Explain confidence interval with an example

Question

Explain confidence interval in simple terms and provide a concrete example.

Codemia · Accepted Answer

To explain confidence intervals, we want to assess the average user engagement increase after implementing a new feature in Grafana Labs. The analytical question is: "What is the estimated average increase in user engagement due to the new feature, and how confident can we be in this estimate?"

**Data Needed:** 
- User engagement metrics before and after implementing the feature (e.g., daily active users, session duration).
- A randomized sample of users who experienced the new feature and a control group who did not.
- Sample sizes for both groups to ensure sufficient power for statistical analysis.

We will conduct a controlled experiment (A/B test) with randomization. The key steps include:
1. Randomly assign users to either the treatment group (new feature) or control group (no feature).
2. Collect user engagement data for a defined period (e.g., 30 days).
3. Calculate the mean engagement for both groups.
4. Use the formula for the confidence interval for the difference in means:
   
   $$ CI = (\bar{X}_{treatment} - \bar{X}_{control}) \pm Z * SE $$
   
   where $ Z $ is the Z-score for the desired confidence level (e.g., 1.96 for 95%) and $ SE $ is the standard error of the difference in means.

Assume we have:
- Treatment group mean engagement ($ \bar{X}_{treatment} $): 120 minutes
- Control group mean engagement ($ \bar{X}_{control} $): 100 minutes
- Sample sizes: 100 users in each group.
- Standard deviations (SD): Treatment group SD = 30, Control group SD = 25.

First, calculate the pooled standard error (SE):
$$ SE = \sqrt{\frac{SD_{treatment}^2}{n_{treatment}} + \frac{SD_{control}^2}{n_{control}}} = \sqrt{\frac{30^2}{100} + \frac{25^2}{100}} = \sqrt{9 + 6.25} = \sqrt{15.25} \approx 3.91 $$

Next, calculate the confidence interval:
$$ CI = (120 - 100) \pm 1.96 * 3.91 \approx 20 \pm 7.66 $$
Thus, the confidence interval is approximately (12.34, 27.66).

The confidence interval (12.34, 27.66) means we are 95% confident that the new feature increases user engagement by between 12.34 and 27.66 minutes on average compared to the control group. This range gives us an understanding of the effectiveness of the feature. If the interval does not include zero, we can infer that the feature has a statistically significant positive effect on engagement.

Common mistakes in this analysis include:
1. **Ignoring Randomization:** Failing to properly randomize users can introduce bias, leading to incorrect conclusions about the impact of the feature.
2. **Inadequate Sample Size:** A small sample size may lead to wide confidence intervals, making it difficult to draw meaningful conclusions.
3. **Confounding Variables:** Not accounting for variables that may influence engagement can skew results, such as external marketing efforts or seasonal trends.
4. **Misinterpretation of Confidence Intervals:** Confusing confidence intervals with probability; a 95% CI does not mean there’s a 95% chance that the true parameter lies within the interval.

Explain confidence interval with an example

Grafana Labs

What the Interviewer Expects

Key Topics to Cover

How to Approach This

Possible Follow-up Questions

Sharpen Your Skills on Codemia

Sample Answer

Problem Setup

Methodology

Submit Your Answer

Grafana Labs Data Scientist Interview Guide

Related Questions

Explain Bayesian vs frequentist with an example

Explain p-value with an example

Interpret no significant difference from an experiment

Design an A/B test for a recommendation algorithm

Calculate conditional probability for user retention