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CVS Health·Data Scientist·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

CVS Health data scientist interview with a heavy stats focus, basically a self-contained hypothesis testing case study. Five parts, all connected, and the power calculation at the end is the kind of thing you either know cold or you're winging it in real time.

Questions Asked (5)

Q1

Given a before/after payment accuracy experiment, choose an appropriate hypothesis test and formally state the null and alternative hypotheses.

A/B Testing & ExperimentationProduct Analytics & Metrics
Author's notes

Pretty standard setup once you recognize it's two proportions.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the experiment design: the metric is payment accuracy, likely a proportion (e.g., % of claims paid accurately). Then select a two-proportion z-test (or chi-square test) for comparing the before and after groups, and formally state the null and alternative hypotheses in terms of the difference in proportions. Finally, discuss assumptions and potential pitfalls like non-independence or time trends.

Pro tip: Mention that in a before/after design, you must account for temporal confounders (e.g., seasonality, policy changes) and consider using a difference-in-differences approach if a control group is available. Also, clarify whether the same patients are measured repeatedly (paired data) or independent groups, as this affects the test choice.

1. Clarify the metric and design

Confirm that payment accuracy is a binary outcome per claim (accurate vs. not) and that the before and after groups are independent samples of claims. If the same claims are measured before and after, it's paired data.

2. Choose the appropriate test

For independent proportions, use a two-proportion z-test (or chi-square test). For paired proportions, use McNemar's test. State the test and justify why it fits the data structure.

3. State the hypotheses formally

Define p_before and p_after as the true payment accuracy rates. Null: H0: p_after - p_before = 0 (or p_after = p_before). Alternative: Ha: p_after - p_before ≠ 0 (two-sided) or > 0 / < 0 (one-sided) based on the business question.

4. Check assumptions and discuss limitations

Verify sample size (expected counts ≥5), independence, and random sampling. Discuss potential confounders like time trends, and suggest sensitivity analyses (e.g., difference-in-differences if a control group exists).

5. Interpret results in context

Explain how to interpret the p-value and confidence interval for the difference in proportions, and relate it to practical significance for CVS Health (e.g., cost savings, patient outcomes).

Key Points to Mention

  • Two-proportion z-test for independent samples; McNemar's test for paired data
  • Null hypothesis: no difference in payment accuracy rates (p_after = p_before)
  • Alternative hypothesis: difference in rates (two-sided or one-sided based on business goal)
  • Assumptions: independence, random sampling, large sample size (expected counts ≥5)
  • Potential confounders: time trends, seasonality, policy changes; consider difference-in-differences
  • Practical significance: effect size and confidence interval, not just p-value

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.

Q2

Compute the test statistic and two-sided p-value for the difference in proportions between treatment and control. Also explain when you'd use a pooled versus unpooled standard error and justify your choice here.

A/B Testing & ExperimentationTechnical Trade-offs
Author's notes

This is where I actually had to slow down.

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AI HintsAI Generated

Suggested Approach

First, clarify the data structure and hypotheses, then compute the test statistic using the appropriate standard error formula. Explain the rationale for choosing pooled vs. unpooled SE, and finally calculate the two-sided p-value and interpret it in context.

Pro tip: In practice, always check if the null hypothesis assumes equal proportions; if so, use pooled SE for the test, but report unpooled SE for confidence intervals to avoid misleading precision.

1. Clarify the scenario and hypotheses

Identify the sample sizes, number of successes, and proportions for treatment and control groups. State the null hypothesis (H0: p_treatment = p_control) and alternative (two-sided).

2. Compute the test statistic

Calculate the difference in proportions, then compute the standard error. Use pooled SE if testing H0 of equal proportions; otherwise use unpooled. Then compute z = (p_t - p_c) / SE.

3. Determine pooled vs. unpooled SE

Explain that pooled SE is used when the null hypothesis assumes equal proportions (common in hypothesis testing), while unpooled SE is used when variances are not assumed equal (e.g., confidence intervals or when groups have different variances).

4. Calculate the two-sided p-value

Use the standard normal distribution to find the two-tailed p-value: p = 2 * (1 - Φ(|z|)). If sample sizes are small, consider using a t-distribution or exact methods.

