Editing Level of measurement (section)

===Other proposed typologies===
Typologies aside from Stevens's typology have been proposed. For instance, [[Frederick Mosteller|Mosteller]] and [[John Tukey|Tukey]] (1977) and Nelder (1990)<ref>Nelder, J. A. (1990). The knowledge needed to computerise the analysis and interpretation of statistical information. In ''Expert systems and artificial intelligence: the need for information about data''. Library Association Report, London, March, 23–27.</ref> described continuous counts, continuous ratios, count ratios, and categorical modes of data. See also Chrisman (1998), van den Berg (1991).<ref>van den Berg, G. (1991). ''Choosing an analysis method''. Leiden: DSWO Press</ref>

==== Mosteller and Tukey's typology (1977) ====
Mosteller and Tukey<ref name="Mosteller"/> noted that the four levels are not exhaustive and proposed seven instead:
# Names
# Grades (ordered labels like beginner, intermediate, advanced)
# Ranks (orders with 1 being the smallest or largest, 2 the next smallest or largest, and so on)
# Counted fractions (bound by 0 and 1)
# Counts (non-negative integers)
# Amounts (non-negative real numbers)
# Balances (any real number)

For example, percentages (a variation on fractions in the Mosteller–Tukey framework) do not fit well into Stevens's framework: No transformation is fully admissible.<ref name = "Velleman and Wilkinson 1993" />

==== Chrisman's typology (1998) ====
Nicholas R. Chrisman<ref name="Chrisman"/> introduced an expanded list of levels of measurement to account for various measurements that do not necessarily fit with the traditional notions of levels of measurement. Measurements bound to a range and repeating (like degrees in a circle, clock time, etc.), graded membership categories, and other types of measurement do not fit to Stevens's original work, leading to the introduction of six new levels of measurement, for a total of ten:
# Nominal
# Gradation of membership
# Ordinal
# Interval
# Log-interval
# Extensive ratio
# Cyclical ratio
# Derived ratio
# Counts
# Absolute

While some claim that the extended levels of measurement are rarely used outside of academic geography,<ref name = "Wolman 2006">{{cite journal |title=Measurement and meaningfulness in conservation science |journal=Conservation Biology |volume=20 |issue=6 |pages=1626–1634 |year=2006 |last=Wolman |first=Abel G |s2cid=21372776 |doi=10.1111/j.1523-1739.2006.00531.x|pmid=17181798 |bibcode=2006ConBi..20.1626W }}</ref> graded membership is central to [[fuzzy set theory]], while absolute measurements include probabilities and the plausibility and ignorance in [[Dempster–Shafer theory]]. Cyclical ratio measurements include angles and times. Counts appear to be ratio measurements, but the scale is not arbitrary and fractional counts are commonly meaningless. Log-interval measurements are commonly displayed in stock market graphics. All these types of measurements are commonly used outside academic geography, and do not fit well to Stevens's original work.