Half Normal Plot
- Visual tool that helps assess symmetry and normality of a dataset.
- Highlights potential outliers by showing points above and below a reference line.
- Can inform judgment about the dataset’s underlying distribution.
Definition
Section titled “Definition”A half-normal plot is a graphical representation of data used to evaluate the symmetry and normality of a statistical distribution and to identify potential outliers and the underlying distribution of a dataset.
Explanation
Section titled “Explanation”To construct a half-normal plot, the data are first sorted in ascending order. A line is drawn from the minimum value on the x-axis to the maximum value on the y-axis. The plotted points are then divided into two halves: one half lies above the line and the other half lies below it. The relative placement of points in the two halves provides a visual indication of symmetry, normality, and potential outliers.
Examples
Section titled “Examples”Example 1 — 10 observations
Section titled “Example 1 — 10 observations”Data: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Result: In the half-normal plot for this data, the points in the lower half fall below the line and the points in the upper half fall above the line. The distribution is symmetrical, with the same number of observations in each half.
Example 2 — 20 observations
Section titled “Example 2 — 20 observations”Data: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
Result: In the half-normal plot for this data, the distribution is not symmetrical because there are more observations in the upper half than in the lower half. This indicates that the distribution is not normal and may have outliers.
Use cases
Section titled “Use cases”- Evaluating the symmetry of a dataset.
- Assessing normality of a statistical distribution.
- Identifying potential outliers.
- Determining the underlying distribution to support statistical inferences.
Notes or pitfalls
Section titled “Notes or pitfalls”- A larger number of observations in the upper half compared with the lower half can indicate non-normality and the presence of outliers.
- Interpretation is visual and based on the division of points relative to the reference line.
Related terms
Section titled “Related terms”- Normality
- Outlier
- Symmetry (statistical)
- Distribution