the draws: idx = rng.integers(0, n, size=(B, n)), then end[idx].sum(axis=1) / start[idx].sum(axis=1). A 10,000 by n index matrix is usually far cheaper than a Python loop; if the matrix is too large for memory, chunk over B rather than reverting to a loop.
Take the interval from np.quantile(ratios, [0.025, 0.975]). The percentile interval differs from estimate +/- 1.96 * bootstrap SE whenever the resample distribution is skewed, which it will be here, and the skew is the thing you want represented.
Compute the mean-of-ratios version on the same resamples, and state the exact relationship rather than guessing which of the two is larger. With r_i = arr_end_i / arr_start_i, the ratio of sums is the arr_start-weighted mean of exactly those r_i, so sum(end)/sum(start) - mean(r) = Cov(arr_start, r) / mean(arr_start) using the population covariance. The gap is positive when larger accounts retain and expand better than smaller ones, and negative when they do not; a cohort whose small accounts churn at a higher rate has positive covariance, which puts the mean of per-account ratios BELOW the ratio of sums. Requires arr_start_i > 0 for every account, which the fixed-cohort definition guarantees; r_i is floored at 0 and unbounded above, so a handful of 4x expansions among small accounts can flip the sign. Compute the covariance and report it instead of asserting a direction.
Report the interval width beside the concentration of the cohort. If the largest account is 12% of starting ARR, a narrow interval is evidence that the resampling unit is wrong rather than evidence that the estimate is precise.

Follow-up

The cohort has 800 accounts and the largest is 12% of starting ARR. How much do you trust a percentile interval here?
How would you extend this to an interval on the year-over-year change in NRR?
Two accounts merged mid-window and one contract was co-termed into the other. How do you keep the cohort fixed?

Extract top-performing product categories month-over-month using dense ranking and partitioning clauses.

Medium · sql and data manipulation

Approach

State the window function and its partition and ordering out loud before writing it.
Compute rates by summing numerator and denominator separately, never by averaging rates.
Say which table is the grain you start from, and join outward from it.

Follow-up

What breaks if events arrive late or out of order?
How would you verify this result without re-running the same query?

Write a query using SQL window functions to calculate the running 30-day moving average of user engagement metrics across regional customer segments.

Medium · sql and data manipulation

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.
Compute rates by summing numerator and denominator separately, never by averaging rates.

Follow-up

What breaks if events arrive late or out of order?
How does the query change if the join becomes one-to-many?

Collapse retried requests into logical operations per account

Medium · window functions · deduplication · null semantics

fct_api_request carries request_id, account_id, api_key_id, idempotency_key (null when the caller supplied none), is_retry, request_at and http_status. For one ISO week, count logical operations rather than HTTP calls: requests sharing (account_id, api_key_id, idempotency_key) collapse to the earliest one, while every request with a null idempotency_key is its own operation. Return per account the raw request count, the logical operation count and the ratio between them, and state which direction a rising 5xx rate pushes that ratio.

Approach

Split the stream before deduplicating. GROUP BY and PARTITION BY treat NULLs as equal to one another, while the = operator does not, so a single grouping pass folds every null-key request in an account into one 'operation' and can cut the count by orders of magnitude.
Deduplicate the keyed rows with ROW_NUMBER() OVER (PARTITION BY account_id, api_key_id, idempotency_key ORDER BY request_at, request_id) and keep rn = 1. Including request_id in the ORDER BY makes the result deterministic when two rows share a millisecond, which they will.
UNION ALL the null-key rows back in unchanged; they need no dedup and must not pass through the partition.
Aggregate per account: count() over the raw week, count() over the union, and the ratio of the two. Report the ratio, not the difference, so accounts of very different sizes are comparable.
Cross-check against is_retry, which flags a resend of the same idempotency key: raw minus logical should sit close to the count of is_retry rows, and a large gap means clients are resending without a key and the dedup is under-counting duplicates.
Name the inversion explicitly: 5xx responses provoke client retries, so amplification rises exactly when reliability falls, and any engagement metric built on raw request counts will show growth during an outage.

