Box Plot

Box Plot

Overview

Within Compusense Graphing feature, the Box Plot (also known as a box and whisker diagram or boxplot) is one of the available data graphing types. The Box Plot is a non-parametric standardized way of displaying the distribution of data through four groups of equal size known as quartile groups. Data points on the graph outside of a specific range are easily identified as extreme outliers or mild outliers.

The compatible question types with the Box Plot are Category attributes, Line scale attributes, and Choose 1 questions.


Generate the Box Plot

  1. In your test, go to the "Results > Graphs". Filter the data if necessary before going to the next step.

  2. In the left sliding pane, select a Category attribute, or a Line scale attribute, or a Choose 1 question.

  3. In the right sliding pane, select the "Box Plot" data type.



Box Plot Components



1.

Maximum and Minimum .

The maximum point of data spread is the highest value in the panelists' results.

The minimum point of data spread is the lowest value in the panelists' results.


2.

Whiskers . Each quartile group contains 25% of data. The lower whisker represents the data in the first quartile and the upper whisker represents the data in the fourth quartile.

Whiskers can stretch over a wider range of data than the middle quartile groups, but this is not always the case. In our example image, the whiskers for the Sample 1 stretch from the minimum to the maximum data points, but for the Sample 2, the upper whisker is at the same level as the third quartile line.


3.

IQR (Interquartile Range) . The interquartile range represents 50% of data, which is the two middle quartile groups. The box representation of the interquartile range is where the name 'Box Plot' originates from.

The box is bordered by the following lines:

  • Q1 (Lower quartile) - the line between the first and the second quartile groups.
  • Q3 (Upper quartile) - the line between the third and the fourth quartile groups.

Formula: IQR = Q3 - Q1


4.

Median line. Marks the mid-point of the data dividing the box into two parts. Half the data is greater than or equal to this value and half is less. The two parts of the box are not necessarily equal.


5.

Panel mean . The mean value of all data indicated by an X on the plot.


6.

Box table . Hover over any part of the box or whiskers with your mouse (cursor) to bring up a table of individual Box Plot component values for the specific sample.


7.

Extreme Outliers . Panelists whose scores are at least 3 times the IQR above the third quartile (the outer fence) or at least 3 times the IQR below the first quartile (the inner fence). The extreme outliers are indicated by unfilled circles. 

Formulas for:

The outer fence: Q3 + (3 * IQR)

The inner fence: Q1 - (3 * IQR)

Mild Outliers. Panelists whose scores are at least 1.5 times the IQR above the third quartile (the outer fence) or at least 1.5 times the IQR below the first quartile (the inner fence). The mild outliers are indicated by filled circles as seen in the image at the top of this page.

Formulas for:

The outer fence: Q3 + (1.5 * IQR)

The inner fence: Q1 - (1.5 * IQR)

Note Outliers are not necessarily 'bad' data points and should not be removed from the results without further analysis.


8.

Outliers' table . Hover over outlier panelists with your mouse (cursor) to bring up a table containing the panelist name, Code, Sample Set Number, and the score they selected for the specific sample.



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