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108-542: A Likert scale ( / ˈ l ɪ k ər t / LIK -ərt ,) is a psychometric scale named after its inventor, American social psychologist Rensis Likert , which is commonly used in research questionnaires . It is the most widely used approach to scaling responses in survey research, such that the term (or more fully the Likert-type scale ) is often used interchangeably with rating scale , although there are other types of rating scales. Likert distinguished between

216-453: A 'better' response than the preceding value. (This may differ in cases where reverse ordering of the Likert scale is needed). The second, and possibly more important point, is whether the "distance" between each successive item category is equivalent, which is inferred traditionally. For example, in the above five-point Likert item, the inference is that the 'distance' between category 1 and 2

324-446: A 1946 Science article titled "On the theory of scales of measurement". In that article, Stevens claimed that all measurement in science was conducted using four different types of scales that he called "nominal", "ordinal", "interval", and "ratio", unifying both " qualitative " (which are described by his "nominal" type) and " quantitative " (to a different degree, all the rest of his scales). The concept of scale types later received

432-607: A central moment. The ratio type takes its name from the fact that measurement is the estimation of the ratio between a magnitude of a continuous quantity and a unit of measurement of the same kind (Michell, 1997, 1999). Most measurement in the physical sciences and engineering is done on ratio scales. Examples include mass , length , duration , plane angle , energy and electric charge . In contrast to interval scales, ratios can be compared using division . Very informally, many ratio scales can be described as specifying "how much" of something (i.e. an amount or magnitude). Ratio scale

540-588: A classification can be viewed as progress. Numbers may be used to represent the variables but the numbers do not have numerical value or relationship: for example, a globally unique identifier . Examples of these classifications include gender, nationality, ethnicity, language, genre, style, biological species, and form. In a university one could also use residence hall or department affiliation as examples. Other concrete examples are Nominal scales were often called qualitative scales, and measurements made on qualitative scales were called qualitative data. However,

648-470: A granular level psychometric research is concerned with the extent and nature of multidimensionality in each of the items of interest, a relatively new procedure known as bi-factor analysis can be helpful. Bi-factor analysis can decompose "an item's systematic variance in terms of, ideally, two sources, a general factor and one source of additional systematic variance." Key concepts in classical test theory are reliability and validity . A reliable measure

756-404: A high school student's knowledge deduced from a less difficult test. Scores derived by classical test theory do not have this characteristic, and assessment of actual ability (rather than ability relative to other test-takers) must be assessed by comparing scores to those of a "norm group" randomly selected from the population. In fact, all measures derived from classical test theory are dependent on

864-402: A nonrule". Hand says, "Basic psychology texts often begin with Stevens's framework and the ideas are ubiquitous. Indeed, the essential soundness of his hierarchy has been established for representational measurement by mathematicians, determining the invariance properties of mappings from empirical systems to real number continua. Certainly the ideas have been revised, extended, and elaborated, but

972-433: A number of different forms of validity. Criterion-related validity refers to the extent to which a test or scale predicts a sample of behavior, i.e., the criterion, that is "external to the measuring instrument itself." That external sample of behavior can be many things including another test; college grade point average as when the high school SAT is used to predict performance in college; and even behavior that occurred in

1080-425: A positive outcome. On the other hand, even if a researcher presents what he or she believes are equidistant categories, it may not be interpreted as such by the respondent. A good Likert scale, as above, will present a symmetry of categories about a midpoint with clearly defined linguistic qualifiers. In such symmetric scaling, equidistant attributes will typically be more clearly observed or, at least, inferred. It

1188-418: A quantitative relation between sensation intensity and stimulus intensity is not merely false but is in fact meaningless unless and until a meaning can be given to the concept of addition as applied to sensation. That is, if Stevens's sone scale genuinely measured the intensity of auditory sensations, then evidence for such sensations as being quantitative attributes needed to be produced. The evidence needed

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1296-462: A range and repeating (like degrees in a circle, clock time, etc.), graded membership categories, and other types of measurement do not fit to Stevens's original work, leading to the introduction of six new levels of measurement, for a total of ten: While some claim that the extended levels of measurement are rarely used outside of academic geography, graded membership is central to fuzzy set theory , while absolute measurements include probabilities and

1404-559: A relative degree of difference between them. Examples include, on one hand, dichotomous data with dichotomous (or dichotomized) values such as "sick" vs. "healthy" when measuring health, "guilty" vs. "not-guilty" when making judgments in courts, "wrong/false" vs. "right/true" when measuring truth value , and, on the other hand, non-dichotomous data consisting of a spectrum of values, such as "completely agree", "mostly agree", "mostly disagree", "completely disagree" when measuring opinion . The ordinal scale places events in order, but there