Worked solution (25 min)

Filter to the ISO week with request_at >= :week_start AND request_at < :week_start + interval '7 days', and record the raw count per account as the baseline.
Build keyed_dedup: SELECT ... ROW_NUMBER() OVER (PARTITION BY account_id, api_key_id, idempotency_key ORDER BY request_at, request_id) AS rn FROM the week WHERE idempotency_key IS NOT NULL, then keep rn = 1.
Build unkeyed: the same week's rows WHERE idempotency_key IS NULL, taken as-is.
UNION ALL the two, then GROUP BY account_id selecting the logical count; join back to the raw counts and compute raw::numeric / logical.
Validate on one account by comparing raw - logical against COUNT(*) FILTER (WHERE is_retry) for that account and explaining any gap.

Expected result: One row per account with raw_requests, logical_operations and an amplification ratio at or above 1.0, where logical_operations counts each distinct (account_id, api_key_id, idempotency_key) once and each null-key request once.

Verify it yourself

logical_operations is never greater than raw_requests, and the two are equal for accounts whose keys are all distinct.
For accounts with no null idempotency_key, raw_requests - logical_operations is close to the count of is_retry rows.
Deliberately grouping on the key without the null split reproduces a visibly lower count, confirming the NULL collapse is the mechanism.
Re-running the dedup returns the same surviving request_id set, proving the ORDER BY tiebreak made it deterministic.

Follow-up

Which of these two counts belongs in the billable-units metric, and which in an engagement metric?
An account's amplification ratio jumps from 1.05 to 3.0 in a day. Name three causes and the query that separates them.

You observe a sudden 15-percent drop in active daily users over a weekend. Walk through your structured approach for a metric drop diagnosis.

Medium · product sense and metrics

Approach

Restate the decision this analysis has to support, and who acts on the answer.
State what result would change your recommendation, so the answer is falsifiable.
Decompose the metric into the rates that drive it, and say which one you would check first.

Follow-up

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

Define a comprehensive product metric design framework for a newly launched B2B SaaS workflow automation tool.

Medium · product sense and metrics

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.
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 manage competing priorities and tight delivery timelines when working on multiple client-facing AI initiatives simultaneously?

Medium · product sense and metrics

Approach

State what result would change your recommendation, so the answer is falsifiable.
Name one primary metric, then the guardrail that stops it being gamed.
Restate the decision this analysis has to support, and who acts on the answer.

Follow-up

What would you do if the primary metric and the guardrail moved in opposite directions?
How would you detect that the metric is being gamed rather than genuinely improving?

How would you align key results and OKRs with underlying statistical measures for an enterprise analytics dashboard?

Medium · product sense and metrics

Approach

State what result would change your recommendation, so the answer is falsifiable.
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?

Walk through an instance where early stopping ruined an experiment, and explain how you ensure statistical significance without falling prey to p-hacking.

Medium · a/b testing and experimentation

Approach

Name the guardrails that would stop a launch even on a positive primary result.
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.

Follow-up

What would you do if you could not randomise at all?
What would you conclude if the result is positive but the test is underpowered?

How do you determine the required sample size and power for an A/B testing scenario with high variance in baseline user conversion rates?

Medium · a/b testing and experimentation

Approach

State the primary metric and the minimum effect worth shipping, then size the test.
Name the guardrails that would stop a launch even on a positive primary result.
Decide the analysis before seeing data, including how long it runs and when you look.

Follow-up

How would you handle interference between treated and control units?
What would you do if you could not randomise at all?

Triage a sample ratio mismatch before reading the result

Easy · srm · assignment · instrumentation

An account-randomised test assigned arms 50/50 by hashing account_id. Exposure logging recorded 4,200 accounts: 1,987 in treatment and 2,213 in control. A chi-square goodness-of-fit test against the intended 2,100/2,100 split gives chi-square(1) = 12.2, p about 0.0005. The analyst reports the primary metric up 6% in treatment and asks to ship. Explain what the imbalance implies about that 6%, rank the causes you would investigate first given this domain's data, and name for each the single query against fct_api_request or dim_account that confirms or eliminates it.

