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Topic: Ordinal measurement

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	Ordinal number - Wikipedia, the free encyclopedia
		An ordinal is finite if and only if the opposite order is also well-ordered, which is the case if and only if each of its subsets has a greatest element.
		Arithmetic operations on ordinals can be captured by algorithms that transform Cantor normal forms, similar to, but more complicated than, the algorithms for integer arithmetic in terms of the decimal notation usually taught in primary education.
		Ordinals which don't have an immediate predecessor can always be written as a limit of a net of other ordinals (but not necessarily as the limit of a sequence, i.e.
	en.wikipedia.org /wiki/Ordinal_number (1634 words)

	Frequently Asked Questions About Level of Measurement
		Measurement of some attribute of a set of things is the process of assigning numbers or other symbols to the things in such a way that relationships of the numbers or symbols reflect relationships of the attribute being measured.
		As a measure of response effort, the number of pellets might be approximately ratio level, but we would need to consider whether the rat's responses were executed in a consistent way, whether the rat may miss the lever, and so forth.
		Suppose that we had an ordinal scale of temperature, and the null hypothesis was that the distribution of temperatures in July is identical to the distribution in December.
	www.people.vcu.edu /~pdattalo/702SuppRead/FAQs_measure.html (5638 words)

	[No title]
		A variable measured at the nominal level must be classifiable into at least two different categories The categories must be mutually exclusive The categories must be equivalent so we don't compare apples and oranges The categories must be exhaustive Background variables are often measured at the nominal level e.g.
		Ordinal measurement scales Measurements with ordinal scales are ordered in the sense that higher numbers represent higher values.
		For example, if anxiety were measured on an interval scale, then a difference between a score of 10 and a score of 11 would represent the same difference in anxiety as would a difference between a score of 50 and a score of 51.
	www.uky.edu /CommInfoStudies/JAT/ISC/chike/isc321/4LectureNotes.doc (1675 words)

	[No title]
		Ordinal measurement tells us nothing about the size of the difference between ranks; rank 2 may be just behind rank 1 or a long way behind it.
		Interval measurement means that the absolute differences (intervals) between measurements are meaningful, but the ratios between measurements are not, because the scale does not have an 'absolute zero' point..
		Many measures such as weight, age, psychological reaction time or the frequencies of an event are examples of ratio measurement scales.
	www.unm.edu /~marni1/stats/measurement.htm (1750 words)

	Week 3 Lecture Notes (Site not responding. Last check: 2007-09-12)
		Reliability and validity of measures: primary concern is the relationship between a measure and the concept that it is intended to mirror.
		Ordinal measurement creates a scale that might ideally represent the variable, and the scores we assign to individuals show whether they fall higher or lower than others on the scale.
		Measure population size by nation: intervals of measurement are equal (one person is one person).
	www.uccs.edu /~pkeilbac/courses/methods/lectures/week3.html (1563 words)

	Measurement
		Measurement is the assignment of numbers to objects in such a way that physical relationships and operations among the objects correspond to arithmetic relationships and operations among the numbers.
		Different levels of measurement are defined by the number and kind of correspondences that hold between the physical relations among objects and the arithmetic relations among the scores.
		The different levels of measurement are distinguished by which arithmetic operations on the measured scores have counterparts in physical operations on the objects.
	www.analytictech.com /mb313/measurem.htm (1792 words)

	Article Template
		That is, the variables represented nominal scale are named nominal variables, the variables represented ordinal scale are called ordinal variables and so forth.
		Ordinal variables, like nominal variables, classify persons or objects but also rank them in terms of the degree to which they possess a characteristic of interest.In other words, ordinal variables put persons or objects in order from highest to lowest or from most to least.
		Interval variables have all the characteristics of nominal and ordinal variables, but also have equal intervals.Most of the tests used in educational research, such as achievement, aptitude, motivation, and attitude tests are treated as interval variables.
	coe.sdsu.edu /eet/Articles/measurescales/start.htm (573 words)

