Violin Plot | Tunny docs

Overview

A violin plot shows the estimated probability density of a numeric variable as a filled curve, mirrored around a central axis so it reads like a violin. The width of the curve at a given value is proportional to how likely that value is, so the shape of the distribution — its peaks, tails, and skew — is visible directly instead of being reduced to a few summary numbers.

It sits between the histogram and the box plot. Like a histogram it shows the shape of the distribution, including whether it has one peak or several; unlike a histogram it is a smooth continuous curve, so the apparent shape does not depend on a bin size. Like a box plot it can be lined up side by side for comparison; unlike a box plot, it does not discard the shape between the quartiles. It is worth reading alongside Histogram and Box Plot.

Kernel Density Estimation

The curve is a kernel density estimate (KDE). Each observation contributes a kernel — a smooth bump centred on its value — and the estimate is their average:

$\hat{f}(x) = \frac{1}{n h} \sum_{i=1}^{n} K!\left(\frac{x - x_i}{h}\right)$

Tunny Dashboard uses a Gaussian kernel $K(t) = \frac{1}{\sqrt{2\pi}} e^{-t^2/2}$ and evaluates the estimate on a fixed grid of 128 points spanning the data range plus two bandwidths at each end. Because the estimate is a sum of bumps, values that cluster in two places produce two peaks — exactly the multimodality a box plot cannot show.

Bandwidth

The bandwidth $h$ controls how wide each kernel is, and therefore how smooth the curve looks. Tunny Dashboard chooses it automatically with a robust variant of Scott's rule:

$h = 1.06 \cdot \min\left(\sigma, \frac{\mathrm{IQR}}{1.34}\right) \cdot n^{-1/5}$

The constant $1.06$ is Scott's normal-reference factor and $\sigma$ is the population standard deviation. The $\min(\sigma, \mathrm{IQR}/1.34)$ term is the robust part: the usual normal-reference form uses $\sigma$ alone, but a single outlier can inflate $\sigma$ and over-smooth the whole curve. Taking the smaller of the two spread estimates keeps the bandwidth close to the bulk of the data — the same idea as the Freedman–Diaconis rule for histograms. This $\min$ form comes from Silverman's rule of thumb.

If the bandwidth is zero or non-finite — every value identical, or the spread collapsing to zero — a density estimate is not meaningful. Such a group is skipped and reported instead of being drawn.

Reading a Violin Plot

A single peak means the values concentrate around one region; the peak's position is a robust read on the distribution's centre.
Two or more peaks mean the values cluster into distinct groups. This is the main reason to prefer a violin plot over a box plot: two very different bimodal distributions can share the same five-number summary.
A long, thin tail means rare values stretch the range. The curve stays narrow there because few observations support it.
Comparison across violins: with every violin scaled to the same maximum width, a tall, narrow shape means the values are tightly concentrated, while a short, wide shape means they are spread out. Comparing widths is only meaningful because the scale is shared, and the app draws a median marker so the centre of each distribution stays visible.

Characteristics and Limitations

The apparent shape depends on the bandwidth. A small bandwidth can reveal spurious bumps in small samples; a large one can merge genuine modes. The automatic rule is a starting point, not a definitive answer, so a shape that appears at only one bandwidth should be treated with care.
The estimate is smoothed and can extend slightly beyond the smallest and largest observed values, because the grid spans two bandwidths past each end. The curve estimates the underlying distribution; it is not a record of the data.
The equal-width scaling makes shapes comparable but hides sample size: a level with a handful of trials and a level with thousands both reach the same width. Check the trial counts when a difference looks important.
A group needs at least two finite, non-identical values to estimate a density; smaller or constant groups are skipped.

Where It Is Used in the App

Violin Plot widget: shows the density of each numeric objective or parameter side by side, or splits one numeric column by the levels of a categorical parameter. It is the first view to reach for when the shape of a distribution — especially whether it is multimodal — matters more than its mean or quartiles.

References

Scott, D. W. (1979). On optimal and data-based histograms. Biometrika, 66(3), 605–610. https://doi.org/10.1093/biomet/66.3.605
Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman & Hall.
Wand, M. P., & Jones, M. C. (1995). Kernel Smoothing. Chapman & Hall.