1512-412: A scale proper, which emerges from collective responses to a set of items (usually eight or more), and the format in which responses are scored along a range. Technically speaking, a Likert scale refers only to the former. The difference between these two concepts has to do with the distinction Likert made between the underlying phenomenon being investigated and the means of capturing variation that points to

1620-699: A scientist who advanced the development of psychometrics. In 1859, Darwin published his book On the Origin of Species . Darwin described the role of natural selection in the emergence, over time, of different populations of species of plants and animals. The book showed how individual members of a species differ among themselves and how they possess characteristics that are more or less adaptive to their environment. Those with more adaptive characteristics are more likely to survive to procreate and give rise to another generation. Those with less adaptive characteristics are less likely. These ideas stimulated Galton's interest in

1728-399: A set of such items that are highly correlated (that show high internal consistency ) but also that together will capture the full domain under study (which requires less-than perfect correlations). Others hold to a standard by which "All items are assumed to be replications of each other or in other words items are considered to be parallel instruments". By contrast, modern test theory treats

1836-409: A statement. Sometimes an even-point scale is used, where the middle option of "neither agree nor disagree" is not available. This is sometimes called a "forced choice" method, since the neutral option is removed. The neutral option can be seen as an easy option to take when a respondent is unsure, and so whether it is a true neutral option is questionable. A 1987 study found negligible differences between

1944-422: A statistical thinking. Precisely here we see the cancer of testology and testomania of today." More recently, psychometric theory has been applied in the measurement of personality , attitudes , and beliefs , and academic achievement . These latent constructs cannot truly be measured, and much of the research and science in this discipline has been developed in an attempt to measure these constructs as close to

2052-803: A variable on a nominal level). L. L. Thurstone made progress toward developing a justification for obtaining the interval type, based on the law of comparative judgment . A common application of the law is the analytic hierarchy process . Further progress was made by Georg Rasch (1960), who developed the probabilistic Rasch model that provides a theoretical basis and justification for obtaining interval-level measurements from counts of observations such as total scores on assessments. Typologies aside from Stevens's typology have been proposed. For instance, Mosteller and Tukey (1977) and Nelder (1990) described continuous counts, continuous ratios, count ratios, and categorical modes of data. See also Chrisman (1998), van den Berg (1991). Mosteller and Tukey noted that

2160-404: Is 40th, it cannot be said that Devi's position is four times as good as that of Ganga. Ordinal scales only permit the ranking of items from highest to lowest. Ordinal measures have no absolute values, and the real differences between adjacent ranks may not be equal. All that can be said is that one person is higher or lower on the scale than another, but more precise comparisons cannot be made. Thus,

2268-563: Is Wundt's influence that paved the way for others to develop psychological testing. In 1936, the psychometrician L. L. Thurstone , founder and first president of the Psychometric Society, developed and applied a theoretical approach to measurement referred to as the law of comparative judgment , an approach that has close connections to the psychophysical theory of Ernst Heinrich Weber and Gustav Fechner . In addition, Spearman and Thurstone both made important contributions to

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2376-607: Is a field of study within psychology concerned with the theory and technique of measurement . Psychometrics generally covers specialized fields within psychology and education devoted to testing, measurement, assessment, and related activities. Psychometrics is concerned with the objective measurement of latent constructs that cannot be directly observed. Examples of latent constructs include intelligence , introversion , mental disorders , and educational achievement . The levels of individuals on nonobservable latent variables are inferred through mathematical modeling based on what

2484-429: Is a lack of consensus on appropriate procedures for determining the number of latent factors . A usual procedure is to stop factoring when eigenvalues drop below one because the original sphere shrinks. The lack of the cutting points concerns other multivariate methods, also. Multidimensional scaling is a method for finding a simple representation for data with a large number of latent dimensions. Cluster analysis

2592-488: Is adjusted with the Spearman–Brown prediction formula to correspond to the correlation between two full-length tests. Perhaps the most commonly used index of reliability is Cronbach's α , which is equivalent to the mean of all possible split-half coefficients. Other approaches include the intra-class correlation , which is the ratio of variance of measurements of a given target to the variance of all targets. There are

2700-519: Is an approach to finding objects that are like each other. Factor analysis, multidimensional scaling, and cluster analysis are all multivariate descriptive methods used to distill from large amounts of data simpler structures. More recently, structural equation modeling and path analysis represent more sophisticated approaches to working with large covariance matrices . These methods allow statistically sophisticated models to be fitted to data and tested to determine if they are adequate fits. Because at

2808-401: Is difficult, and that such measurements are often misused by laymen, such as with personality tests used in employment procedures. The Standards for Educational and Psychological Measurement gives the following statement on test validity : "validity refers to the degree to which evidence and theory support the interpretations of test scores entailed by proposed uses of tests". Simply put, a test

