数据处理中四种基本数据类型的区别（Nominal, ordinal, interval, ratio data）

Nominal,Ordinal,Interval and Ratio分别是定类、定序、定距、定比,定类变量值只是分类,如性别变量的男女；定序变量值可以排序,但不能加减,如年级变量；定距变量值是数字型变量,可以加减；定比变量值和定距变量值唯一区别是不存在基准0,即当变量值为0时不是表示没有,如温度变量,当温度为0时,并不是表示没有温度,这样温度就为定距变量,而不是定比变量.

Originally from http://www.psy.gla.ac.uk/~steve/best/ordinal.html

Basic definitions

Nominal	Just names, IDs
Ordinal	Have / represent rank order (e.g. fully agree, mostly agree, somewhat agree)
Interval	Has a fixed size of interval between data points. (E.g. degrees Centigrade)
Ratio	Has a true zero point (e.g. mass, length)

Summary table: The four data types

Attribute	Nominal	Ordinal	Interval	Ratio
Name2	Categorical	Sequence	Equal interval	Ratio
Name3	Set	Fully ordered, rank ordered	Unit size fixed	Zero or ref.pt fixed
Statistics	Count, Mode, chi-squared	+ median, rank order correlation	+ ANOVA, mean, SDev	+ logs??
Example1	Set of participants, makes of car	order of finishing a race	centigrade scale	Degrees Kelvin or absolute
Transformations/ rescaling allowed	Rename	Montonic (any curve that always increases)	Linear	-
Transformations 2	Hash function	Montonic	Add and multiply	multiply?
Transformation examples	1:1 mapping, Assign colours for lines on a chart	Sorting. Log or exp	Z-transform, renormalise IQ scores	Scale (zoom in or out)
Types of relativity	A≠B	A>B	\|(A-B)\| > \|(C-D)\|	?
Types of absolute	Identity of individual entities	order, seqeuence	intervals, differences	ratios, proportions

Transformations

Thurstone scaling takes in ordinal data and generates an interval scale.
Spreadsheet (re)sorting takes any kind of data and generates ordinal data as represented, say, by the row number after sorting.

Log (or log-log, or exp()) transformations create interval data out of ratio or other interval data. This corresponds to the fact that even when a measurement scale has a zero (a ratio scale), the measure of interest may not e.g. may be a difference.

An alternative list of types

(Attributed to Mosteller & Tukey.)

Names
Grades	ordered labels such as Freshman, Sophomore, Junior, Senior
Ranks	starting from one, which may represent either the largest or smallest
Counted fractions	bounded by zero and one. These include percentages, for example.
Counts	non-negative integers
Amounts	non-negative real numbers
Balances	unbounded, positive or negative values.

Circles	(partially ordered, but in a circle). e.g. the points of the compass