Package smile.data.measure

Class IntervalScale

java.lang.Object
smile.data.measure.NumericalMeasure
smile.data.measure.IntervalScale
All Implemented Interfaces:
Serializable, Measure
public class IntervalScale extends NumericalMeasure
The interval scale allows for the degree of difference between items, but not the ratio between them. Examples include temperature with the Celsius scale, which has two defined points (the freezing and boiling point of water at specific conditions) and then separated into 100 intervals. Ratios are not meaningful since 20 °C cannot be said to be "twice as hot" as 10 °C. Other examples include date when measured from an arbitrary epoch (such as AD) since multiplication/division cannot be carried out between any two dates directly. However, ratios of differences can be expressed; for example, one difference can be twice another.

The mode, median, and arithmetic mean are allowed to measure central tendency of interval variables, while measures of statistical dispersion include range and standard deviation. Since one can only divide by differences, one cannot define measures that require some ratios, such as the coefficient of variation. More subtly, while one can define moments about the origin, only central moments are meaningful, since the choice of origin is arbitrary. One can define standardized moments, since ratios of differences are meaningful, but one cannot define the coefficient of variation, since the mean is a moment about the origin, unlike the standard deviation, which is (the square root of) a central moment.

See Also:

  • Constructor Details

    • IntervalScale

      public IntervalScale(NumberFormat format)
      Constructor.
      Parameters:
      format - the number format.

  • Method Details