How do you visually represent statistical uncertainty in a chart?
This tests your ability to communicate statistical nuance beyond simple averages. A great answer discusses error bars (specifying CI vs. SD), then moves to richer visualizations like graded error bars or violin plots.
What's really being asked
This question tests your statistical literacy and data visualization skills. The interviewer wants to see if you understand that a point estimate, like an average conversion rate, is incomplete without a measure of its uncertainty. They are evaluating your ability to choose the right visualization to communicate complex results clearly and honestly, avoiding common misinterpretations. It separates candidates who just report numbers from those who can tell a statistically sound story with data.
The full answer
A strong answer proposes a few options, ordered by complexity and audience. First, the simplest method is adding error bars to the bar chart, but you must specify what they represent. A 95% confidence interval is standard for A/B tests. Second, for a more nuanced view, suggest replacing the bars with a visualization that shows the distribution, like a box plot (showing quartiles) or a violin plot (showing the full probability density). Third, mention advanced techniques like graded error bars (using different color intensities for different confidence levels, e.g., 80% and 95%) or hypothetical outcome plots (HOPs), which animate potential outcomes to give an intuitive feel for the uncertainty.
The mistakes people make
The biggest red flag is saying "I'd add error bars" without any further qualification. This is an incomplete answer because error bars can represent standard deviation, standard error of the mean, or a confidence interval—all of which mean very different things. Another weak answer is suggesting 3D charts or other "chart junk" that adds complexity without clarifying the uncertainty. Finally, failing to consider the audience is a mistake; a simple confidence interval might be best for a business stakeholder, while a violin plot might be better for a data science team.
What usually comes next
Expect questions like: "When would you use a 90% vs. a 95% confidence interval?", "How would you explain a confidence interval to a non-technical product manager?", or "What if the distributions are not normal? How does that affect your choice of visualization?". Be prepared to discuss the trade-off between statistical rigor and ease of interpretation.
A concrete example
For an A/B test comparing conversion rates, don't just show Bar A at 5.2% and Bar B at 5.5%. Show Bar A at 5.2% with an error bar representing a 95% confidence interval of [4.9%, 5.5%]. Show Bar B at 5.5% with a CI of [5.1%, 5.9%]. The overlap in the confidence intervals immediately communicates that while B's average is higher, the difference may not be statistically significant. For an even better view, a violin plot for each would show the shape of the posterior distribution of the conversion rate, giving a much richer picture of the uncertainty than a single interval.
Interview question
To best communicate the full probability density of a metric's potential outcomes when comparing two groups in an A/B test, which visualization is most appropriate?
- a.A bar chart with 95% confidence interval error bars
- b.Graded error bars showing both 80% and 95% confidence intervals
- c.A box plot showing quartiles and outliers for each group
- d.A violin plot for each groupCorrect
Why? this is the answer
Violin plots are specifically highlighted in the card as showing the 'full probability density' and providing a 'much richer picture of the uncertainty' compared to other methods. While confidence intervals and box plots show aspects of uncertainty or distribution, they do not convey the entire probability density shape as effectively as a violin plot.
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Read the original → clauswilke.com
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