2916-408: 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. A nominal scale consists only of a number of distinct classes or categories, for example: [Cat, Dog, Rabbit]. Unlike the other scales, no kind of relationship between

3024-615: Is itself sometimes erroneously referred to as being or having a scale, with this error creating pervasive confusion in the literature and parlance of the field. A Likert item is simply a statement that the respondent is asked to evaluate by giving it a quantitative value on any kind of subjective or objective dimension, with level of agreement/disagreement being the dimension most commonly used. Well-designed Likert items exhibit both "symmetry" and "balance". Symmetry means that they contain equal numbers of positive and negative positions whose respective distances apart are bilaterally symmetric about

3132-420: Is little prima facie evidence to suggest that such attributes are anything more than ordinal (Cliff, 1996; Cliff & Keats, 2003; Michell, 2008). In particular, 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. The interval type allows for defining

3240-426: Is no attempt to make the intervals of the scale equal in terms of some rule. Rank orders represent ordinal scales and are frequently used in research relating to qualitative phenomena. A student's rank in his graduation class involves the use of an ordinal scale. One has to be very careful in making a statement about scores based on ordinal scales. For instance, if Devi's position in his class is 10th and Ganga's position

3348-657: Is no widely agreed upon theory. Some of the better-known instruments include the Minnesota Multiphasic Personality Inventory , the Five-Factor Model (or "Big 5") and tools such as Personality and Preference Inventory and the Myers–Briggs Type Indicator . Attitudes have also been studied extensively using psychometric approaches. An alternative method involves the application of unfolding measurement models,

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3456-572: Is not allowed. The mode is allowed. In 1946, Stevens observed that psychological measurement, such as measurement of opinions, usually operates on ordinal scales; thus means and standard deviations have no validity , but they can be used to get ideas for how to improve operationalization of variables used in questionnaires . Most psychological data collected by psychometric instruments and tests, measuring cognitive and other abilities, are ordinal, although some theoreticians have argued they can be treated as interval or ratio scales. However, there

3564-568: Is not valid unless it is used and interpreted in the way it is intended. Two types of tools used to measure personality traits are objective tests and projective measures . Examples of such tests are the: Big Five Inventory (BFI), Minnesota Multiphasic Personality Inventory (MMPI-2), Rorschach Inkblot test , Neurotic Personality Questionnaire KON-2006 , or Eysenck Personality Questionnaire . Some of these tests are helpful because they have adequate reliability and validity , two factors that make tests consistent and accurate reflections of

3672-488: Is observed from individuals' responses to items on tests and scales. Practitioners are described as psychometricians, although not all who engage in psychometric research go by this title. Psychometricians usually possess specific qualifications, such as degrees or certifications, and most are psychologists with advanced graduate training in psychometrics and measurement theory. In addition to traditional academic institutions, practitioners also work for organizations such as

3780-515: Is often used to express an order of magnitude such as for temperature in Orders of magnitude (temperature) . The geometric mean and the harmonic mean are allowed to measure the central tendency, in addition to the mode, median, and arithmetic mean. The studentized range and the coefficient of variation are allowed to measure statistical dispersion. All statistical measures are allowed because all necessary mathematical operations are defined for

3888-503: Is one that measures a construct consistently across time, individuals, and situations. A valid measure is one that measures what it is intended to measure. Reliability is necessary, but not sufficient, for validity. Both reliability and validity can be assessed statistically. Consistency over repeated measures of the same test can be assessed with the Pearson correlation coefficient, and is often called test-retest reliability. Similarly,

3996-448: Is recommended over the standard Wilcoxon signed-rank test . Responses to several Likert questions may be summed providing that all questions use the same Likert scale and that the scale is a defensible approximation to an interval scale, in which case the central limit theorem allows treatment of the data as interval data measuring a latent variable. If the summed responses fulfill these assumptions, parametric statistical tests such as

4104-409: Is related to measures of other constructs as required by theory. Content validity is a demonstration that the items of a test do an adequate job of covering the domain being measured. In a personnel selection example, test content is based on a defined statement or set of statements of knowledge, skill, ability, or other characteristics obtained from a job analysis . Item response theory models

4212-413: Is simply determined by the researcher designing the survey, who makes the decision based on a desired level of detail. However, by convention Likert items tend to be assigned progressive positive integer values. Likert scales typically range from 2 to 10 – with 3, 5, or, 7 being the most common. Further, this progressive structure of the scale is such that each successive Likert item is treated as indicating

4320-444: Is that measurement is "the assignment of numerals to objects or events according to some rule." This definition was introduced in a 1946 Science article in which Stevens proposed four levels of measurement . Although widely adopted, this definition differs in important respects from the more classical definition of measurement adopted in the physical sciences, namely that scientific measurement entails "the estimation or discovery of

