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Questions and Answers
What does observed score variance reflect?
What does observed score variance reflect?
True score variance
Which of the following is considered a lead source of error in content sampling?
Which of the following is considered a lead source of error in content sampling?
What should be avoided when estimating internal consistency reliability?
What should be avoided when estimating internal consistency reliability?
What is internal consistency an index of?
What is internal consistency an index of?
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What formula is used to estimate reliability for the whole test when dichotomously scored items are used?
What formula is used to estimate reliability for the whole test when dichotomously scored items are used?
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What is the KR-21 formula used for?
What is the KR-21 formula used for?
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Cronbach's alpha can be used for polytomously scored items.
Cronbach's alpha can be used for polytomously scored items.
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What is an essential property of any measure?
What is an essential property of any measure?
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What is content validity primarily a function of?
What is content validity primarily a function of?
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Which of the following defines criterion-related validity?
Which of the following defines criterion-related validity?
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What is reliability in the context of classroom assessment?
What is reliability in the context of classroom assessment?
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Which type of reliability answers the question, 'Will the scores be stable over time'?
Which type of reliability answers the question, 'Will the scores be stable over time'?
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What does internal consistency reliability measure?
What does internal consistency reliability measure?
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A measure can be valid without being reliable.
A measure can be valid without being reliable.
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What is the formula for the Classical True Score Model?
What is the formula for the Classical True Score Model?
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Random error affects reliability but does not impact validity.
Random error affects reliability but does not impact validity.
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Which of the following is a source of random error?
Which of the following is a source of random error?
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What does the standard error of measurement indicate?
What does the standard error of measurement indicate?
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The closer the standard error is to ______, the better.
The closer the standard error is to ______, the better.
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Assuming no practice or other instruction had occurred, and given that the test had high reliability (r = .90), then differences between the two test scores for each employee should be, on average.
Assuming no practice or other instruction had occurred, and given that the test had high reliability (r = .90), then differences between the two test scores for each employee should be, on average.
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Reliability of measurement is concerned with:
Reliability of measurement is concerned with:
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The longer the time interval between a prediction and the event to be predicted, the:
The longer the time interval between a prediction and the event to be predicted, the:
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If a grammar test is given twice and shows inconsistent scores, then the test is most likely:
If a grammar test is given twice and shows inconsistent scores, then the test is most likely:
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This reliability coefficient is usually greater over the short-term than the long-term.
This reliability coefficient is usually greater over the short-term than the long-term.
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Which of the following is not a method of building reliability into a test?
Which of the following is not a method of building reliability into a test?
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What type of reliability is applicable if a human resource professional wants to compute the reliability of a test after a single administration?
What type of reliability is applicable if a human resource professional wants to compute the reliability of a test after a single administration?
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If a thermometer measured the temperature in an oven as 400 F five days in a row when the temperature was actually 397 F, this measuring instrument would be considered:
If a thermometer measured the temperature in an oven as 400 F five days in a row when the temperature was actually 397 F, this measuring instrument would be considered:
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When reliability is determined by correlating scores on two different forms of the same test, the type of reliability we are assessing is:
When reliability is determined by correlating scores on two different forms of the same test, the type of reliability we are assessing is:
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What is the lowest reliability coefficient that is considered acceptable for a group?
What is the lowest reliability coefficient that is considered acceptable for a group?
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Which of the following is most likely a threat to reliability?
Which of the following is most likely a threat to reliability?
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At a minimum all tests must have (12) _____________ validity and (13) ___________ reliability.
At a minimum all tests must have (12) _____________ validity and (13) ___________ reliability.
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At a minimum all tests must have _____________ validity and ___________ reliability.
At a minimum all tests must have _____________ validity and ___________ reliability.
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At a minimum, all tests must have _____________ validity and ___________ reliability.
At a minimum, all tests must have _____________ validity and ___________ reliability.
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Study Notes
Overview of Psychometrics
- Psychometrics involves assessing the reliability and validity of classroom measurement tools.
