Statistics notes - types of data

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This is more for overview of my own than for teaching or exercise.

Overview of the areas

Arithmetic · 'elementary mathematics' and similar concepts
Set theory, Category theory
Geometry and its relatives · Topology
Elementary algebra - Linear algebra - Abstract algebra
Calculus and analysis
Logic
Semi-sorted
 : Information theory · Number theory · Decision theory, game theory · Recreational mathematics · Dynamical systems · Unsorted or hard to sort


Math on data:

  • Statistics as a field
some introduction · areas of statistics
types of data · on random variables, distributions
Virtues and shortcomings of...
on sampling · probability
glossary · references, unsorted
Footnotes on various analyses

Other data analysis, data summarization, learning

Regression · Classification, clustering, decisions · dimensionality reduction · Optimization theory, control theory
Connectionism, neural nets · Evolutionary computing



This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)


One possible typology

Ratio data (ordered, meaningful zero point, linear scale, (often) continuous)

Examples:

  • weight
  • length
  • time amount - reaction time, hours of study, time required to run a marathon
  • age
  • temperature in Kelvin
  • number of responses (overlap with discrete numeric)


Interval data (ordered, no meaningful zero point, possible linear scale, (often) continuous)

Discrete numeric data (ordered, linear scale, discrete)

Ordinal data (ordered, but no obvious numbering so not linear; discrete)

Examples:

  • highest level of education
  • questionnaire items of the disagree/disagree, happy/unhappy type
  • socioeconomic status
  • age groups ('age up to 20', 'age 20-29', 'age 30-39') (note: in this case based on ratio data)
  • ranks

Asking people to rate on a few-point scale is often seen as ordinal, while there is overlap with continuous interval data.


Nominal/categorical data (unordered; qualitative; discrete)

Examples:

  • labels, such as {T,A,G,C}
  • choosing from multiple choice options
  • distinguishers such as {green,blue} or {true,false}, (discrete) gender, blood type
  • brand names
  • left/right-handedness
  • political affiliation


More words

More complex cases

Implications

Further terms that matter

Continuous data refers to valued numbering that is not restricted to be discrete/integer.

so ratio or interval data in the above list.


Quantitative data - basically anything not categorical, so referring to nominal/categorical.

Variables, dimensions, and measurement, and experiments