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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, degrees Kelvin) 
Attribute  Nominal  Ordinal  Interval  Ratio 




 



 
Statistics  Count, Mode, chisquared  + 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  Ztransform, renormalise IQ scores  Scale (zoom in or out) 
Types of relativity  A≠B  A>B  (AB) > (CD)  ? 
Types of absolute  Identity of individual entities  order, seqeuence  intervals, differences  ratios, proportions 
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  nonnegative integers 
Amounts  nonnegative real numbers 
Balances  unbounded, positive or negative values. 
Circles  (partially ordered, but in a circle). e.g. the points of the compass 
Fill in the table Thurstone as a transf? Ztransf Curve shapes e.g. logexp. v.diff graphs, but .. Has a zero / not. Has a unit / not Proportions preserved; intervals preserved; Diffs are absolute Full ordering / partial ordering / UK house numbering BUT: No bimodal test.
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