- Reliability indicates consistency in scores; validity ensures those scores accurately measure intended constructs.
- A measurement can be reliable without being valid, but a valid measure must first be reliable.
Classical Reliability Indices
- Reliability represents the stability of test scores over time and across applications.
- Repeated administrations of a test should yield similar scores if measuring the same attribute.
Types of Reliability
- Test-Retest Reliability: Assesses stability over time by correlating scores from the same test administered at different times.
- Parallel Forms Reliability: Examines the equivalence of two different forms of the same test administered to the same group.
- Internal Consistency Reliability: Evaluates how well items within a test measure the same construct during a single administration.
- Inter-Rater Reliability: Measures the consistency among different raters evaluating the same performance or item.
Theoretical Foundations
- Classical True Score Model: Represents observed score (O) as the sum of true score (T) and error (E).
- True scores reflect actual knowledge, while error scores result from variability not related to the attribute being measured.
Types of Errors
- Random Error: Varies across testing sessions and affects reliability; includes factors like mood, fatigue, or environmental conditions.
- Systematic Error: Consistent across tests and can impact validity; includes poorly worded items or irrelevant content.
Standard Error of Measurement (SEM)
- SEM quantifies the amount of measurement error; smaller SEM indicates more precise estimates of true scores.
- Used to construct confidence intervals around an individual’s score, helping to estimate true performance levels.
Standard Error of the Estimate (SEyx)
- SEyx gauges how accurately a test score predicts a criterion value.
- High correlations between test scores and criterion values increase prediction accuracy.
Improving Reliability
- Use heterogeneous examinee groups to strengthen reliability.
- Ensure optimal test length, quality of items, and providing a conducive testing environment to mitigate fatigue and distractions.
Reliability Estimation Procedures
- Procedures vary based on the intended use of test scores and include methods for assessing both equivalence (alternate forms) and stability (test-retest).
- Common statistical methods include Pearson's r for correlation and internal consistency measures like Coefficient Alpha.
Reliability Standards
- A reliability coefficient of .80 or higher is acceptable for group assessments.
- Individual decision-making requires a reliability coefficient of at least .90, ideally .95.
Coefficient Estimations
- Coefficient of Equivalence: High correlations (e.g., .80 or .90) indicate interchangeable form scores, vital to reducing testing biases.
- Coefficient of Stability: Determines the impact of time on test scores; stability coefficients are influenced by the time interval and the measured trait’s nature.
Internal Consistency
- Important for tests administered in a single session; indicates how well individual items represent the overall knowledge or skill assessed.
- The quality of items and their homogeneity significantly affect internal consistency reliability estimates.### Speeded Tests and Internal Consistency
- Speeded tests are those where completion time impacts the final score, such as timed typing tests.
- Internal consistency (IC) assesses item homogeneity and item quality in tests.
- IC for dichotomously scored items (correct/incorrect) can be estimated using:
- Pearson's r combined with the Spearman-Brown Prophecy formula.
- KR-20 or KR-21 formulas, which involve dividing tests into halves and correlating.
- Cronbach’s alpha for reliability estimation.
Estimating Internal Consistency for Dichotomously Scored Items
- The Spearman-Brown Prophecy formula provides an adjusted IC coefficient when a test is halved:
- (\rho_{xx} = \frac{2\rho_{AB}}{1 + \rho_{AB}})
- Example: If (\rho_{xx} = 0.71), estimated total test IC coefficient becomes 0.83.
- KR-20 requires item p-values and is labor-intensive, while KR-21 assumes all items have identical p-values and is simpler to compute.
- KR-21 formula:
- ( KR21 = \frac{k \cdot \bar{x}(k - \bar{x})}{(k - 1)(k)(s^2)} )
- Example of KR-21 application shows at least 23% of variance is due to true score variance.
Internal Consistency for Polytomously Scored Items
- Cronbach’s alpha is used for polytomously scored items, assuming each item is a subtest.
