This framework of distinguishing levels of measurement originated in psychology and is widely criticized by scholars in other disciplines. On the theory of scales of measurement”. Subsequent qualitative data analysis an expanded sourcebook pdf has given meaning to this assertion, but given his attempts to invoke scale type ideas it is doubtful if he understood it himself no measurement theorist I know accepts Stevens’s broad definition of measurement in our view, the only sensible meaning for ‘rule’ is empirically testable laws about the attribute. Discovery of an exception to a classification can be viewed as progress.
Examples of these classifications include gender, nationality, ethnicity, language, genre, style, biological species, and form. In a university one could also use hall of affiliation as an example. Nominal scales were often called qualitative scales, and measurements made on qualitative scales were called qualitative data. However, the rise of qualitative research has made this usage confusing. The numbers in nominal measurement are assigned as labels and have no specific numerical value or meaning. The nominal level is the lowest measurement level used from a statistical point of view.
IQ scores reflect an ordinal scale, in which all scores are meaningful for comparison only. There is no absolute zero, and a 10-point difference may carry different meanings at different points of the scale. Most measurement in the physical sciences and engineering is done on ratio scales. All statistical measures are allowed because all necessary mathematical operations are defined for the ratio scale. The only rule not allowed would be random assignment, for randomness amounts in effect to a nonrule”.
However, so-called nominal measurement involves arbitrary assignment, and the “permissible transformation” is any number for any other. The use of the mean as a measure of the central tendency for the ordinal type is still debatable among those who accept Stevens’s typology. Many behavioural scientists use the mean for ordinal data, anyway. For example, applications of measurement models in educational contexts often indicate that total scores have a fairly linear relationship with measurements across the range of an assessment. Thus, some argue that so long as the unknown interval difference between ordinal scale ranks is not too variable, interval scale statistics such as means can meaningfully be used on ordinal scale variables. Typologies aside from Stevens’ typology has been proposed. Stevens’s framework: No transformation is fully admissible.
Cyclical ratio measurements include angles and times. Counts appear to be ratio measurements, but the scale is not arbitrary and fractional counts are commonly meaningless. Log-interval measurements are commonly displayed in stock market graphics. All these types of measurements are commonly used outside academic geography, and do not fit well to Stevens’ original work. Stevens used to define measurement. Stevens’s theory of scale types. Another issue is that the same variable may be a different scale type depending on how it is measured and on the goals of the analysis.
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For example, hair color is usually thought of as a nominal variable, since it has no apparent ordering. Hue is an interval level variable. Measurement scales and statistics: a clash of paradigms”. Invariably one came up against fundamental physical limits to the accuracy of measurement. The art of physical measurement seemed to be a matter of compromise, of choosing between reciprocally related uncertainties. Multiplying together the conjugate pairs of uncertainty limits mentioned, however, I found that they formed invariant products of not one but two distinct kinds. Although, formally speaking, interval measurement can always be obtained by specification, such specification is theoretically meaningful only if it is implied by the theory and model relevant to the measurement procedure.
Such arguments would be based on the fact that such measures do not really meet the requirements of an interval scale, because it cannot be demonstrated that equal numerical differences at different points on the scale are comparable. An IQ score is not an equal-interval score, as is evident in Table A. 4 in the WISC-III manual. When we come to quantities like IQ or g, as we are presently able to measure them, we shall see later that we have an even lower level of measurement—an ordinal level. This means that the numbers we assign to individuals can only be used to rank them—the number tells us where the individual comes in the rank order and nothing else. Ideally, a scale of measurement should have a true zero-point and identical intervals.