Debate on Stevens.27s typology Level of measurement

1 debate on stevens s typology

1.1 other proposed typologies

1.1.1 mosteller , tukey s typology (1977)
1.1.2 chrisman s typology (1998)


1.2 scale types , stevens s operational theory of measurement

1.2.1 same variable may different scale type depending on context

debate on stevens s typology

while stevens s typology adopted, still being challenged other theoreticians, particularly in cases of nominal , ordinal types (michell, 1986).

duncan (1986) objected use of word measurement in relation nominal type, stevens (1975) said of own definition of measurement assignment can consistent rule. rule not allowed random assignment, randomness amounts in effect nonrule . however, so-called nominal measurement involves arbitrary assignment, , permissible transformation number other. 1 of points made in lord s (1953) satirical paper on statistical treatment of football numbers.

the use of mean measure of central tendency ordinal type still debatable among accept stevens s typology. many behavioural scientists use mean ordinal data, anyway. justified on basis ordinal type in behavioural science in fact somewhere between true ordinal , interval types; although interval difference between 2 ordinal ranks not constant, of same order of magnitude.

for example, applications of measurement models in educational contexts indicate total scores have linear relationship measurements across range of assessment. thus, argue long unknown interval difference between ordinal scale ranks not variable, interval scale statistics such means can meaningfully used on ordinal scale variables. statistical analysis software such spss requires user select appropriate measurement class each variable. ensures subsequent user errors cannot inadvertently perform meaningless analyses (for example correlation analysis variable on nominal level).

l. l. thurstone made progress toward developing justification obtaining interval type, based on law of comparative judgment. common application of law analytic hierarchy process. further progress made georg rasch (1960), developed probabilistic rasch model provides theoretical basis , justification obtaining interval-level measurements counts of observations such total scores on assessments.

other proposed typologies

typologies aside stevens typology has been proposed. instance, mosteller , tukey (1977), nelder (1990) described continuous counts, continuous ratios, count ratios, , categorical modes of data. see chrisman (1998), van den berg (1991).

mosteller , tukey s typology (1977)

mosteller , tukey noted 4 levels not exhaustive , proposed:

for example, percentages (a variation on fractions in mosteller-tukey framework) not fit stevens’s framework: no transformation admissible.

chrisman s typology (1998)

nicholas r. chrisman introduced expanded list of levels of measurement account various measurements not fit traditional notions of levels of measurement. measurements bound range , repeating (like degrees in circle, clock time, etc.), graded membership categories, , other types of measurement not fit stevens original work, leading introduction of 6 new levels of measurement, total of ten:

while claim extended levels of measurement used outside of academic geography, graded membership central fuzzy set theory, while absolute measurements include probabilities , plausibility , ignorance in dempster-shafer theory. cyclical ratio measurements include angles , times. counts appear ratio measurements, scale not arbitrary , fractional counts commonly meaningless. log-interval measurements commonly displayed in stock market graphics. these types of measurements commonly used outside academic geography, , not fit stevens original work.

scale types , stevens s operational theory of measurement

the theory of scale types intellectual handmaiden stevens s operational theory of measurement , become definitive within psychology , behavioral sciences, despite michell s characterization being quite @ odds measurement in natural sciences (michell, 1999). essentially, operational theory of measurement reaction conclusions of committee established in 1932 british association advancement of science investigate possibility of genuine scientific measurement in psychological , behavioral sciences. committee, became known ferguson committee, published final report (ferguson, et al., 1940, p. 245) in stevens s sone scale (stevens & davis, 1938) object of criticism:

…any law purporting express quantitative relation between sensation intensity , stimulus intensity not merely false in fact meaningless unless , until meaning can given concept of addition applied sensation.

that is, if stevens s sone scale genuinely measured intensity of auditory sensations, evidence such sensations being quantitative attributes needed produced. evidence needed presence of additive structure – concept comprehensively treated german mathematician otto hölder (hölder, 1901). given physicist , measurement theorist norman robert campbell dominated ferguson committee s deliberations, committee concluded measurement in social sciences impossible due lack of concatenation operations. conclusion later rendered false discovery of theory of conjoint measurement debreu (1960) , independently luce & tukey (1964). however, stevens s reaction not conduct experiments test presence of additive structure in sensations, instead render conclusions of ferguson committee null , void proposing new theory of measurement:

paraphrasing n.r. campbell (final report, p.340), may measurement, in broadest sense, defined assignment of numerals objects , events according rules (stevens, 1946, p.677).

stevens influenced ideas of harvard academic, nobel laureate physicist percy bridgman (1927), doctrine of operationism stevens used define measurement. in stevens s definition, example, use of tape measure defines length (the object of measurement) being measurable (and implication quantitative). critics of operationism object confuses relations between 2 objects or events properties of 1 of of objects or events (hardcastle, 1995; michell, 1999; moyer, 1981a,b; rogers, 1989).

the canadian measurement theorist william rozeboom (1966) , trenchant critic of stevens s theory of scale types.

same variable may different scale type depending on context

another issue same variable may different scale type depending on how measured , on goals of analysis. example, hair color thought of nominal variable, since has no apparent ordering. however, possible order colors (including hair colors) in various ways, including hue; known colorimetry. hue interval level variable.