Creating Box Plots in Visual Notebooks

Create a Box Plot in Visual Notebooks. Box Plots are used to visualize the distribution of a dataset.

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Configuration

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Visualization Settings

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General

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Legend

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Node Inputs/Outputs

Figure 1: Example box plot

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Examples

Many scientists research penguins for various studies ranging from behavior and predator threats to genetics (their relationship with other species) and migratory patterns. To protect and conserve species is only one reason they are researched so often.

The below examples show a box plot to see the relationship between different variables in different species of penguins. The example data is available in the Visual Notebooks sample datasets.

1. Connect an existing node to the Box Plot node.
2. (optional) If you would like to differentiate this node, enter a name in the Name field. In this case, "Penguin Size" has been entered. This name also appears in the node and as a tab in the dataset.
3. Double-click the Box Plot node. If the Visualization is blank, switch to Dataset and select Run, then switch back to Visualization.
4. Select one or more numeric fields to view. In this case, the "body_mass_g" field is selected.
5. Select Apply.

The dataframe shown below is used in this example. It represents the distribution of penguin body mass measurements in grams against the median measurement. The median is displayed as the horizontal line inside the rectangle.

Figure 2: Example basic box plot

Next, add Group Y-Axis by information to break down the data by category. In this case, species (String) is added. In Configure Visualization Settings, make additional adjustments. In this case, the defaults were changed to these selections:

• A plot title is added
• 3 plots per row is selected
• Show Statistics is toggled on

Figure 3: Example box plot grouped by Y with statistics

In the following examples, the visualization has been configured to include multiple plots in parallel view and to show Statistics.

Figure 4: Example box plots in parallel view with statistics

Next, a comparison of bill length vs. bill depth is shown. To create this view, select both "bill_length_mm" and "bill_depth_mm" for the Select Numeric Columns field.

In Configure Visualization Settings, adjust other settings. In this case, the defaults were changed to these selections:

• Show multiple plots in parallel view is toggled on
• bill_length_mm label is changed to "Bill Length"
• bill_depth_mm label is changed to "Bill Depth"

The dataframe in Figure 5 shows the comparison of bill length distribution to bill depth distribution in millimeters.

Figure 7: Example bill length and depth

Finally, we compare bill length by species and bill depth by species with statistics.

• Select both "bill_length_mm" and "bill_depth_mm" for the Select Numeric Columns field
• In Group Y-axis by, select species (String)

In Configure Visualization Settings, adjust other settings. In this case, the defaults were changed to these selections:

• bill_length_mm label is changed to "Bill Length"
• bill_depth_mm label is changed to "Bill Depth"
• Show Statistics is toggled on
• Show multiple plots in parallel view is toggled on

The dataframe shown below shows the comparison between the bill length distribution by species and the bill depth distribution by species.

Figure 9: Example bill length by species with statistics

Figure 11: Example bill depth by species with statistics

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Background – Quartile Calculation

The Box Plot node produces the first and third quartiles (Q1 and Q3) of your data as part of its output. Interestingly enough, quartile calculation is not an exact science. There are over a dozen commonly used algorithms to calculate quartiles, all of which produce different results. In Visual Notebooks, we use an algorithm that, when met with a quartile index that is a non-integer, uses a weighted average of the two values in your data that surround that quartile index. This weighted average depends on the position of the quartile index in that interval. This algorithm is equivalent to how quartiles are calculated by numpy.percentile by default. Here is the algorithm:

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Our Quartile Algorithm

Let us assume that $ColumnData$ is an array of your column data that has been sorted in ascending order and is 0-indexed. And let us assume that $i$ is the quartile we are calculating (usually $1$ or $3$).

• First, we calculate a value $Numerator$:

  $$Numerator = i \cdot (length(ColumnData) - 1)$$

• Next, we calculate a value $Index$:

  $$Index = \frac{Numerator}{4} \rightarrow \text{round down to nearest integer (floor)}$$

• Now, we calculate a value $Remainder$ (this is almost always an integer):

  $$Remainder = Numerator - 4(Index)$$

• Now, we define a value $NextID$ as:

  $$NextID = Index + 1$$

• Now, we calculate the weighted average $q$ between the datapoints corresponding to $Index$ and $NextID$:

  $$q = \begin{cases} ColumnData[Index] + \frac{(ColumnData[NextID] - ColumnData[Index]) \cdot Remainder}{4} &\text{if } Remainder > 0 \ ColumnData[Index] &\text{else} \end{cases}$$

• And this $q$ is the quartile value we show in the Box Plot node.