piecenorms-package {piecenorms}

piecenorms: Calculate a Piecewise Normalised Score Using Class Intervals

Description

piecenorms has been built to calculate normalised data piecewise using class intervals. This is useful in communication of highly skewed data.

Details

For highly skewed data, the package classInt provides a series of options for selecting class intervals. The classInts can be used as the breaks for calculating the piecewise normalisation function piecenorm. The function also allows the user to select their own breaks manually.

For any call to piecenorm, the user provides a vector of observations, a vector of breaks and a direction for the normalisation. The data is then cut into classes and normalised within its class.

Number of Bins:

n = \text{length}(\text{brks}) - 1

Normalisation Class Intervals:

\left(\frac{i-1}{n}, \frac{i}{n}\right] \forall i \in \{1:n\}

In cases where there is only one bin defined as c(min(obs), max(obs)), the function piecenorm resolves to standard minmax normalisation.

The piecenorms package also provides a normalisr R6 class that

• Classifies data into a likely distribution family

• Provides a recommendation of an appropriate normalisation technique

• Provides functionality to apply this normalisation technique to a new data set

This is useful when the user would like to analyse how distributions have changed over time.

Note

As with any non-linear transformation, piecewise normalization preserves ordinal invariance within each class but does not preserve global relative magnitudes. However, it does maintain relative magnitudes within each class. On the other hand, more standard techniques like min-max normalization preserves both ordinal invariance and global relative magnitudes.

Definitions of each are as follows:

• Ordinal Invariance: The property that the order of the data points is preserved. If one normalized value is larger than another, it reflects the same order as in the original data.

• Non-Preservation of Relative Magnitudes (Global): This refers to the loss of the proportionality of the original data values when normalized. If one value is twice as large as another in the original data, this relationship might not be preserved in the normalized data.

• Ordinal Invariance: The property that the order of the data points is preserved. If one normalized value is larger than another, it reflects the same order as in the original data.

Author(s)

Maintainer: David Hammond [e-mail]

See Also

Useful links:

• https://github.com/david-hammond/piecenorms

• Report bugs at https://github.com/david-hammond/piecenorms/issues