what does a domain sampling model within the classical test theory framework assume? course hero

What are the assumptions of classical test theory?

Classical test theory makes the following assumptions about measurement error: E e = 0. ρ t, e = 0. ρ e 1, t 2 = 0. ρ e 1, e 2 = 0. From these assumptions, we see that the expected value of the observed score is equal to the expected value of the true score plus the expected value of the error: E X = E t + E e.

Can classical test theory be applied to any context?

Classical test theory is simple. It can be applied to any context and be put into practice without the need for particularly advanced mathematical skills. However, the problem is that the results it yields will always be linked to the population in which the test was validated.

What are the classical test theory and Item Response Theory?

The classical test theory and item response theory are two approaches to psychometrics. Learn about psychometric tests and explore the differences and characteristics of classical test theory and item response theory. Updated: 12/28/2021

What is classical test theory in statistics?

Classical test theory is concerned with the relations between the three variables X {displaystyle X} , T {displaystyle T} , and E {displaystyle E} in the population. These relations are used to say something about the quality of test scores.

What is the use of classical test theory?

Classical test theory and item response theory can be useful in providing a quantitative assessment of items and scales during the content validity phase of patient-reported outcome measures. Depending on the particular type of measure and the specific circumstances, either one or both approaches should be considered to help maximize the content validity of PRO measures.

How large should a sample be for a test?

Nevertheless, sample sizes based on classical test theory should be large enough for the descriptive and exploratory pursuit of meaningful estimates from the data. While it’s not appropriate to give one number for sample size in all such cases, starting with a sample of 30 to 50 subjects may be reasonable in many circumstances. If no clear trends emerge, adding more subjects may be needed to observe any noticeable patterns. It should be emphasized that an appropriate sample size depends on the situation at hand, such as the number of response categories. An 11-point numeric rating scale, for instance, may not have enough observations in the extreme categories and may require a larger sample size. In addition to an increase in the sample size, another way to have a more even level of observations across categories of a scale is to plan for it at the design stage by recruiting individuals who provide sufficient representation across the response categories.

What is step 2 in a survey?

Step 2 is to examine each item and determine the proportion of individual respondents in the sample who endorse or respond to each item (or to a particular category or adjacent category groups of an item) in the upper group and lower group.

How to determine response categories?

An item’s response categories can be assessed by analyzing the item response curves, which is produced descriptively in classical test theory by plotting the percentage of subjects choosing each response option on the y-axis and the total score, expressed as such or percentiles or other metric, on the x-axis. Figure 1provides an illustration. Item 1 is equally good at discriminating across the continuum of the attribute (the concept of interest). Item 2 discriminates better at the lower end than at the upper end of the attribute. Item 3 discriminates better at the upper end, especially between 70thand 80thpercentiles.

What is the significance of means and standard deviations in a PRO measure?

In the development of a PRO measure, the means and standard deviations of the items can provide fundamental clues about which items are useful for assessing the concept of interest. Generally, the higher the variability of the item scores and the closer the mean score of the item is to the center of its distribution (i.e., median), the better the item will perform in the target population.

What is true score?

True scores quantify values on an attribute of interest, defined here as the underlying concept, construct, trait, or ability of interest (the “thing” intended to be measured). As values of the true score increase, responses to items representing the same concept should also increase (i.e., there should be a monotonically increasing relationship between true scores and item scores), assuming that item responses are coded so that higher responses reflect more of the concept.

How can quantitative methods support development of PRO measures?

Specifically, quantitative methods can support development of PRO measures by addressing several core questions of content validity. What is the range of item responses relative to the sample (distribution of item responses and their endorsement)? Are the response options used by patients as intended? Does a higher response option imply more of a health problem than a lower response option? What is the distance between response categories in terms of the underlying concept?

What is the classical test theory?

According to classical test theory, a score obtained in the process of measurement is influenced by two things: (1) the true score of the object, person, event, or other phenomenon being measured and (2) error (i.e., everything other than the true score of the phenomenon of interest).

How does classical test theory address multiple sources of error?

Addressing multiple sources of error is an interesting idea, but classical test theory directs researchers to focus on one source of error with different computing methods. For example, if one computes a test–retest reliability coefficient, the variation over time in the observed score is counted as error, but the variation due to item sampling is not. If one computes Cronbach coefficient Alpha, the variation due to the sampling of different items is counted as error, but the time-based variation is not. This creates a problem if the reliability estimates yielded from different methods are substantively different. To counteract this problem, Marcoulides suggested reconceptualizing classical reliability in a broader notion of generalizability. Instead of asking how stable, how equivalent, or how consistent the test is, and to what degree the observed scores reflect the true scores, the generalizability theory asks how the observed scores enable the researcher to generalize about the examinees' behaviors given that multiple sources of errors are taken into account.

