Statistical data type

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, <a href="/facts/Statistical_data/AUBFN97o">data</a> can have any of various types. Statistical data types include <a href="/facts/Categorical_variable/3UQNkLqs">categorical</a> (e.g. <a href="/facts/Country/hormuwdR">country</a>), <a href="/facts/Directional_statistics/ucnUv52T">directional</a> (<a href="/facts/Angle/gFUTEQYq">angles</a> or <a href="/facts/Direction_(geometry)/Tj24mTJ8">directions</a>, e.g. wind measurements), <a href="/facts/Count_data/vPP2VEyk">count</a> (a <a href="/facts/Whole_number/5dNqPnwg">whole number</a> of events), or <a href="/facts/Interval_data/8GAxPxFv">real intervals</a> (e.g. measures of <a href="/facts/Temperature/QyGe4gmj">temperature</a>). 
The data type is a fundamental concept in statistics and controls what sorts of <a href="/facts/Probability_distribution/EpsKKVRu">probability distributions</a> can logically be used to describe the variable, the permissible operations on the variable, the type of <a href="/facts/Regression_analysis/n6z5Tf7K">regression analysis</a> used to predict the variable, etc. The concept of data type is similar to the concept of <a href="/facts/Level_of_measurement/8GAxPxFv">level of measurement</a>, but more specific. For example, count data requires a different distribution (e.g. a <a href="/facts/Poisson_distribution/CvCzXkHr">Poisson distribution</a> or <a href="/facts/Binomial_distribution/UMoFMjDj">binomial distribution</a>) than non-negative <a href="/facts/Real-valued/mGYQu2xt">real-valued</a> data require, but both fall under the same <a href="/facts/Level_of_measurement/8GAxPxFv">level of measurement</a> (a <a href="/facts/Ratio_scale/VFXU56H9">ratio scale</a>).
Various attempts have been made to produce a taxonomy of <a href="/facts/Level_of_measurement/8GAxPxFv">levels of measurement</a>. The psychophysicist <a href="/facts/Stanley_Smith_Stevens/0JHM5XCT">Stanley Smith Stevens</a> defined nominal, ordinal, interval, and ratio scales. Nominal measurements do not have meaningful rank order among values, and permit any one-to-one transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and permit any order-preserving transformation. Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary (as in the case with <a href="/facts/Longitude/HsC61ML9">longitude</a> and <a href="/facts/Temperature/QyGe4gmj">temperature</a> measurements in degree <a href="/facts/Celsius/okAEu1CA">Celsius</a> or degree <a href="/facts/Fahrenheit/2TVmyJod">Fahrenheit</a>), and permit any linear transformation. Ratio measurements have both a meaningful zero value and the distances between different measurements defined, and permit any rescaling transformation.
Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as <a href="/facts/Categorical_variable/3UQNkLqs">categorical variables</a>, whereas ratio and interval measurements are grouped together as <a href="/facts/Variable_(mathematics)/VbQlrvKz">quantitative variables</a>, which can be either <a href="/facts/Probability_distribution/EpsKKVRu">discrete</a> or <a href="/facts/Probability_distribution/EpsKKVRu">continuous</a>, due to their numerical nature. Such distinctions can often be loosely correlated with <a href="/facts/Data_type/fcx5hgVL">data type</a> in computer science, in that dichotomous categorical variables may be represented with the <a href="/facts/Boolean_data_type/0GWYLDoC">Boolean data type</a>, polytomous categorical variables with arbitrarily assigned <a href="/facts/Integer/PUwwrawx">integers</a> in the <a href="/facts/Integer_(computer_science)/zWabo5M9">integral data type</a>, and continuous variables with the <a href="/facts/Real_data_type/LnUlswXp">real data type</a> involving <a href="/facts/Floating_point/eIckahxe">floating point</a> computation. But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented. 
Other categorizations have been proposed. For example, <a href="/facts/Frederick_Mosteller/LdkVt2Tj">Mosteller</a> and <a href="/facts/John_Tukey/2a5FbPWb">Tukey</a> (1977) distinguished grades, ranks, counted fractions, counts, amounts, and balances. Nelder (1990) described continuous counts, continuous ratios, count ratios, and categorical modes of data. See also Chrisman (1998), van den Berg (1991).
The issue of whether or not it is appropriate to apply different kinds of statistical methods to data obtained from different kinds of measurement procedures is complicated by issues concerning the transformation of variables and the precise interpretation of research questions. "The relationship between the data and what they describe merely reflects the fact that certain kinds of statistical statements may have truth values which are not invariant under some transformations. Whether or not a transformation is sensible to contemplate depends on the question one is trying to answer" (Hand, 2004, p. 82).

Statistical data type open-in-new

Statistical data type