Approach

State the rule before diagnosing anything: a sample ratio mismatch below a 0.001 alarm threshold invalidates the readout. Whatever mechanism removed 113 accounts from one arm almost certainly removed them non-randomly, which makes it a selection effect on the outcome. The 6% is not to be adjusted, caveated or shipped; it is unusable until the mechanism is named.
Verify the test is testing the right thing. chi-square = (1987 - 2100)^2 / 2100 + (2213 - 2100)^2 / 2100 = 6.08 + 6.08 = 12.16 on one degree of freedom. Confirm the denominator is the intended assignment count rather than the observed total, and that you are testing assignment rather than an analysis population that has already been filtered.
Rank causes by how this domain actually breaks rather than by textbook order: is_internal accounts filtered after assignment instead of before; exposure logged on a code path that returns 5xx more often in one arm, silently dropping those accounts; assignment recorded at first request but exposure at a later event, so accounts that churned in between appear in only one arm; dim_account type-2 versioning giving one account_id two surrogate keys and two hash inputs; deployment_model = 'self_hosted' accounts that never emit exposure telemetry at all.
Attach one discriminating query to each: count arms before the is_internal filter; compare the http_status >= 500 rate by arm on the exposure endpoint in fct_api_request; compare the distribution of created_at and churned_at by arm in dim_account; count distinct account_sk per account_id inside the experiment window; cross-tabulate arm against deployment_model.
Compare counts at three fixed stages, assignment, first exposure, and analysis population, and localise the divergence to one of them. The stage where the arms first separate names the subsystem, and everything downstream of it is a symptom.
Report the outcome as abort, fix, rerun, and be explicit about what survives: the variance estimate for re-powering, the instrumentation fix, and nothing whatsoever about the effect size.

Worked solution (20 min)

Recompute the statistic: two terms of 113^2 / 2100 = 6.08, total 12.16, p about 0.0005 on one degree of freedom, below the 0.001 alarm line.
Pull arm counts at assignment, at first exposure, and in the analysis population, and find the first stage at which they diverge.
At that stage, cross-tabulate arm against is_internal, deployment_model, and the 5xx rate on the exposure endpoint.
Write the abort note naming the mechanism, the corrected code path, and the rerun date, with the effect estimate explicitly withheld.

Expected result: chi-square(1) = 12.16, p about 0.0005, so a 0.001 alarm threshold fires and the readout is abandoned. The divergence is localised to a single pipeline stage by comparing arm counts at assignment, at exposure and at analysis, and the most likely causes in this domain are post-assignment internal-account filtering or exposure logging that fails asymmetrically on 5xx responses.

Verify it yourself

A 113-account shortfall on 2,100 expected is a 5.4% deficit in one arm, which under a sound hash is roughly a 1-in-2,000 event. That is what the 0.001 threshold is calibrated to catch.
Counts at the assignment stage should already be balanced if the bucketing is correct. If they are not, the bug is in the hash or the salt, not in the logging.
Any fix that restores balance by filtering on a variable measured after exposure has conditioned on a post-treatment variable and reintroduces the bias it appears to remove.

Follow-up

The imbalance disappears once you restrict to accounts with at least one successful request. Does that fix the experiment or confirm the bug?
What alarm threshold would you set for this check, and why is 0.05 the wrong one for a diagnostic you run on every experiment every day?
How would you detect a mismatch confined to one segment while the overall split looks clean?

Blended gross margin fell while every segment improved

Medium · mix shift · simpsons paradox · as-of join

Blended gross margin across paying accounts fell from 71 percent to 66 percent over two quarters, yet margin improved inside every plan_tier and every deployment_model. You have fct_usage_daily (account_id, sku_code, usage_date, net_amount_cents, cogs_cents), fct_subscription_period (account_id, plan_tier, term_start_date, term_end_date) and dim_account (account_id, deployment_model, is_internal, effective_from, effective_to). Produce an exact decomposition of the five-point move into mix, rate and interaction terms, and name the segment shift that carries it.

Approach

Write blended margin as a revenue-weighted average of segment margins, m = sum over i of w_i * m_i, where w_i is the segment's share of net_amount_cents. Margin is a ratio of sums, so only revenue weights reproduce the blended figure.
Apply the exact three-term decomposition: delta_m = sum(delta_w_i * m_i0) + sum(w_i0 * delta_m_i) + sum(delta_w_i * delta_m_i), read as mix, rate and interaction. It is exact by construction, so the three terms must sum to the observed change with no residual.
Build segments from as-of joins: take the fct_subscription_period version whose term brackets each usage_date and the dim_account version whose effective_from and effective_to bracket it, rather than joining on is_current and backdating today's attributes over last year's usage.
Run the decomposition on more than one segmentation, at minimum plan_tier, deployment_model and sku_code, since the mix that actually moved may not be the one anybody already suspected.
Once the driving segment is identified, determine whether the shift came from acquisition landing new accounts in a lower-margin segment or from existing accounts migrating, because those have different owners and different remedies.