	Ordinal vs. Ratio Revisited Again
		One example shows that we have the strong tendency to treat ordinal scales as interval, contrary to the empirical fact that the spacing between the categories is unknown.
		That is, ordinal homomorphisms do not restrict the spacing of the categories, but only their order, since the spacing is unknown.
		Had the measures given in Roberts' example of the meaninglessness of averaged ordinal scores been ratio, all permissible transformations would have invariantly maintained the same proportionate difference between the individual measures and between the groups' average measures.
	www.rasch.org /rmt/rmt182e.htm (1749 words)

	Economics Interactive (Site not responding. Last check: 2007-09-12)
		All variables that are cardinally measurable are also ordinally measurable, although the reverse may not be true.
		Ordinal measurement of utility Satisfaction is not cardinally measurable.
		Thus, ordinal utility analysis cannot tell us, for example, that one fried chicken yields 147 utils more satisfaction for the president than a few pieces of dry white toast—all that really matters is that he prefers the chicken to the toast.
	www.unc.edu /~rbyrns/Economicae/Essays/CardOrdinal.htm (516 words)

	Draft 1
		Since a criterion measurement that can be used for assessing item quality typically is lacking, the items as a group are assumed to measure what they are supposed to measure, and scores based on this assumption are used to evaluate individual items.
		While an unreliable measure cannot be a valid measure of anything, a reliable measure is not a valid measure unless it correlates with the dimension of interest and does not correlate with irrelevant factors (Heise and Bohrnstedt 1970).
		Lacking a criterion measure to use as a standard for correlations, validity has to be assessed in terms of judgments about whether item content obviously measures the dimension of interest, or in terms of how well measurements work in predicting outcomes that are theoretically expected.
	www.indiana.edu /~socpsy/papers/Measurement.htm (4398 words)

	POWERMUTT: Levels of Measurement
		Party is, on its face, a pure example of a nominal variable, with the values of the variable being simply the names of the parties (or arbitrary numbers used, for convenience, in place of the names).
		Level of measurement is important because the higher the level of measurement of a variable (note that "level of measurement" is itself an ordinal measure) the more powerful are the statistical techniques that can be used to analyze it.
		You can also use certain measures that tell you how strong the relationship is between region and vote, and the likelihood that the relationship occurred by chance.
	www.csupomona.edu /~jlkorey/POWERMUTT/Topics/levels_of_measurement.html (1786 words)

	Ch1 Measurement Pt2
		Although indirect measurement has played a prominent role in the development of the hard-core physical sciences, such as physics and chemistry, it is especially important in those realms of scientific research that are concerned with what goes on inside living organisms.
		Thus, the protuberance or depression of the skull in one location was taken as a measure of self-esteem (the greater the protuberance, the higher the self-esteem, and vice versa); elsewhere, it was a measure of cautiousness, benevolence, combativeness, or of some other item in a rather long list of such attributes.
		The shortcoming of the phrenologists' measures was not that they were unreliable, but that they were not measuring what they were supposed to be measuring.
	faculty.vassar.edu /lowry/ch1pt2.html (3484 words)

	Research Methods Handout 6A (Site not responding. Last check: 2007-09-12)
		There are different meanings of measurement processes: numbers or other ways of defining categories do not always mean the same thing.
		There are important controversies in the social and behavioral sciences about the proper level of measurement for certain variables such as intelligence.
		This level of measurement is not common in the social sciences.
	www.mtsu.edu /~jsanborn/resmeth/rmh6a.htm (259 words)

	Utility measurement and ordinal utility (from utility and value) -- Encyclopædia Britannica (Site not responding. Last check: 2007-09-12)
		More results on "Utility measurement and ordinal utility (from utility and value)" when you join.
		Measurement is fundamental to the sciences; to engineering, construction, and other technical fields; and to almost all everyday activities.
		Measurements of these figures are much used in surveying land, in building, plastering, and papering, in drawing and engineering, and in...
	www.britannica.com /eb/article?tocId=34299 (873 words)