Why is CTT not well developed?

The statistical treatment of CTT is not well developed. One of the reasons for this is the fact that its model is not based on the assumption of parametric families for the distributions of Xjt and TJt in Eqs. (5) and (6). Direct application of standard likelihood or Bayesian theory to the estimation of classical item and test parameters is therefore less straightforward. Fortunately, nearly all classical parameters are defined in terms of first-order and second-order (product) moments of score distributions. Such moments are well estimated by their sample equivalents (with the usual correction for the variance estimator if we are interested in unbiased estimation). CTT item and test parameters are therefore often estimated using “plug-in estimators,” that is, with sample moments substituted for population moments in the definition of the parameter.

What is content sampling?

Content sampling refers to the sampling of items that make up the measure. If the sampled items are from the same domain, measurement error within a measure will be lower. Heterogeneity of behavior can lead to an increase in measurement error when the items represent different domain of behaviors.

Which model does not satisfy the unique maximum condition?

The normal ogive model, the logistic model, the logistic positive exponent model, the acceleration model, and models derived from Bock's nominal response model all satisfy the unique maximum condition. Notably, however, the three-parameter logistic model for dichotomous responses, which has been widely used for multiple-choice test data, does not satisfy the unique maximum condition, and multiple MLEs of θ may exist for some response patterns.

Can classical test theory be used to construct tests?

Even though classical item parameters depend on the population and the other items in the test, in practice classical test theory is often applied to construct tests. When the assumption can be made that the population for the test does hardly change, test construction may be possible for classical test forms.

Is reliability invariant or invariant?

Thus reliability is not invariant with respect to the sample of test-takers, and is therefore not a characteristic of the test itself; in addition, neither are the common measures of item discrimination (such as the item-total correlation) or item difficulty (percent getting the item correct).

Who proposed the classical test theory?

Spearman proposed classical test theory at the beginning of the 20th century. The researcher then proposed a very simple model for the test scores: classical linear regression model.

What are the two most important concepts in classical test theory?

In this sense, perhaps the two most important concepts within classical test theory are reliability and validity.

What are the assumptions of linear regression?

The three assumptions of the classical linear regression model 1 The true score (V) is the mathematical expectation of the empirical score: V = E (X).#N#Thus, a person’s true test score is the average score of the same test if someone were to take it infinitely. 2 There’s no relationship between the number of true scores and the errors that affect these scores: r (v, e) = 0#N#The true score is independent of the measurement error.

What is validity in testing?

Validity refers to the degree to which empirical evidence and theory support the interpretation of test scores (2).

What is the true test score?

Thus, a person’s true test score is the average score of the same test if someone were to take it infinitely. The true score is independent of the measurement error. Errors made on one occasion would not covariate with those made on a different test. Classical test theory is simple.

What does it mean when a psychologist applies a test to one or several people?

Thus, when a psychologist applies a test to one or several people, what they obtain are the empirical scores of those people. However, this doesn’t tell us a lot about the degree of accuracy of these scores. For example, the person may have gotten a low score because they weren’t feeling well that day or even because the physical conditions of the place where they took the test weren’t optimal.

Is a psychometric test a measure of psychological evaluation?

Tests are sophisticated measurement instruments. In many cases, they’re incredibly helpful in the context of a psychological evaluation. However, a test must meet a minimum psychometric numeral score to be helpful. In addition, the specialist who applies it must know the protocol to administer it and respect it.

Who developed the classical test theory?

Classical test theory as we know it today was codified by Novick (1966) and described in classic texts such as Lord & Novick (1968) and Allen & Yen (1979/2002). The description of classical test theory below follows these seminal publications.

What is classical test theory?

Classical test theory is an influential theory of test scores in the social sciences. In psychometrics, the theory has been superseded by the more sophisticated models in item response theory (IRT) and generalizability theory (G-theory).

What are the shortcomings of classical test theory?

One of the most important or well-known shortcomings of classical test theory is that examinee characteristics and test characteristics cannot be separated: each can only be interpreted in the context of the other. Another shortcoming lies in the definition of reliability that exists in classical test theory, which states that reliability is "the correlation between test scores on parallel forms of a test". The problem with this is that there are differing opinions of what parallel tests are. Various reliability coefficients provide either lower bound estimates of reliability or reliability estimates with unknown biases. A third shortcoming involves the standard error of measurement. The problem here is that, according to classical test theory, the standard error of measurement is assumed to be the same for all examinees. However, as Hambleton explains in his book, scores on any test are unequally precise measures for examinees of different ability, thus making the assumption of equal errors of measurement for all examinees implausible (Hambleton, Swaminathan, Rogers, 1991, p. 4). A fourth, and final shortcoming of the classical test theory is that it is test oriented, rather than item oriented. In other words, classical test theory cannot help us make predictions of how well an individual or even a group of examinees might do on a test item.

