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Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. [1] Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio.
The concept of data type is similar to the concept of level of measurement, but more specific. For example, count data requires a different distribution (e.g. a Poisson distribution or binomial distribution) than non-negative real-valued data require, but both fall under the same level of measurement (a ratio scale).
Some data are measured at the interval level. Numbers indicate the magnitude of difference between items, but there is no absolute zero point. Examples are attitude scales and opinion scales. Some data are measured at the ratio level. Numbers indicate magnitude of difference and there is a fixed zero point. Ratios can be calculated.
[1]: 2 These data exist on an ordinal scale, one of four levels of measurement described by S. S. Stevens in 1946. The ordinal scale is distinguished from the nominal scale by having a ranking. [2] It also differs from the interval scale and ratio scale by not having category widths that represent equal increments of the underlying attribute. [3]
These extensions converge with the family of intra-class correlations (ICCs), so there is a conceptually related way of estimating reliability for each level of measurement from nominal (kappa) to ordinal (ordinal kappa or ICC—stretching assumptions) to interval (ICC, or ordinal kappa—treating the interval scale as ordinal), and ratio (ICCs).
For example, most temperature scales (e.g., Celsius, Fahrenheit etc.) are interval scales with arbitrary zeros, so the computed coefficient of variation would be different depending on the scale used. On the other hand, Kelvin temperature has a meaningful zero, the complete absence of thermal energy, and thus is a ratio scale. In plain language ...
A base-10 log scale is used for the Y-axis of the bottom left graph, and the Y-axis ranges from 0.1 to 1000. The top right graph uses a log-10 scale for just the X-axis, and the bottom right graph uses a log-10 scale for both the X axis and the Y-axis. Presentation of data on a logarithmic scale can be helpful when the data:
The calculation of likelihood ratios for tests with continuous values or more than two outcomes is similar to the calculation for dichotomous outcomes; a separate likelihood ratio is simply calculated for every level of test result and is called interval or stratum specific likelihood ratios. [6]