5. Interpret and justify choice

Interpret the p-value in the context of the business problem. Justify why you chose pooled or unpooled SE, emphasizing that the choice depends on the hypothesis and assumptions.

Key Points to Mention

  • Difference in proportions formula: (p_treatment - p_control)
  • Pooled standard error formula: sqrt(p_pool * (1 - p_pool) * (1/n_t + 1/n_c))
  • Unpooled standard error formula: sqrt(p_t*(1-p_t)/n_t + p_c*(1-p_c)/n_c)
  • Use pooled SE when testing H0: p_t = p_c because it assumes equal variances under the null.
  • Use unpooled SE for confidence intervals or when variances are not assumed equal.
  • Two-sided p-value calculation using z-score and normal approximation, with considerations for small samples.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.

Q3

Build a 95% confidence interval for the difference in proportions (treatment minus control) using the experiment data.

A/B Testing & ExperimentationProduct Analytics & Metrics
Author's notes

Straightforward after the test statistic question.

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AI HintsAI Generated

Suggested Approach

First, clarify the data structure: identify the number of successes and total observations in each group. Then compute the sample proportions, their difference, and the standard error using the pooled or unpooled formula. Finally, construct the 95% confidence interval using the appropriate z-critical value (1.96) and interpret the result in the context of the experiment.

Pro tip: Always check the assumptions: ensure that the sample sizes are large enough for the normal approximation to hold (e.g., at least 10 successes and 10 failures in each group). If not, mention alternative methods like exact or Bayesian approaches.

1. Identify the data and parameters

Determine the number of successes and total observations for both treatment and control groups. Define p_treatment and p_control as the proportions of interest.

2. Calculate sample proportions and difference

Compute the sample proportions: p_hat_treatment = x_treatment / n_treatment and p_hat_control = x_control / n_control. Then calculate the observed difference: d = p_hat_treatment - p_hat_control.

3. Compute the standard error

Calculate the standard error of the difference using the formula: SE = sqrt( p_hat_treatment*(1-p_hat_treatment)/n_treatment + p_hat_control*(1-p_hat_control)/n_control ). Note: For confidence intervals, use unpooled standard error.

4. Determine the critical value and margin of error

For a 95% confidence interval, the critical z-value is approximately 1.96. The margin of error is ME = 1.96 * SE.

5. Construct and interpret the interval

The confidence interval is d ± ME. Interpret it in the context of the experiment: e.g., 'We are 95% confident that the true difference in proportions (treatment minus control) lies between [lower bound] and [upper bound].'

Key Points to Mention

  • Assumptions for normal approximation: independence, random assignment, and sufficient sample size (at least 10 successes and 10 failures per group).
  • Use of unpooled standard error for confidence intervals, as opposed to pooled for hypothesis testing.
  • The z-critical value of 1.96 for 95% confidence level.
  • Interpretation of the confidence interval in terms of the difference in proportions and its practical significance.
  • Potential need for continuity correction or alternative methods if sample sizes are small.
  • Consideration of whether the experiment was randomized and if the groups are independent.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.

Q4

Summarize the experimental results in a single sentence for a non-technical stakeholder, and address whether the improvement is practically significant.

Stakeholder ManagementProduct Analytics & Metrics
Author's notes

The practical significance piece is what they actually care about.

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AI HintsAI Generated

Suggested Approach

Start with a clear, jargon-free one-sentence summary that highlights the business impact (e.g., increased conversion or reduced cost). Then, explain practical significance by comparing the effect size to a meaningful threshold (e.g., ROI, operational feasibility) and acknowledging any limitations or uncertainties.

Pro tip: Tie the improvement to a specific business metric that matters to CVS Health, such as customer retention or prescription adherence, and quantify the impact in dollars or member outcomes to make it tangible.

1. Craft a plain-language summary

Distill the experimental result into one sentence that a non-technical stakeholder can understand, focusing on the 'what' and 'so what' without statistical terms.

2. Quantify the improvement

State the effect size (e.g., 5% lift in conversion) and translate it into a business-relevant unit (e.g., additional prescriptions filled per month).

3. Assess practical significance

Compare the improvement to a pre-defined threshold of meaningfulness (e.g., minimum detectable effect, cost of implementation) and discuss whether it justifies action.