4428-515: Is that the appropriate type of analysis is dependent on how the Likert scale has been presented. The validity of such measures depends on the underlying interval nature of the scale. If interval nature is assumed for a comparison of two groups, the paired samples t -test is not inappropriate. If non-parametric tests are to be performed the Pratt (1959) modification to the Wilcoxon signed-rank test

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4536-404: Is the intellectual handmaiden to Stevens's "operational theory of measurement", which was to become definitive within psychology and the behavioral sciences , despite Michell's characterization as its being quite at odds with measurement in the natural sciences (Michell, 1999). Essentially, the operational theory of measurement was a reaction to the conclusions of a committee established in 1932 by

4644-404: Is the median. A percentile or quartile measure is used for measuring dispersion. Correlations are restricted to various rank order methods. Measures of statistical significance are restricted to the non-parametric methods (R. M. Kothari, 2004). The median , i.e. middle-ranked , item is allowed as the measure of central tendency ; however, the mean (or average) as the measure of central tendency

4752-449: Is the same as between category 3 and 4. In terms of good research practice, an equidistant presentation by the researcher is important; otherwise a bias in the analysis may result. For example, a four-point Likert item with categories "Poor", "Average", "Good", and "Very Good" is unlikely to have all equidistant categories since there is only one category that can receive a below-average rating. This would arguably bias any result in favor of

4860-503: Is to summarize them via a latent variable model , for example using factor analysis or item response theory . Likert scale data can, in principle, be used as a basis for obtaining interval level estimates on a continuum by applying the polytomous Rasch model , when data can be obtained that fit this model. In addition, the polytomous Rasch model permits testing of the hypothesis that the statements reflect increasing levels of an attitude or trait, as intended. For example, application of

4968-460: Is when a Likert scale is symmetric and equidistant that it will behave more like an interval-level measurement. So while a Likert scale is indeed ordinal , if well presented it may nevertheless approximate an interval-level measurement. This can be beneficial since, if it was treated just as an ordinal scale, then some valuable information could be lost if the 'distance' between Likert items were not available for consideration. The important idea here

5076-625: The Standards for Educational and Psychological Testing , which describes standards for test development, evaluation, and use. The Standards cover essential topics in testing including validity, reliability/errors of measurement, and fairness in testing. The book also establishes standards related to testing operations including test design and development, scores, scales, norms, score linking, cut scores, test administration, scoring, reporting, score interpretation, test documentation, and rights and responsibilities of test takers and test users. Finally,

5184-601: The British Association for the Advancement of Science to investigate the possibility of genuine scientific measurement in the psychological and behavioral sciences. This committee, which became known as the Ferguson committee , published a Final Report (Ferguson, et al., 1940, p. 245) in which Stevens's sone scale (Stevens & Davis, 1938) was an object of criticism: …any law purporting to express

5292-556: The Educational Testing Service and Psychological Corporation . Some psychometric researchers focus on the construction and validation of assessment instruments, including surveys , scales , and open- or close-ended questionnaires . Others focus on research relating to measurement theory (e.g., item response theory , intraclass correlation ) or specialize as learning and development professionals. Psychological testing has come from two streams of thought:

5400-580: The Rasch model are employed, numbers are not assigned based on a rule. Instead, in keeping with Reese's statement above, specific criteria for measurement are stated, and the goal is to construct procedures or operations that provide data that meet the relevant criteria. Measurements are estimated based on the models, and tests are conducted to ascertain whether the relevant criteria have been met. The first psychometric instruments were designed to measure intelligence . One early approach to measuring intelligence

5508-593: The Standards cover topics related to testing applications, including psychological testing and assessment , workplace testing and credentialing , educational testing and assessment , and testing in program evaluation and public policy. In the field of evaluation , and in particular educational evaluation , the Joint Committee on Standards for Educational Evaluation has published three sets of standards for evaluations. The Personnel Evaluation Standards

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5616-582: The analysis of variance can be applied. Typical cutoffs for thinking that this approximation will be acceptable is a minimum of four and preferably eight items in the sum. To model binary Likert responses directly, they may be represented in a binomial form by summing agree and disagree responses separately. The chi-squared , Cochran's Q test , or McNemar test are common statistical procedures used after this transformation. Non-parametric tests such as chi-squared test , Mann–Whitney test , Wilcoxon signed-rank test , or Kruskal–Wallis test . are often used in

5724-414: The coefficient of variation . More subtly, while one can define moments about the origin , only central moments are meaningful, since the choice of origin is arbitrary. One can define standardized moments , since ratios of differences are meaningful, but one cannot define the coefficient of variation, since the mean is a moment about the origin, unlike the standard deviation, which is (the square root of)