What does reliability mean in tests?

Reliability is supposed to say something about the general quality of the test scores in question. The general idea is that, the higher reliability is, the better. Classical test theory does not say how high reliability is supposed to be. Too high a value for. , say over .9, indicates redundancy of items.

What is the theory of CTT?

Classical test theory (CTT) is a body of related psychometric theory that predicts outcomes of psychological testing such as the difficulty of items or the ability of test-takers . It is a theory of testing based on the idea that a person's observed or obtained score on a test is the sum of a true score (error-free score) and an error score.

What is the definition of true score?

A person's true score is defined as the expected number-correct score over an infinite number of independent administrations of the test.

Who was responsible for figuring out how to correct a correlation coefficient for attenuation due to measurement error?

In 1904, Charles Spearman was responsible for figuring out how to correct a correlation coefficient for attenuation due to measurement error and how to obtain the index of reliability needed in making the correction. Spearman's finding is thought to be the beginning of Classical Test Theory by some (Traub, 1997).

What is the population correlation between an error score on one test and a second test?

4. The population correlation between an error score on one test and a second test is 0. (Two tests are uncorrelated)error score and a true score is equal to zero.

What is the obtained score from the test?

1. The obtained score from the test is a sum of the true score and the error score

What are the two theories of test development?

Two major theories about the development of tests are classical test theory and line item response theory . Classical test theory (CTT) is all about reliability. CTT explains how we can calculate a true score, which is basically the score a test taker would achieve if there were no error at all in the test-taking process, with error in this case being, of course, the amount of error found in the testing. Since this is basically impossible, we look at someone's observed score, which is the score he or she actually achieved. CTT basically tells us how consistent a test is, as in how reliable it is.

What is the study of testing and measurement?

Psychometrics is the study of developing tests and measurements. In this lesson, we'll talk about two different theories of how psychologists can create good tests and measurement: classical test theory and item response theory. Updated: 03/24/2021

What is psychometric test?

In particular, in this lesson we're talking about psychometric tests, which are scientific and systematic ways to test someone's ability to do a job or measure their personality or some mental ability (abilities which can be things like math or even critical thinking). Psychometrics means the study of developing measurements.

What is the study of measuring?

Psychometrics means the study of developing measurements. So there's an entire field of study dedicated to just how we write things, like exams. Psychometric tests are standardized, and they are designed to assess a particular variable. The people who write them try to make them objective and unbiased. In this lesson, we'll talk about two of these kinds of test theories: classical test theory and item response theory. Think of these as theories about how psychologists create tests and measures.

What does the word "test" mean in psychology?

In particular, in this lesson we're talking about psychometric tests, which are scientific and systematic ways to test someone's ability to do a job or measure their personality or some mental ability (abilities which can be things like math or even critical thinking).

Why do you get the same score on a CTT test?

So, assuming the conditions are the same, you'd get the same score on a test because the test itself is well designed. There are three ideas we need to keep in mind when we're talking about CTT: test score, error, and true score. The test score is what we call the observed score.

What is error in testing?

Error refers to, well, exactly what it sounds like! It's the amount of error that is found in a test or measure. This might be a mistake in the test, or it might also refer to things in the external environment that we can't totally control but that impact testing.

How many examinees can be used for classical test theory?

Classical test theory can work effectively with 50 examinees, and provide useful results with as little as 20. Depending on the IRT model you select (there are many), the minimum sample size can be 100 to 1,000.

How does IRT differ from classical test theory?

Classical Test Theory and Item Response Theory differ in how test forms are designed and built. Classical test theory works best when there are lots of items of middle difficulty, as this maximizes the coefficient alpha reliability. However, there are definitely situations where the purpose of the assessment is otherwise. IRT provides stronger methods for designing such tests, and then scoring as well.

Is CTT analysis a test dependent?

CTT analyses are sample-dependent and test-dependent, which means that such analyses are performed on a single test form and set of students. It is possible to combine data across multiple test forms to create a sparse matrix, but this has a detrimental effect on some of the statistics (especially alpha), even if the test is of high quality, and the results will not reflect reality.

Does item response theory account for guessing?

Item response theory has a parameter to account for guessing, though some psychometricians argue against its use. Classical test theory has no effective way to account for guessing.