	Descriptive Statistics (Site not responding. Last check: 2007-09-12)
		Interval measurement orders variables, has an arbitrary (not absolute) zero point, and establishes equal intervals between units of measurement.
		Different measures rarely have the same mean and standard deviation, making it impossible to compare the performance of an individual across different tests.
		Norms are established by administering a test to a large sample of representative subjects and equating raw scores with equivalent scores such as standard scores or percentile ranks.
	faculty-staff.ou.edu /B/Nancy.H.Barry-1/psymet.html (832 words)

	Levels of Measurement (Site not responding. Last check: 2007-09-12)
		The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable.
		At lower levels of measurement, assumptions tend to be less restrictive and data analyses tend to be less sensitive.
		In general, it is desirable to have a higher level of measurement (e.g., interval or ratio) rather than a lower one (nominal or ordinal).
	www.socialresearchmethods.net /kb/measlevl.htm (659 words)

	MESA Memo 64: Measurement for Psychology
		In Figure 1 the measure distance along the horizontal axis which corresponds to a 10 percentile raw score increment from 88% to 98% up the vertical axis is 5 times greater than the measure distance corresponding to a 10 percentile raw score increment from 45% to 55%.
		Each measure is accompanied by a realistic estimate of its precision and a mean square residual-from-expectation evaluation of the extent to which the raw ordinal data from which the measure has been estimated fit the measurement model.
		This is a universal characteristic of all measurement.
	www.rasch.org /memo64.htm (10441 words)

	Introduction to theScales of Measurement
		It is important to know what scale of measurement was used for a variable, because it determines what statistics are appropriate to use in analyzing the data.
		In ordinal measurement, the numbers have one key numeric property: the bigger the number, the more that case has of the attribute being measured.
		If these numbers of measured on an interval scale, then a difference of 1 degree (as in 212 versus 211), means the same thing anywhere along the scale (as in, say, -2 and -1).
	www.analytictech.com /mb313/intromeas.htm (674 words)

	Scales of Measurement (Site not responding. Last check: 2007-09-12)
		Intervals between adjacent scale values are equal with respect the the attribute being measured.
		Each "higher" level of measurement includes the measurement principle of the "lower" level of measurement.
		For example, the numbers 8 and 9 in an interval scale indicate that the object assigned a 9 has more of the attribute being measured than does the object assigned an 8 (ordinal property) and that all persons assigned a 9 have equivalent amounts of the attribute being measured (nominal property).
	web.uccs.edu /lbecker/SPSS/scalemeas.htm (395 words)

	Fitness
		It is the set of operational measurements of the property of comparative fitness.
		Viewed as an account of the operational measurement of fitness, probabilistically expected reproductive rates are unobjectionable, indeed attractive.
		Suppose we measure the fitness differences between population a and population b to be in the ratio of 7:3 (e.g.
	plato.stanford.edu /entries/fitness (4660 words)

	Principles of Human Action: Ordinal Measurement (Site not responding. Last check: 2007-09-12)
		At first glance it might seem that values might be measured in monetary terms, which are subject to arithmetic calculations.
		Then is the value of X not exactly twice the value of Y? The latter conclusion, however, rests on the premise that a second $40,000 in my monetary stock has the same value to me as my first $40,000—a premise which will be proven fallacious in Section 4.
		Although ordinal measurements are not subject to arithmetic calculations, the orderings they measure (such as value scales) possess definite mathematical properties.
	www.mindspring.com /~cunningr/pp/cc/HF30017a.html (241 words)

	POWERMUTT: Measurement Basics (Site not responding. Last check: 2007-09-12)
		A measure is valid if it actually measures the concept we are attempting to measure.
		A measure can be reliable without being valid (if we are consistently getting the wrong result).
		Compute a new variable that measures Gore’s vote as a percent of the total vote.
	www.csupomona.edu /~jlkorey/POWERMUTT/Topics/measurement_basics.html (2993 words)