5832-880: The degree of difference between measurements, but not the ratio between measurements. Examples include temperature scales with the Celsius scale , which has two defined points (the freezing and boiling point of water at specific conditions) and then separated into 100 intervals, date when measured from an arbitrary epoch (such as AD), location in Cartesian coordinates, and direction measured in degrees from true or magnetic north. Ratios are not meaningful since 20 °C cannot be said to be "twice as hot" as 10 °C (unlike temperature in kelvins ), nor can multiplication/division be carried out between any two dates directly. However, ratios of differences can be expressed; for example, one difference can be twice another; for example,

5940-450: The "neutral"/zero value (whether or not that value is presented as a candidate). Balance means that the distance between each candidate value is the same, allowing for quantitative comparisons such as averaging to be valid across items containing more than two candidate values. The format of a typical five-level Likert item, for example, could be: Likert scaling is a bipolar scaling method , measuring either positive or negative response to

6048-500: The Rasch model, and the broader class of models to which it belongs, was explicitly founded on requirements of measurement in the physical sciences. Psychometricians have also developed methods for working with large matrices of correlations and covariances. Techniques in this general tradition include: factor analysis , a method of determining the underlying dimensions of data. One of the main challenges faced by users of factor analysis

6156-473: The accuracy topic. For example, the student accuracy standards help ensure that student evaluations will provide sound, accurate, and credible information about student learning and performance. Because psychometrics is based on latent psychological processes measured through correlations , there has been controversy about some psychometric measures. Critics, including practitioners in the physical sciences , have argued that such definition and quantification

6264-682: The analysis of Likert scale data. Alternatively, Likert scale responses can be analyzed with an ordered probit model, preserving the ordering of responses without the assumption of an interval scale. The use of an ordered probit model can prevent errors that arise when treating ordered ratings as interval-level measurements. Consensus-based assessment (CBA) can be used to create an objective standard for Likert scales in domains where no generally accepted or objective standard exists. Consensus-based assessment (CBA) can be used to refine or even validate generally accepted standards. A common practice for analyzing responses to collections of Likert scale items

6372-605: The broadest sense, is defined as the assignment of numerals to objects and events according to rules (Stevens, 1946, p. 677). Stevens was greatly influenced by the ideas of another Harvard academic, the Nobel laureate physicist Percy Bridgman (1927), whose doctrine of operationalism Stevens used to define measurement. In Stevens's definition, for example, it is the use of a tape measure that defines length (the object of measurement) as being measurable (and so by implication quantitative). Critics of operationalism object that it confuses

6480-408: The classes can be relied upon. Thus measuring with the nominal scale is equivalent to classifying . Nominal measurement may differentiate between items or subjects based only on their names or (meta-)categories and other qualitative classifications they belong to. Thus it has been argued that even dichotomous data relies on a constructivist epistemology . In this case, discovery of an exception to

6588-577: The committee also included several psychologists. The committee's report highlighted the importance of the definition of measurement. While Stevens's response was to propose a new definition, which has had considerable influence in the field, this was by no means the only response to the report. Another, notably different, response was to accept the classical definition, as reflected in the following statement: These divergent responses are reflected in alternative approaches to measurement. For example, methods based on covariance matrices are typically employed on

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6696-519: The development of modern tests. The origin of psychometrics also has connections to the related field of psychophysics . Around the same time that Darwin, Galton, and Cattell were making their discoveries, Herbart was also interested in "unlocking the mysteries of human consciousness" through the scientific method. Herbart was responsible for creating mathematical models of the mind, which were influential in educational practices for years to come. E.H. Weber built upon Herbart's work and tried to prove

6804-449: The difficulty of each item (the ICCs ) as information to be incorporated in scaling items. A Likert scale is the sum of responses on several Likert item s. Because many Likert scales pair each constituent Likert item with its own instance of a visual analogue scale (e.g., a horizontal line, on which the subject indicates a response by circling or checking tick-marks), an individual item

6912-418: The disciplines is required. Kept independent, they can give only wrong answers or no answers at all regarding certain important problems." Psychometrics addresses human abilities, attitudes, traits, and educational evolution. Notably, the study of behavior, mental processes, and abilities of non-human animals is usually addressed by comparative psychology , or with a continuum between non-human animals and

7020-447: The early theoretical and applied work in psychometrics was undertaken in an attempt to measure intelligence . Galton often referred to as "the father of psychometrics," devised and included mental tests among his anthropometric measures. James McKeen Cattell , a pioneer in the field of psychometrics, went on to extend Galton's work. Cattell coined the term mental test , and is responsible for research and knowledge that ultimately led to

7128-456: The equal distance assumption many researchers believe are required for parametric statistical procedures and tests. Rensis Likert , the developer of the scale, pronounced his name / ˈ l ɪ k ər t / LIK -ərt . Some have claimed that Likert's name "is among the most mispronounced in [the] field", because many people pronounce the name of the scale as / ˈ l aɪ k ər t / LY -kərt . Psychometrics Psychometrics