Follow-up

The interaction term is sometimes large. What does it mean operationally, and when would you prefer a log-mean decomposition that distributes it across the other two terms?
Revenue-weighted average margin is one construction. What changes if leadership wants margin weighted by account count, and which question does each version answer?

Suggested practice checklist

For someone who has spent the last year in notebooks, dashboards or modelling work and has not written raw SQL under time pressure. The first four days rebuild query fluency against a fixture you control and can verify by hand; the last three attach that fluency to the rest of the loop.

Day 1 — Build a fixture you can check answers against

Create a local Postgres or SQLite database with four tables (users, sessions, events, orders) holding roughly 200 rows you generated yourself, so you know the contents well enough to predict every result.
Deliberately seed the cases that break queries: a user with no sessions, a session with no events, two orders sharing a timestamp, a NULL in one join key, and one duplicated user row.
Before writing any SQL, hand-compute five answers on paper (how many users placed at least one order, median orders per ordering user, and three others) and save them as the ground truth for the week.

Deliverable: A one-command seed script plus a text file of five hand-computed answers to grade every later query against.

Day 2 — Joins, filters and NULL semantics

Answer "which users have no orders" three ways (LEFT JOIN with IS NULL, NOT EXISTS, NOT IN) and confirm that the NOT IN version returns zero rows once the subquery contains a NULL, because the comparison is never TRUE.
Reproduce the LEFT JOIN that silently collapses to an inner join by putting a right-table predicate in WHERE, then fix it by moving the predicate into the ON clause, and record both row counts.
Create a fan-out bug on purpose by joining orders to order_items and summing the order total, then correct it with a pre-aggregated subquery and explain in one line which table changed the grain.

Deliverable: One annotated .sql file holding the three join traps, each with the wrong result and the corrected result side by side.

Day 3 — Window functions and frames

Write three window queries against the fixture: a running order total per user, the rank of each order within its user by value, and the day gap to that user's previous order, then check each against the day-one ground truth.
Run ROW_NUMBER, RANK and DENSE_RANK over a column containing ties, print all three side by side, and write one sentence on when each is the correct choice.
Switch one query from the default frame (RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW, which is what you get when ORDER BY is present and no frame is written) to ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW, and explain why the output differs only when the ORDER BY column has duplicates.

Deliverable: Three verified window queries plus a short note explaining the RANGE versus ROWS difference in your own words.

Day 4 — The four analytical query patterns

Write a monthly retention grid: first order month per user, then months-since-first as the column, and verify that month zero equals the cohort size exactly.
Sessionize the events table under a 30-minute inactivity rule using LAG plus a cumulative sum over a new-session flag.
Build a four-step funnel that counts distinct users rather than events at each step, and state the rule you applied to a user who reaches step three without ever logging step two.

Deliverable: One file with the retention, sessionization and funnel patterns, each carrying a one-line note on the assumption it bakes in.

Day 5 — Write SQL the way you will have to write it live

Set a 12-minute timer and solve three medium prompts in a plain editor with no execution and no autocomplete, then run them and tally syntax errors separately from logic errors.
Narrate one solution aloud while writing it, stating the grain of each intermediate result (one row per user, one row per user-day) before you type its body.
Rewrite your slowest solution as a CTE chain where every CTE name states its grain, and time yourself re-solving it from blank.

Deliverable: A recording of one narrated solution plus an error tally that separates syntax from logic.

Day 6 — One day for everything that is not SQL

Write the preconditions of the two-sample t-test from memory, then check them: independent observations, and a difference in means whose sampling distribution is approximately normal, which at large sample sizes follows from the central limit theorem rather than from normality of the raw values.
Write the difference between an odds ratio from logistic regression and a relative risk, and state the condition under which the two are close (low outcome prevalence).
Prepare a 90-second answer to "how would you know this model is any good" that names the metric, the baseline you would beat, and the cost of the errors you care about.

Deliverable: One page of notes covering test preconditions, the odds-ratio caveat and the model-quality answer.

Day 7 — Full loop rehearsal

Run a 45-minute mock with someone willing to interrupt: 20 minutes of SQL, 15 minutes defining a metric, 10 minutes on a past project.
Re-solve from blank the two queries you were slowest on this week and compare the times against day five.
Write a five-line answer to "walk me through a project" that puts a number in the first sentence and names the decision the work changed.

