Plotting Q-Q Plots

A Q-Q Plot (Quantile-Quantile Plot) is a probability plot used to compare two probability distributions by plotting their quantiles against each other. If the two distributions being compared are similar, the points in the Q-Q plot will approximately lie on the line y = x. In a Q-Q plot it is possible to compare two empirical probability distribution or an empirical one with a standard probability distribution.

It contains the following attributes:

Attribute	Mandatory	Constraints

Attribute	Mandatory	Constraints
x	Either x or y must be specified	It cannot be a nominal value
y	Either x or y must be specified	It cannot be a nominal value

Properties

The following example is based on the Adult dataset.

Scenario data can be found in the Datasets folder in your Rulex installation.

Category	Properties	Description

Category	Properties	Description
General parameters	Compared distribution	The distribution comparison mode can be selected from the following values, consequently selecting he corresponding options below. Possible values are normal, beta or exponential.
General parameters	Number of quantiles	Defines the number of quantiles displayed in the plot.
Normal distribution parameters	Mean	Normal distribution is a continuous probability distribution where values are symmetrically distributed around the average value, defined here as the Mean μ. The Standard Deviation σ defines how far the displayed values can deviate from the mean. Normal distribution is defined as follows: where: µ is the mean or expectation of the distribution σ is the standard deviation, and σ²is the variance.
Normal distribution parameters	Standard deviation
Beta distribution parameters	Alpha	Beta distribution displays a probabilistic display of probabilities, by defining Alpha (α) and Beta (β) values, which will be used to define the distribution as follows: where:
Beta distribution parameters	Beta
Exponential distribution parameters	Lambda	Exponential distribution calculates the time which occurs between two events, where the Lambda (λ) value specified here is the average number of events in 1 unit of time. The exponential distribution is given by:

Examples

The following examples are based on the Adult dataset.

Type	Description	Result

Type	Description	Result
Basic Q-Q plot with x attribute only	Dragging and dropping the age attribute onto an x cell and selecting Q-Q Plot in the Plot cell will display the Q-Q plot of the age attribute compared with the Normal distribution (default comparison).
Basic Q-Q plot with x and y attributes	Dragging and dropping the hours-per-week onto a y cell will display the Q-Q plot of the age attribute compared with the hours-per-week distribution.