7236-440: The equivalence of different versions of the same measure can be indexed by a Pearson correlation , and is called equivalent forms reliability or a similar term. Internal consistency, which addresses the homogeneity of a single test form, may be assessed by correlating performance on two halves of a test, which is termed split-half reliability ; the value of this Pearson product-moment correlation coefficient for two half-tests

7344-417: The existence of a psychological threshold, saying that a minimum stimulus was necessary to activate a sensory system . After Weber, G.T. Fechner expanded upon the knowledge he gleaned from Herbart and Weber, to devise the law that the strength of a sensation grows as the logarithm of the stimulus intensity. A follower of Weber and Fechner, Wilhelm Wundt is credited with founding the science of psychology. It

7452-421: The first, from Darwin , Galton , and Cattell , on the measurement of individual differences and the second, from Herbart , Weber , Fechner , and Wundt and their psychophysical measurements of a similar construct. The second set of individuals and their research is what has led to the development of experimental psychology and standardized testing. Charles Darwin was the inspiration behind Francis Galton,

7560-507: The four levels are not exhaustive and proposed seven instead: For example, percentages (a variation on fractions in the Mosteller–Tukey framework) do not fit well into Stevens's framework: No transformation is fully admissible. Nicholas R. Chrisman introduced an expanded list of levels of measurement to account for various measurements that do not necessarily fit with the traditional notions of levels of measurement. Measurements bound to

7668-439: The mathematical rigour that it lacked at its inception with the work of mathematical psychologists Theodore Alper (1985, 1987), Louis Narens (1981a, b), and R. Duncan Luce (1986, 1987, 2001). As Luce (1997, p. 395) wrote: S. S. Stevens (1946, 1951, 1975) claimed that what counted was having an interval or ratio scale. Subsequent research has given meaning to this assertion, but given his attempts to invoke scale type ideas it

7776-458: The model often indicates that the neutral category does not represent a level of attitude or trait between the disagree and agree categories. Not every set of Likert scaled items can be used for Rasch measurement. The data has to be thoroughly checked to fulfill the strict formal axioms of the model. However, the raw scores are the sufficient statistics for the Rasch measures, a deliberate choice by Georg Rasch , so, if you are prepared to accept

7884-464: The most applicable methods. This disagreement can be traced back, in many respects, to the extent to which Likert items are interpreted as being ordinal data. There are two primary considerations in this discussion. First, Likert scales are arbitrary. The value assigned to a Likert item has no objective numerical basis, either in terms of measure theory or scale (from which a distance metric can be determined). The value assigned to each Likert item

7992-509: The most general being the Hyperbolic Cosine Model (Andrich & Luo, 1993). Psychometricians have developed a number of different measurement theories. These include classical test theory (CTT) and item response theory (IRT). An approach that seems mathematically to be similar to IRT but also quite distinctive, in terms of its origins and features, is represented by the Rasch model for measurement. The development of

8100-404: The name of universal psychometrics , has also been proposed. el pensamiento psicologico especifico, en las ultima decadas, fue suprimido y eliminado casi totalmente, siendo sustituido por un pensamiento estadistico. Precisamente aqui vemos el cáncer de la testología y testomania de hoy. Level of measurement Level of measurement or scale of measure is a classification that describes

8208-581: The nature of information within the values assigned to variables . Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal , ordinal , interval , and ratio . This framework of distinguishing levels of measurement originated in psychology and has since had a complex history, being adopted and extended in some disciplines and by some scholars, and criticized or rejected by others. Other classifications include those by Mosteller and Tukey , and by Chrisman. Stevens proposed his typology in

8316-488: The only non-trivial operations that generically apply to objects of the nominal type. The mode , i.e. the most common item, is allowed as the measure of central tendency for the nominal type. On the other hand, the median , i.e. the middle-ranked item, makes no sense for the nominal type of data since ranking is meaningless for the nominal type. The ordinal type allows for rank order (1st, 2nd, 3rd, etc.) by which data can be sorted but still does not allow for

8424-633: The ordinal scale level in Likert scales. For example, in a set of items A ,  B ,  C rated with a Likert scale circular relations like A  >  B , B  >  C and C  >  A can appear. This violates the axiom of transitivity for the ordinal scale. Research by Labovitz and Traylor provide evidence that, even with rather large distortions of perceived distances between scale points, Likert-type items perform closely to scales that are perceived as equal intervals. So these items and other equal-appearing scales in questionnaires are robust to violations of

8532-452: The ordinal type in behavioural science is in fact somewhere between the true ordinal and interval types; although the interval difference between two ordinal ranks is not constant, it is often of the same order of magnitude. 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

