SLIDE 44 709.049 09 Holzinger Group 44
Scale Empirical Operation Mathem. Group Structure Transf. in Basic Statistics Mathematical Operations
ORDINAL
Determination
Isotonic x’ = f(x) x … mono‐ tonic incr. x ↦ f(x) Median, Percentiles =, ≠, >, <
INTERVAL
Determination
intervals or differences General linear x’ = ax + b x ↦ rx+s Mean, Std.Dev. Rank‐Order Corr., Prod.‐ Moment Corr. =, ≠, >, <, ‐, +
RATIO
Determination
ratios Similarity x’ = ax x ↦ rx Coefficient of variation =, ≠, >, <, ‐, +, , Stevens, S. S. (1946) On the theory of scales of measurement. Science, 103, 677‐680.
NOMINAL
Determination
Permutation x’ = f(x) x … 1‐to‐1 x ↦ f(x) Mode, contingency correlation =, ≠
Slide 2‐15: Categorization of Data (Classic “scales”)