- Coefficient alpha formula:
- (\alpha = \frac{k}{k - 1} \left(1 - \frac{\sum \sigma_i^2}{\sigma_x^2}\right))
- Example calculation of alpha yields a low IC coefficient of 0.375, indicating only 38% of the variance is true score variance.
- Variance for dichotomously scored items is computed as (\sigma^2 = p(1-p)).
Validity Indices
- Measures must be valid and reliable; validity is assessed through logical argument and empirical evidence.
- Types of validity include:
- Content validity: Ensures the measure represents the content area it aims to assess.
- Criterion-related validity: Correlates performance on a measure with another valid benchmark.
- Construct validity: Validates the theoretical constructs associated with the measure.
Content Validity
- A valid test should show moderate to high internal consistency; logical arguments and expert judgment play critical roles.
- Generalizability of results is critical and relies on a representative item sampling.
- Applications include tests, organizational development, and employee assessments.
Criterion-related Validity
- Validity established through correlation between test performance and established measures.
- Predictive validity forecasts performance based on known variables; concurrent validity compares performance across instruments.
- Validation involves selecting appropriate criteria and administering measurements to a representative sample.
Construct Validity
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Involves theorizing relationships among constructs, which are not directly observable but consist of measurable variables.
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Establishing construct validity requires logical arguments and empirical evidence, including validity coefficients and factor analysis.
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Construct validation is resource-intensive and involves confirming or disconfirming findings through repeated studies.### Methods of Construct Validity
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Method 1: Correlation Between Measures
- Administers two measures: one for the construct and one for a designated variable (e.g., job satisfaction vs. salary).
- Positive correlation towards expected values supports construct validity, though no standardized validity coefficient exists.
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Method 2: Difference Studies
- Validity assessed by comparing two distinct groups given a measure, expecting the trained group to perform better.
- Example: Supervisors trained vs. untrained on a performance measure. Expected outcomes support validity if results align.
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Method 3: Factor Analysis
- Advanced statistical method to identify latent variables (factors) predicted by a theory.
- Differentiates between exploratory and confirmatory factor analysis.
- Clusters of interrelated variables indicate underlying relationships; subjective interpretation is common.
- Confirming that all expected factors cluster as theorized supports construct validity.
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Method 4: Convergent and Divergent Validity
- Convergent Validity: Comparison between a well-established measure and a new observational measure, expecting high correlation.
- Divergent Validity: Ensures the measure is distinct from others, requiring low correlation with measures of different constructs.
Performance Assessment Reliability and Validity
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Performance Assessment Reliability
- Reliability ensures consistency across examinees, combining true scores with error scores.
- Aim to minimize random and systematic errors, which can obscure true performance.
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Factors Affecting Reliability
- Vague assessment specifications can confuse examinees.
- Inappropriate performance specifications (e.g., for young children) may introduce errors.
- Managing numerous performance indicators can also increase randomness.
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Bias Errors Impacting Reliability
- Various bias errors identified by Haladyna can lead to misrated performances, such as:
- Response Set: Consistently marking the same on a scale.
- Leniency Error: Overrating despite actual performance differences.
- Central Tendency Error: Rating mostly in the middle range.
- Halo Error: Influenced by unrelated characteristics, such as demeanor.
- Various bias errors identified by Haladyna can lead to misrated performances, such as:
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Improving Performance Assessment Reliability
- Use structured checklists and rating scales.
- Select knowledgeable, motivated raters and conduct effective training.
- Validate rating patterns for consistency to enhance reliability.
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Validity of Direct Performance Assessments
- Must possess at least content validity.
- If predicting future performance, criterion-related predictive validity is necessary.
- Validity threats include poor instructions, rater bias, and the influence of irrelevant impressions.
Key Questions on Reliability and Validity
- Maintain reliability to support accurate predictions and decision-making; reliability coefficients ideally > 0.80.
- Reliability is measured through test-retest stability, inter-rater agreement, and internal consistency.
- Distinguish between systematic error (consistent inaccuracies) and random error (unpredictable fluctuations).
- Identify validity types: content, criterion-related (concurrent and predictive), and construct validity, essential for evaluating test effectiveness.
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