8640-441: The past, for example, when a test of current psychological symptoms is used to predict the occurrence of past victimization (which would accurately represent postdiction). When the criterion measure is collected at the same time as the measure being validated the goal is to establish concurrent validity ; when the criterion is collected later the goal is to establish predictive validity . A measure has construct validity if it

8748-518: The plausibility and ignorance in Dempster–Shafer theory . 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's original work. The theory of scale types

8856-445: The premise that numbers, such as raw scores derived from assessments, are measurements. Such approaches implicitly entail Stevens's definition of measurement, which requires only that numbers are assigned according to some rule. The main research task, then, is generally considered to be the discovery of associations between scores, and of factors posited to underlie such associations. On the other hand, when measurement models such as

8964-556: The quality of any test as a whole within a given context. A consideration of concern in many applied research settings is whether or not the metric of a given psychological inventory is meaningful or arbitrary. In 2014, the American Educational Research Association (AERA), American Psychological Association (APA), and National Council on Measurement in Education (NCME) published a revision of

9072-447: The questionnaire is completed, each item may be analyzed separately or in some cases item responses may be summed to create a score for a group of items. Hence, Likert scales are often called summative scales. Whether individual Likert items can be considered as interval-level data, or whether they should be treated as ordered-categorical data is the subject of considerable disagreement in the literature, with strong convictions on what are

9180-630: The ratio of some magnitude of a quantitative attribute to a unit of the same attribute" (p. 358) Indeed, Stevens's definition of measurement was put forward in response to the British Ferguson Committee, whose chair, A. Ferguson, was a physicist. The committee was appointed in 1932 by the British Association for the Advancement of Science to investigate the possibility of quantitatively estimating sensory events. Although its chair and other members were physicists,

9288-583: The ratio scale. While Stevens's typology is widely adopted, it is still being challenged by other theoreticians, particularly in the cases of the nominal and ordinal types (Michell, 1986). Duncan (1986), for example, objected to the use of the word measurement in relation to the nominal type and Luce (1997) disagreed with Stevens's definition of measurement. On the other hand, Stevens (1975) said of his own definition of measurement that "the assignment can be any consistent rule. The only rule not allowed would be random assignment, for randomness amounts in effect to

9396-448: The raw scores as valid, then you can also accept the Rasch measures as valid. An important part of data analysis and presentation is the visualization (or plotting) of data. The subject of plotting Likert (and other) rating data is discussed at length in two papers by Robbins and Heiberger. In the first they recommend the use of what they call diverging stacked bar charts and compare them to other plotting styles. The second paper describes

9504-416: The relations between two objects or events for properties of one of those of objects or events (Moyer, 1981a, b; Rogers, 1989). The Canadian measurement theorist William Rozeboom was an early and trenchant critic of 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. For example, hair color

9612-409: The relationship between latent traits and responses to test items. Among other advantages, IRT provides a basis for obtaining an estimate of the location of a test-taker on a given latent trait as well as the standard error of measurement of that location. For example, a university student's knowledge of history can be deduced from his or her score on a university test and then be compared reliably with

9720-405: The remarkable thing is his insight given the relatively limited formal apparatus available to him and how many decades have passed since he coined them." 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. This is often justified on the basis that

9828-455: The rest of animals by evolutionary psychology . Nonetheless, there are some advocators for a more gradual transition between the approach taken for humans and the approach taken for (non-human) animals. The evaluation of abilities, traits and learning evolution of machines has been mostly unrelated to the case of humans and non-human animals, with specific approaches in the area of artificial intelligence . A more integrated approach, under

9936-487: The rise of qualitative research has made this usage confusing. If numbers are assigned as labels in nominal measurement, they have no specific numerical value or meaning. No form of arithmetic computation (+, −, ×, etc.) may be performed on nominal measures. The nominal level is the lowest measurement level used from a statistical point of view. Equality and other operations that can be defined in terms of equality, such as inequality and set membership , are

10044-404: The sample tested, while, in principle, those derived from item response theory are not. The considerations of validity and reliability typically are viewed as essential elements for determining the quality of any test. However, professional and practitioner associations frequently have placed these concerns within broader contexts when developing standards and making overall judgments about

10152-491: The study of human beings and how they differ one from another and how to measure those differences. Galton wrote a book entitled Hereditary Genius which was first published in 1869. The book described different characteristics that people possess and how those characteristics make some more "fit" than others. Today these differences, such as sensory and motor functioning (reaction time, visual acuity, and physical strength), are important domains of scientific psychology. Much of

10260-584: The ten-degree difference between 15 °C and 25 °C is twice the five-degree difference between 17 °C and 22 °C. Interval type variables are sometimes also called "scaled variables", but the formal mathematical term is an affine space (in this case an affine line ). The mode , median , and arithmetic mean are allowed to measure central tendency of interval variables, while measures of statistical dispersion include range and standard deviation . Since one can only divide by differences , one cannot define measures that require some ratios, such as

