## Appearance

#### Probability density function

Probability density functions are displayed along a central axis for each object set/group possessing the measurement displayed on the y-axis. The probability density function is calculated by summing up individual distribution functions for the measurement of each object, given by a Gaussian distribution:

`f(x;μ,σ) = e^(-1/2*((x-μ)/σ)^2) / (σ*(2*Pi)^(1/2)),`

with `μ`

being the measured value and `σ`

(the approximated bandwidth) of:

`σ = 1.06 * sd * n^(-1/5) / 2,`

with `sd`

being the standard deviation and `n`

being the number of data points.

See the Wikipedia pages for Probability density function and Kernel density estimation for more information.

#### Swarm / Box and whisker plot

A **swarm plot** is overlaid if the number of objects per object set/group is equal to or less than 150. In this display, each point is an object within the object set.

If the number of objects for any object set/group is greater than 150, a **box and whisker plot** is overlaid. Herein, 1) a point marks the median of all objects of an object set / group for the selected measurement, 2) a thicker box ranges from the top 25% of the data (upper quartile) to the lower 25% (lower quartile) - enclosing the central 50% and 3) a thinner line ranges from minimum to maximum (see image on the right).

#### Significance (Welch's t-test)

When hovering over a violin, the significance (p-value = probability that two mean values originate from the same sample) for that mean value towards the other mean values is displayed according to Welch's t-test and by a star-rating - legend on the right of the plot (image on the right):

- if the p value is greater than 0.05, the star rating is
**o** - if p is smaller than 0.05, but greater than 0.01, the star rating is
***** - if p is smaller than 0.01, but greater than 0.005, the star rating is
****** - if p is smaller than 0.005, the star rating is
** *****

When clicking on a violin, this violin's star ratings are displayed and locked. While locked, hovering above the stars will display the associated p-value. To release the lock, click anywhere else other than on a violin.

## General usage

### Select measurement

As with all charts, to select a measurement, hover over the measurement name (on the y-axis) until it turns red and then click to bring up a menu of the available measurements.

### Select object sets/groups

To modify the object sets/groups that are displayed, hover above the object sets/groups names on the x-axis until they turn red and left click. This will bring up the menu of object sets/groups for you to select and unselect.

A plus-sign on the right of the x axis indicates additional object sets/groups which are currently not displayed. To add these object sets/groups click the plus button and select the sets/groups you want. By default, the number of object sets/groups displayed is fixed, depending on the size of the chart panel, but will be changed automatically if more object sets/groups are selected.