4. Acknowledge limitations and next steps

Briefly mention any caveats (e.g., short test duration, segment-specific effects) and suggest a follow-up or rollout decision.

Key Points to Mention

  • Avoid statistical jargon like p-value or confidence interval; use terms like 'likely' or 'we are confident'.
  • Relate the metric to a key performance indicator for CVS Health, such as customer satisfaction or cost savings.
  • Provide context on the baseline and the magnitude of change (e.g., from 10% to 10.5% conversion).
  • Discuss the cost or effort required to implement the change and whether the lift outweighs it.
  • Mention any potential risks or unintended consequences (e.g., impact on other metrics).
  • Recommend a clear action: scale, iterate, or abandon, based on the practical significance.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.

Q5

Using the normal approximation, calculate the per-group sample size needed to detect an absolute improvement from 96.0% to 96.2% accuracy with 80% power at a two-sided alpha of 0.05. Show the formula and plug in the Z-scores explicitly.

A/B Testing & ExperimentationProduct Analytics & Metrics
Author's notes

Hardest part of the whole thing.

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AI HintsAI Generated

Suggested Approach

Start by clearly stating the two-proportion Z-test formula for sample size per group, then plug in the given proportions, alpha, and power. Compute the Z-scores explicitly (Z_alpha/2 = 1.96, Z_beta = 0.84), and carefully calculate the numerator and denominator to arrive at the required sample size. Finally, round up to the nearest integer and briefly interpret the result in the context of detecting a small absolute difference.

Pro tip: When the baseline proportion is very high (like 96%), the required sample size can be surprisingly large; mention that this is due to the small absolute difference and the variance being near its maximum for proportions around 0.5, but actually variance is p(1-p) which is smaller for extreme p, so the large sample size is driven by the tiny effect size. Also, note that in practice, you might consider alternative designs like using a more sensitive metric or increasing the effect size of interest.

1. State the formula

Present the standard formula for sample size per group for comparing two proportions: n = (Z_{α/2} * sqrt(2 * p̄ * (1-p̄)) + Z_β * sqrt(p1*(1-p1) + p2*(1-p2)))^2 / (p1 - p2)^2, where p̄ = (p1+p2)/2. Alternatively, use the simpler formula: n = (Z_{α/2} + Z_β)^2 * (p1*(1-p1) + p2*(1-p2)) / (p1 - p2)^2, but clarify which one you're using.

2. Identify parameters

Assign values: p1 = 0.96, p2 = 0.962, absolute difference Δ = 0.002. For two-sided α = 0.05, Z_{α/2} = 1.96. For 80% power, Z_β = 0.84 (or 0.8416).

3. Compute intermediate values

Calculate p1*(1-p1) = 0.96*0.04 = 0.0384, p2*(1-p2) = 0.962*0.038 = 0.036556. Sum = 0.074956. Also compute p̄ = (0.96+0.962)/2 = 0.961, so 2*p̄*(1-p̄) = 2*0.961*0.039 = 0.074958 (if using the first formula).

4. Plug into formula and solve

Using the simpler formula: n = (1.96 + 0.84)^2 * (0.0384 + 0.036556) / (0.002)^2 = (2.8)^2 * 0.074956 / 0.000004 = 7.84 * 0.074956 / 0.000004 ≈ 0.58765 / 0.000004 = 146,912.5. Round up to 146,913 per group. If using the first formula, the result will be very similar.

5. Interpret and sanity-check

State that approximately 146,913 subjects per group are needed. Discuss that this large number is due to the tiny absolute difference (0.2 percentage points) and high baseline accuracy, which makes detection challenging. Mention that such a large sample may not be feasible, so consider practical alternatives.

Key Points to Mention

  • Use of two-proportion Z-test for sample size calculation.
  • Correct Z-scores: 1.96 for two-sided alpha 0.05, 0.84 for 80% power.
  • Formula for sample size per group: n = (Z_{α/2} + Z_β)^2 * (p1(1-p1) + p2(1-p2)) / (p1 - p2)^2.
  • Calculation of variance terms: p1(1-p1) and p2(1-p2).
  • Rounding up to the next integer and interpreting the result in business context.
  • Acknowledging the large sample size and discussing potential trade-offs or alternative approaches.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.