10368-414: The theory and application of factor analysis , a statistical method developed and used extensively in psychometrics. In the late 1950s, Leopold Szondi made a historical and epistemological assessment of the impact of statistical thinking on psychology during previous few decades: "in the last decades, the specifically psychological thinking has been almost completely suppressed and removed, and replaced by

10476-464: The true score as possible. Figures who made significant contributions to psychometrics include Karl Pearson , Henry F. Kaiser, Carl Brigham , L. L. Thurstone , E. L. Thorndike , Georg Rasch , Eugene Galanter , Johnson O'Connor , Frederic M. Lord , Ledyard R Tucker , Louis Guttman , and Jane Loevinger . The definition of measurement in the social sciences has a long history. A current widespread definition, proposed by Stanley Smith Stevens ,

10584-568: The underlying construct. The Myers–Briggs Type Indicator (MBTI), however, has questionable validity and has been the subject of much criticism. Psychometric specialist Robert Hogan wrote of the measure: "Most personality psychologists regard the MBTI as little more than an elaborate Chinese fortune cookie." Lee Cronbach noted in American Psychologist (1957) that, "correlational psychology, though fully as old as experimentation,

10692-506: The underlying phenomenon. When responding to a Likert item, respondents specify their level of agreement or disagreement on a symmetric agree-disagree scale for a series of statements. Thus, the range captures the intensity of their feelings for a given item. A scale can be created as the simple sum or average of questionnaire responses over the set of individual items (questions). In so doing, Likert scaling assumes distances between each choice (answer option) are equal. Many researchers employ

10800-429: 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. Statistical analysis software such as SPSS requires the user to select the appropriate measurement class for each variable. This ensures that subsequent user errors cannot inadvertently perform meaningless analyses (for example correlation analysis with

10908-627: The use of "undecided" and "neutral" as the middle option in a five-point Likert scale. Likert scales may be subject to distortion from several causes. Respondents may: Designing a scale with balanced keying (an equal number of positive and negative statements and, especially, an equal number of positive and negative statements regarding each position or issue in question) can obviate the problem of acquiescence bias, since acquiescence on positively keyed items will balance acquiescence on negatively keyed items, but defensive, central tendency, and social desirability biases are somewhat more problematic. After

11016-403: The use of an ordinal scale implies a statement of "greater than" or "less than" (an equality statement is also acceptable) without our being able to state how much greater or less. The real difference between ranks 1 and 2, for instance, may be more or less than the difference between ranks 5 and 6. Since the numbers of this scale have only a rank meaning, the appropriate measure of central tendency

11124-529: The use of the Likert function in the HH package for R, and gives many examples of its use. The five response categories are often believed to represent an interval level of measurement . However, this can only be the case if the intervals between the scale points correspond to empirical observations in a metric sense. Reips and Funke (2008) show that this criterion is much better met by a visual analogue scale . In fact, there may also appear phenomena which even question

11232-527: Was later rendered false by the discovery of the theory of conjoint measurement by Debreu (1960) and independently by Luce & Tukey (1964). However, Stevens's reaction was not to conduct experiments to test for the presence of additive structure in sensations, but instead to render the conclusions of the Ferguson committee null and void by proposing a new theory of measurement: Paraphrasing N. R. Campbell (Final Report, p. 340), we may say that measurement, in

11340-635: Was published in 1988, The Program Evaluation Standards (2nd edition) was published in 1994, and The Student Evaluation Standards was published in 2003. Each publication presents and elaborates a set of standards for use in a variety of educational settings. The standards provide guidelines for designing, implementing, assessing, and improving the identified form of evaluation. Each of the standards has been placed in one of four fundamental categories to promote educational evaluations that are proper, useful, feasible, and accurate. In these sets of standards, validity and reliability considerations are covered under

11448-400: Was slower to mature. It qualifies equally as a discipline, however, because it asks a distinctive type of question and has technical methods of examining whether the question has been properly put and the data properly interpreted." He would go on to say, "The correlation method, for its part, can study what man has not learned to control or can never hope to control ... A true federation of

11556-452: Was the presence of additive structure —a concept comprehensively treated by the German mathematician Otto Hölder (Hölder, 1901). Given that the physicist and measurement theorist Norman Robert Campbell dominated the Ferguson committee's deliberations, the committee concluded that measurement in the social sciences was impossible due to the lack of concatenation operations. This conclusion

11664-639: Was the test developed in France by Alfred Binet and Theodore Simon . That test was known as the Test Binet-Simon  [ fr ] .The French test was adapted for use in the U. S. by Lewis Terman of Stanford University, and named the Stanford-Binet IQ test . Another major focus in psychometrics has been on personality testing . There has been a range of theoretical approaches to conceptualizing and measuring personality, though there

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