	Levels of Measurement (Site not responding. Last check: 2007-09-12)
		The four levels of measurement are: nominal, ordinal, interval, and ratio.
		Interval Measurement: As in ordinal measurement the attributes are ranked, but in interval measurement the distances between the rankings have meaning and are equal in value.
		Other examples of interval scores are intelligence measures, and manual muscle testing (where a zero doesn't necessary indicate no contraction in the muscle, we just can't determine it by those means).
	www.fiu.edu /~otweb/courses/levels_of_measurement.htm (469 words)

	Elementary Concepts in Statistics
		Ordinal variables allow us to rank order the items we measure in terms of which has less and which has more of the quality represented by the variable, but still they do not allow us to say "how much more." A typical example of an ordinal variable is the socioeconomic status of families.
		The statistical significance of a result is the probability that the observed relationship (e.g., between variables) or a difference (e.g., between means) in a sample occurred by pure chance ("luck of the draw"), and that in the population from which the sample was drawn, no such relationship or differences exist.
		Therefore, every good measure of relations between variables must take into account the overall differentiation of individual scores in the sample and evaluate the relation in terms of (relatively) how much of this differentiation is accounted for by the relation in question.
	www.statsoft.com /textbook/esc.html (4450 words)

	Book: Ordinal Measurement in the Behavioral Sciences (Site not responding. Last check: 2007-09-12)
		It provides the necessary background on ordinal measurement to permit its use to assess psychological and psychophysical tests and scales and interpret the data obtained.
		Ordinal methods more closely reflect the original data, are simple to apply, and can be used in samples of any size.
		ordinal test theory and the unfolding methods that are applicable to cross-cultural studies.
	www.assess.com /Books/b-20930.htm (315 words)

	Basic Statistics Review - Unit 1 - 103.b
		While ordinal numbers provide information about amount with respect to greater than or less than, they do not provide information about how much more or less.
		As with nominal measurement, ordinal measurement may be used exclusively or multiply.
		There may be an issue of ties when an ordinal scale is being used exclusively.
	www.msu.edu /user/sw/statrev/strv103b.htm (414 words)

	Levels of Measurement
		Reflecting only differences in kind, not differences in degree or amount, nominal scale is most primitive form of measurement.
		Fahrenheit scale possesses equal intervals; it’s appropriate to interpret the difference between 40°F and 60°F as representing exactly the same amount of heat as does the difference between 60°F and 80°F.
		If people are weighed on a bathroom scale, measurement is ratio. The distinctive property of ratio measurement is a true zero.
	www.angelfire.com /sd/APSY210/Spring02/Levels.of.meas.handout.htm (126 words)

	STAT-110 Notes (Ch. 3, Sec. 3) (Site not responding. Last check: 2007-09-12)
		In order to be sure that we know what kind of measurement is appropriate for our desired result, we will define different scales of measurement.
		Measuring hair color is an example of a nominal scale.
		The person that comes in first was faster (has more of the property of "speed") than the person who came in second, but we do not know how much faster the winner was, only that he was faster.
	www.stat.sc.edu /~west/courses/110/spring99/lecture/33.html (296 words)

	MULTIDIMENSIONAL SCALING
		In addition to the traditional human similarity judgment, the data can be an "objective" similarity measure (the driving time between pairs of cities) or an index calculated from multivariate data (the proportion of agreement in the votes cast by pairs of senators).
		Torgerson's development required the data to be at the ratio level of measurement, although this was soon generalized to the interval level [8].
		While the data could contain random error, this early type of MDS required that the data be dissimilarities (not similarities), complete (no missing values), and symmetric (the dissimilarity of objects I and J had to equal that of objects J and 1).
	forrest.psych.unc.edu /teaching/p208a/mds/mds.html (3286 words)

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