Classical Test Theory Overview
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Questions and Answers

What are two main ways classical test theory can enhance test measurement?

  • Through better measurement practices (correct)
  • By writing items that cover a wider range of the construct (correct)
  • Through increasing the variability of true scores
  • By adding more items to the test

    • What does a higher reliability indicate about the standard error of measurement (SEM)?

  • Higher reliability has no impact on SEM
  • Higher reliability results in a constant SEM
  • Higher reliability equals higher SEM
  • Higher reliability equals lower SEM (correct)

    • Which formula represents the relationship between observed score and true score?

  • Observed score = True score - Error
  • Observed score = True score + Error (correct)
  • True score = Observed score + Error
  • True score = Observed score - Error

    • What is the essence of tau equivalent measurements?

    <p>They must measure the same construct with equal scores</p> Signup and view all the answers

    Which assumption is upheld regarding true scores and error scores in classical test theory?

    <p>True score and error score are statistically independent</p> Signup and view all the answers

    What statement correctly describes construct irrelevant variance (CIV) test bias?

    <p>CIV is unrelated to the construct being measured</p> Signup and view all the answers

    What does the assumption about the mean of errors indicate in CTT?

    <p>With a large number of examinees, mean error approaches zero</p> Signup and view all the answers

    What does reliability (Rxx) represent in classical test theory?

    <p>It divides true score variance by observed score variance</p> Signup and view all the answers

    What are the two main ways classical test theory can increase test theory?

    <p>Through better measurement practices</p> Signup and view all the answers

    What is the relationship between construct irrelevant variance (CIV) test bias and systematic error?

    <p>The predisposition is unrelated to the construct being measured.</p> Signup and view all the answers

    What does the formula for the standard error of measurement (SEM) say about reliability?

    <p>Higher reliability = lower SEM.</p> Signup and view all the answers

    What is the formula for reliability where true score variance is divided by observed score variance?

    <p>Reliability (Rxx) = TSV / OSV.</p> Signup and view all the answers

    What is the focus of classical test theory?

    <p>Estimating random error in measurement.</p> Signup and view all the answers

    What is tau equivalent regarding measurement?

    <p>Measures the same construct, independent, equal scores, equal error variance.</p> Signup and view all the answers

    What is the formula that goes with the logical assumption of error?

    <p>xo = Xt + Xe.</p> Signup and view all the answers

    What is the formula for the assumption of independence?

    <p>True score and error score is zero (rte = 0).</p> Signup and view all the answers

    What is the formula for the mean of errors assumption?

    <p>E(ε) = 0.</p> Signup and view all the answers

    Study Notes

    Classical Test Theory

    • Classical Test Theory (CTT) aims to improve test theory through:
      • Better measurement practices: refining the methods used to collect and analyze data.
      • Measuring a broader range of the construct: developing items that capture a wider spectrum of the construct being measured.

    Construct Irrelevant Variance (CIV)

    • Construct Irrelevant Variance (CIV) is a type of test bias that arises when test items measure factors unrelated to the intended construct.
    • Systematic error is a consistent and predictable deviation in measurement, which can be influenced by CIV.

    Standard Error of Measurement (SEM)

    • SEM is a measure of the accuracy of individual test scores.
    • Higher reliability leads to lower SEM.
    • The formula for SEM is: 𝑠𝑒𝑚 = 𝑠𝑜 1 − 𝑅𝑥𝑥

    Reliability

    • Reliability (Rxx) is the degree to which a test consistently measures the construct of interest.
    • It is calculated as: Reliability (Rxx) = TSV/ OSV (True Score Variance divided by Observed Score Variance)
    • Increasing the Observed Score Variance without increasing True Score Variance results in decreased reliability.

    Focus of Classical Test Theory

    • CTT focuses on estimating random error in measurement.
    • True score (TS) is a theoretical concept representing the individual's true ability or trait.
    • CTT uses observed scores (OS) to estimate true scores.

