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Likert Scale
A Likert scale ( , commonly mispronounced as ) is a psychometric scale commonly involved in research that employs 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. The scale is named after its inventor, psychologist Rensis Likert. Likert distinguished between 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 the underlying phenomenon. When responding to a Likert item, respondents specify their level of agreement or disagr ...
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Psychometrics
Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally refers to 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 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. ...
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Wilcoxon Signed-rank Test
The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used either to test the location of a population based on a sample of data, or to compare the locations of two populations using two matched samples., p. 350 The one-sample version serves a purpose similar to that of the one-sample Student's ''t''-test. For two matched samples, it is a paired difference test like the paired Student's ''t''-test (also known as the "''t''-test for matched pairs" or "''t''-test for dependent samples"). The Wilcoxon test can be a good alternative to the ''t''-test when population means are not of interest; for example, when one wishes to test whether a population's median is nonzero, or whether there is a better than 50% chance that a sample from one population is greater than a sample from another population. History The test is named for Frank Wilcoxon (1892–1965) who, in a single paper, proposed both it and the rank-sum test for two independent samples. The test was ...
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Polytomous Rasch Model
The polytomous Rasch model is generalization of the dichotomous Rasch model. It is a measurement model that has potential application in any context in which the objective is to measure a trait or ability through a process in which responses to items are ''scored'' with successive integers. For example, the model is applicable to the use of Likert scales, rating scales, and to educational assessment items for which successively higher integer scores are intended to indicate increasing levels of competence or attainment. Background and overview The polytomous Rasch model was derived by Andrich (1978), subsequent to derivations by Rasch (1961) and Andersen (1977), through resolution of relevant terms of a general form of Rasch's model into ''threshold'' and ''discrimination'' parameters. When the model was derived, Andrich focused on the use of Likert scales in psychometrics, both for illustrative purposes and to aid in the interpretation of the model. The model is sometimes ...
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Armstrong's Axioms
Armstrong's axioms are a set of references (or, more precisely, inference rules) used to infer all the functional dependencies on a relational database. They were developed by William W. Armstrong in his 1974 paper. The axioms are sound in generating only functional dependencies in the closure of a set of functional dependencies (denoted as F^) when applied to that set (denoted as F). They are also complete in that repeated application of these rules will generate all functional dependencies in the closure F^+. More formally, let \langle R(U), F \rangle denote a relational scheme over the set of attributes U with a set of functional dependencies F. We say that a functional dependency f is logically implied by F, and denote it with F \models f if and only if for every instance r of R that satisfies the functional dependencies in F, r also satisfies f. We denote by F^ the set of all functional dependencies that are logically implied by F. Furthermore, with respect to a set of i ...
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Consensus-based Assessment
Consensus-based assessment expands on the common practice of consensus decision-making and the theoretical observation that expertise can be closely approximated by large numbers of novices or journeymen. It creates a method for determining measurement standards for very ambiguous domains of knowledge, such as emotional intelligence, politics, religion, values and culture in general. From this perspective, the shared knowledge that forms cultural consensus can be assessed in much the same way as expertise or general intelligence. Measurement standards for general intelligence Consensus-based assessment is based on a simple finding: that samples of individuals with differing competence (e.g., experts and apprentices) rate relevant scenarios, using Likert scales, with similar mean ratings. Thus, from the perspective of a CBA framework, cultural standards for scoring keys can be derived from the population that is being assessed. Peter Legree and Joseph Psotka, working together ...
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Ordered Probit
In statistics, ordered probit is a generalization of the widely used probit analysis to the case of more than two outcomes of an ordinal dependent variable (a dependent variable for which the potential values have a natural ordering, as in poor, fair, good, excellent). Similarly, the widely used logit method also has a counterpart ordered logit. Ordered probit, like ordered logit, is a particular method of ordinal regression. For example, in clinical research, the effect a drug may have on a patient may be modeled with ordered probit regression. Independent variables may include the use or non-use of the drug as well as control variables such as age and details from medical history such as whether the patient suffers from high blood pressure, heart disease, etc. The dependent variable would be ranked from the following list: complete cure, relieve symptoms, no effect, deteriorate condition, death. Another example application are Likert-type items commonly employed in survey ...
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McNemar Test
In statistics, McNemar's test is a statistical test used on paired nominal data. It is applied to 2 × 2 contingency tables with a dichotomous trait, with matched pairs of subjects, to determine whether the row and column marginal frequencies are equal (that is, whether there is "marginal homogeneity"). It is named after Quinn McNemar, who introduced it in 1947. An application of the test in genetics is the transmission disequilibrium test for detecting linkage disequilibrium. The commonly used parameters to assess a diagnostic test in medical sciences are sensitivity and specificity. Sensitivity (or recall) is the ability of a test to correctly identify the people with disease. Specificity is the ability of the test to correctly identify those without the disease. Now presume two tests are performed on the same group of patients. And also presume that these tests have identical sensitivity and specificity. In this situation one is carried away by these findings ...
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Cochran's Q Test
In statistics, in the analysis of two-way randomized block designs where the response variable can take only two possible outcomes (coded as 0 and 1), Cochran's Q test is a non-parametric statistical test to verify whether ''k'' treatments have identical effects. It is named after William Gemmell Cochran. Cochran's Q test should not be confused with Cochran's C test, which is a variance outlier test. Put in simple technical terms, Cochran's Q test requires that there only be a binary response (e.g. success/failure or 1/0) and that there be more than 2 groups of the same size. The test assesses whether the proportion of successes is the same between groups. Often it is used to assess if different observers of the same phenomenon have consistent results (interobserver variability). Background Cochran's Q test assumes that there are ''k'' > 2 experimental treatments and that the observations are arranged in ''b'' blocks; that is, Description Cochran's Q test is :Null h ...
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Chi-squared Test
A chi-squared test (also chi-square or test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical variables (''two dimensions of the contingency table'') are independent in influencing the test statistic (''values within the table''). The test is valid when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof. Pearson's chi-squared test is used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table. For contingency tables with smaller sample sizes, a Fisher's exact test is used instead. In the standard applications of this test, the observations are classified into mutually exclusive classes. If the null hypothesis that there are no di ...
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Binomial Distribution
In probability theory and statistics, the binomial distribution with parameters ''n'' and ''p'' is the discrete probability distribution of the number of successes in a sequence of ''n'' independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: ''success'' (with probability ''p'') or ''failure'' (with probability q=1-p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., ''n'' = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance. The binomial distribution is frequently used to model the number of successes in a sample of size ''n'' drawn with replacement from a population of size ''N''. If the sampling is carried out without replacement, the draws are not independent and so the resulting ...
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