具體細節見自己寫的文檔，F盤
Nominal,Ordinal,Interval and Ratio分別是定類、定序、定距、定比,定類變量值只是分類,如性別變量的男女；定序變量值可以排序,但不能加減,如年級變量；定距變量值是數字型變量,可以加減；定比變量值和定距變量值唯一區別是不存在基準0,即當變量值爲0時不是表示沒有,如溫度變量,當溫度爲0時,並不是表示沒有溫度,這樣溫度就爲定距變量,而不是定比變量.
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