    Tau Equivalent and Essentially Tau Equivalent Tests

    • Tau equivalent tests measure the same construct, are independent, have equal scores, and equal error variance.
    • Essentially tau equivalent tests are similar to tau equivalent tests, but allow for differences in means and error variance.
    • The key difference is that essentially tau equivalent tests vary only by a constant while tau equivalent tests have equal true scores.

    Reliability Formulas

    • There are four main formulas related to reliability in CTT:
      • Test-retest reliability measures consistency over time
      • Parallel forms reliability compares different versions of the same test
      • Internal consistency reliability assesses the consistency of items within a test
      • Inter-rater reliability measures agreement among raters

    Formula for Logical Assumption of Error

    • xo = Xt + Xe
    • Observed score (xo) is the sum of the true score (Xt) and error score (Xe).

    Formula for Assumption of Independence

    • True score and error score are independent (rte = 0).
    • This means there is no correlation between the true score and the error score.
    • Error relates randomly to the true score.

    Formula for Mean of Errors Assumption

    • E(ε) = 0
    • The mean of the error scores is zero.
    • In a large enough sample, the average error will be zero.

    Classical Test Theory (CTT)

    • Increasing Reliability
      • Better measurement practices
        • Includes methods like ensuring clear instructions for test takers, ensuring consistent testing conditions, and using standardized procedures.
      • Wider range of construct measurement
        • This involves creating items that assess a wider range of the construct, effectively capturing the full spectrum of the trait or skill being measured.

    Relationship between CTT Concepts

    • Construct Irrelevant Variance (CIV), Test Bias, and Systematic Error are closely related. CIV refers to variability in test scores that are not related to the construct being measured. Test bias occurs when a test systematically favors one group over another. Systematic error is a consistent, predictable error in measurement.

    Standard Error of Measurement (SEM)

    • SEM directly relates to reliability:
      • Higher reliability translates to lower SEM, signifying more precise measurement.
      • Formula: SEM = SD√(1 - Rxx), where SD is the observed score standard deviation and Rxx is the reliability coefficient.

    Reliability Formula

    • Reliability (Rxx) = True Score Variance (TSV) / Observed Score Variance (OSV)
      • Increasing OSV without an increase in TSV leads to decreased reliability. This is because more noise in observed scores makes it harder to distinguish true score variability.

    Key Focus of CTT

    • CTT emphasizes estimating random error in measurement.
    • The central concept is the true score, which represents the hypothetical score an individual would get if there were no measurement error.
    • CTT uses observed scores to estimate true scores by accounting for the effects of random error.

    Tau-Equivalent Tests

    • Tau-equivalent tests measure the same construct, are independent, have equal scores, and equal error variance.
    • Essentially tau-equivalent tests are similar but allow for differences in means and error variance.
    • Essential tau-equivalent tests only vary by a constant, while tau-equivalent tests also possess an equal true score.

    Formulas for Reliability

    • Four different formulas for assessing reliability:
      • Test-retest reliability: Measures consistency over time.
      • Parallel Forms Reliability: Measures consistency between two versions of the same test.
      • Internal Consistency Reliability: Measures consistency within a single test.
      • Inter-rater Reliability: Measures consistency between different raters.

    The Logical Assumption of Error

    • Xo = Xt + Xe
      • Observed score (Xo) is equal to True score (Xt) plus Error (Xe).

    The Assumption of Independence

    • The second CTT assumption is the independence of true score and error score.
      • True score and error score have zero correlation (rte = 0).
        • Error relates only randomly to the true score.
      • True score and error score are two separate variables, meaning they do not overlap in what they measure.
      • Error is statistically independent of the true score.

    The Mean of Errors Assumption

    • E(ε) = 0
      • This means the mean error is zero for a sufficiently large number of examinees.

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    Description

    This quiz explores the fundamentals of Classical Test Theory (CTT), including its emphasis on effective measurement practices and minimizing construct irrelevant variance (CIV). Participants will also learn about the significance of reliability and the standard error of measurement (SEM) in evaluating test scores.

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