This is an accepted version of this page
46-453: The Polity data series is a data series in political science research. Along with the V-Dem Democracy indices project and Democracy Index (The Economist) , Polity is among prominent datasets that measure democracy and autocracy. The Polity study was initiated in the late 1960s by Ted Robert Gurr and is now continued by Monty G. Marshall, one of Gurr's students. It was sponsored by
92-446: 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
138-607: 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
184-588: 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,
230-490: A million data sets. Several characteristics define a data set's structure and properties. These include the number and types of the attributes or variables, and various statistical measures applicable to them, such as standard deviation and kurtosis . The values may be numbers, such as real numbers or integers , for example representing a person's height in centimeters, but may also be nominal data (i.e., not consisting of numerical values), for example representing
276-402: 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
322-489: A person's ethnicity. More generally, values may be of any of the kinds described as a level of measurement . For each variable, the values are normally all of the same kind. Missing values may exist, which must be indicated somehow. In statistics , data sets usually come from actual observations obtained by sampling a statistical population , and each row corresponds to the observations on one element of that population. Data sets may further be generated by algorithms for
368-418: 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
414-462: 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
460-559: 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
506-803: 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
SECTION 10
#1732856194369552-404: 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,
598-616: Is a classification that describes 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
644-572: Is and isn't a democracy. FAIR has criticized the data series for Americentrism with the United States being shown as the only democracy in the world in 1842, being given a nine out of ten during slavery, and a ten out of ten during the Jim Crow era . The organization has also been critical of the data series for ignoring European colonialism in Africa and Asia with those areas being labeled as no data before
690-408: 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
736-420: 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
782-426: 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
828-572: 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
874-511: 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
920-404: 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
966-404: 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
SECTION 20
#17328561943691012-581: 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
1058-664: The Political Instability Task Force (PITF) until February 2020. The PITF is funded by the Central Intelligence Agency . The data series has been criticized for its methodology, Americentrism , and connections to the CIA. Seva Gunitsky, an assistant professor at the University of Toronto , stated that the data series was appropriate "for research that examines constraints on governing elites, but not for studying
1104-414: 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)
1150-870: 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,
1196-711: The 1960s. FAIR has also been critical of the data series' connection to the Central Intelligence Agency . Max Roser , the founder of Our World in Data , stated that Polity IV was far from perfect and was concerned at the data series' connections with the Central Intelligence Agency. Seva Gunitsky, an assistant professor at the University of Toronto , wrote in The Washington Post where he stated that "Polity IV measures might be appropriate for research that examines constraints on governing elites, but not for studying
1242-601: 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
1288-408: 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
1334-414: The data set in question. The data set lists values for each of the variables, such as for example height and weight of an object, for each member of the data set. Data sets can also consist of a collection of documents or files. In the open data discipline, data set is the unit to measure the information released in a public open data repository. The European data.europa.eu portal aggregates more than
1380-467: The expansion of suffrage over the nineteenth century". The 2002 paper "Conceptualizing and Measuring Democracy" claimed several problems with commonly used democracy rankings, including Polity, opining that the criteria used to determine "democracy" were misleadingly narrow. The Polity data series has been criticized by Fairness & Accuracy in Reporting for its methodology and determination of what
1426-401: The expansion of suffrage over the nineteenth century". Gunitsky was critical of the data series for ignoring suffrage . Data set A data set (or dataset ) is a collection of data . In the case of tabular data, a data set corresponds to one or more database tables , where every column of a table represents a particular variable , and each row corresponds to a given record of
Polity data series - Misplaced Pages Continue
1472-507: 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
1518-439: 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
1564-488: 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
1610-452: 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
1656-518: 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
1702-460: The purpose of testing certain kinds of software . Some modern statistical analysis software such as SPSS still present their data in the classical data set fashion. If data is missing or suspicious an imputation method may be used to complete a data set. Several classic data sets have been used extensively in the statistical literature: Loading datasets using Python: Level of measurement Level of measurement or scale of measure
1748-583: 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
1794-416: 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
1840-405: 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
1886-487: 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
Polity data series - Misplaced Pages Continue
1932-584: 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
1978-429: 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
2024-403: 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
2070-522: 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
2116-448: 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
#368631