Deliverable: Mock feedback notes plus a timed project narrative you can deliver without reading it.

The project you argued against

Saying no well is a senior skill and it is rarely rehearsed. Think of a time you told someone their analysis was not worth doing, or that the experiment could not answer their question at the sample size available. Explain what you offered instead. Refusal without an alternative reads as obstruction rather than judgement.

How do you approach feature selection and model explainability using SHAP values when stakeholders demand interpretability in regulated industries?

Medium · behavioural and stakeholder questions

Approach

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

Follow-up

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

Allocate one analyst week across three competing requests

Easy · prioritisation · stakeholders · scoping

Three requests arrive the same morning and you have one week. Finance wants per-account gross margin from fct_usage_daily for a pricing review in three weeks. Sales wants a renewal-risk list for accounts with term_end_date inside 60 days. A product manager wants an experiment readout for a decision being taken on Thursday. Produce your allocation with hours attached, what you say to whoever receives less, and one thing you refuse to do this week, with the reason each decision is defensible to the person it costs.

Approach

The interviewer is probing whether you prioritise on decision timing and reversibility or on who asked most forcefully. Sort by the date each decision is actually taken and by what the default outcome is if nothing arrives.
Apply that sort concretely. The Thursday readout has a hard irreversible deadline and no value afterwards. The pricing review has three weeks of slack. The renewal list has a rolling deadline set by term_end_date, so part of it is urgent this week and the rest is not, which means it can be split rather than deferred whole.
Find the cheapest sufficient version of each request rather than the full version. The readout goes in full. The renewal list ships as a filtered query over renewal-eligible accounts ranked by two inspectable signals rather than as a model. The margin work is scoped to the accounts that dominate the pricing decision, since revenue is heavily skewed and the tail will not change the conclusion.
Make the trade visible in one written note to all three at once, with dates. Telling each person separately that they are the priority is how an allocation becomes a credibility problem.
Refuse something explicitly and say why. The model version of the renewal list is the usual candidate, because it cannot be evaluated without a holdout nobody has agreed to yet, and building it this week forecloses that.
Leave slack. A plan with none is a plan to miss the one deadline that cannot move.

Follow-up

The sales leader escalates to your manager. What did you already do that makes that a short conversation?
Which of the three deadlines would you push back on, and what exactly would you ask for?
What would you change about how these requests reach you so next week is not the same?

State the measured impact of your own work honestly

Hard · impact · causal inference · self-assessment

You are asked for the business impact of a renewal-risk worklist you shipped nine months ago. Customer success used it, and renewals in the covered segment came in 6 points above the prior year. Coverage was assigned by the team itself: they worked the top of your list and also the accounts they were already worried about. Produce the impact claim you are willing to defend, the number you refuse to claim, and the design you would have asked for at the start.

Approach

The interviewer is probing whether you can separate what you shipped from what you caused, and whether you would have built the measurement in rather than reconstructing it afterwards. Both halves are being scored.
Name the confound precisely. Coverage assignment is doubly selected: the largest accounts get an owner because they are valuable, and distressed accounts get one because they are at risk. The naive covered versus uncovered comparison mixes a strong positive selection with a strong negative one and can come out with either sign depending on which rule dominated. Matching on account size does not fix it, because the risk signal that triggered coverage is the same signal that predicts the outcome.
Split the claims by what each needs to be true. Ranking quality is defensible from precision at k on out-of-time renewals. Adoption is defensible from timestamps showing what share of listed accounts were contacted. The outcome claim is not defensible without a design, and saying so is the point of the exercise.
Look for identification before giving up on it. A capacity cut-off, a territory boundary, or a period in which the list existed but was unstaffed can assign coverage for reasons unrelated to account health, and any of those supports a bounded estimate.
State the design you would ask for now and its price: a randomly withheld slice of the list, held for two renewal quarters, with the expected cost in renewals stated openly. That cost is what it takes to be able to answer this question at all.
Give a bounded number rather than none. Six points with an explicit statement of how much of it you can attribute is more useful than either claiming the whole figure or declining to quantify anything.

Follow-up

Your manager wants the 6 points in a promotion packet. What wording do you accept, and what do you strike?
What would have had to be true for the naive covered versus uncovered comparison to be valid?
If the holdout costs the team real renewals, how do you justify asking for it, and to whom?