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Social Science
Psychology
Psych 440 midterm 2
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Terms in this set (193)
What is Measurement Reliability?
Refers to stability or consistency of measurement
Reliability is a matter of
degree
Reliability is not concerned with
-Are we measuring what we intended to measure?
-The appropriateness of how we use information
-Test bias
*all issues with validity
Classical Test Theory
Any measurement score yielded from some test will be the product of two components
True Score
the true standing on some construct
Error
the part of the score that deviates from that true standing on the construct
X=T+ε
X = observed score on some test
T = true score on some construct
ε = error affecting the observed score
Reliability Coefficients
-Numerical values obtained by statistical methods that describe reliability
-similar properties to correlation coefficients
-generally range from 0 to 1
-affected by number of items
The reliability coefficient usually
indicates the proportion of true variance in the test scores divided by the total variance observed in the scores
Total Variance =
True Variance
+
Error Variance
The Reliability Requirement
- Do we always require a high degree of reliability?
- In what situations might you allow for a lower reliability coefficient?
- What are the implications of lower coefficients?
Standard error of measurement sigma
SEM = sd* √(1-α)
Your Cronbach's alpha for a test
is .90. The scale's standard
deviation of 15. What is the
standard error of measurement
for this measure?
SEM = sd* √(1-α)
= 15√(1-0.90) = 15(.316)= 4.74
This means that on average, a
single total test score will be
4.74 points away from the true
mean of all test scores.
Confidence intervals
+/-Z-interval*sigm
Reliability and Error
-Sources of error help us determine which reliability estimate to choose
-Goal is to use the reliability measure that best addresses the sources of error associated with a test
Sources of Error
-Errors in Test Construction
-Errors in Test Administration
-Errors in Test Scoring and Interpretation
Test Construction Error
-Item or content sampling
-differences in item wording or how content is selected
-produced by variation in items within a test or between tests
What is the standardized
mean/SD for a T-score set to?
Mean = 50
SD = 10
JUST ADD THE Z SCORE
The standard error of
measurement of a particular test
of anxiety is 15. A student earns a
score of 55. What is the confidence
interval for this test score at the
95% level?
(The z-score for this level is 1.96)
95% CI: X ± 1.96*SEM
55 ± 1.96*15 = 55 ± 29.4
55+29.4 = 84.4
55-29.4 = 25.6
Answer: 26 to 84
Administration error
-occurs during the administration of the test that could affect performance
-envirom. factors: temperature, noise, lighting...
-test-taker factors: mood, alertness
examiner factors: physical appearance, nonverbal cues
Scoring and Interpretation Error
-Subjectivity of scoring is a source of error variance
-More likely to be a problem with:
• non-objective personality tests
• essay tests
• behavioral observations
• computer scoring errors?
Types of Reliability
- Test-Retest Reliability
-Parallel or Alternate Forms Reliability
- Inter-Rater or Inter-Scorer Reliability
- Split-Half and other Internal Consistency measures
- Choice of reliability measure depends on the test's design and other logistic considerations
Test-Retest Reliability
-The same test is administered twice to the same group with a time interval between administrations
-Coefficient of Stability is calculated by correlating the two sets of test results
Test-Retest Sources of Error
-stability of the construct
-time
-practice effects
-fatigue effects
Parallel forms
Two different versions of a test that measure the same construct
-each form has the same mean and variance
Alternate forms
Two different versions of a test that measure the same construct
-tests do not meet the equal means and variances
Coefficient of Equivalence is calculated by
correlating the two forms of the test
Parallel-Alternate Error
- There are multiple sources of error that can impact the coefficient of equivalence:
• Motivation and Fatigue
• Events that happen between the two administrations
• Item selection will also produce error
- Used most frequently when the construct is highly influenced by practice effects
Inter-Rater or Inter-Scorer
- Represents the degree of agreement (consistency) between multiple scorers
• or judges, raters, observers, etc.
- Calculated with Pearson r
• or Spearman rho depending on the scale
- Proper training procedures and standardized scoring criteria are needed to produce consistent results
Internal Consistency
-a measure of consistency within the test
-the degree to which all items measure the same construct
-3 ways to measure: split half, kuder-richardson, cronbachs alpha
Split-Half Reliability
-simplest way to calculate internal consistency
-steps: split items in half, scores of each half are correlated, correlation coefficient is corrected using spearman-brown
Spearman-Brown
-can be used to estimate the reliability of a test that has been shortened or lengthened
-reliability increases as the length of the test increases, assuming the additional items are of good quality
Calculating the "n" for Spearman-Brown
If you have 300 items, but would like to have a test of only 100 items
n=100/300=.33
Spearman-Brown equation
rsb = n
rxy / [1 + (n - 1)
rxy]
Kuder-Richardson Formulas
...
Coefficient Alpha
-Can be interpreted as the mean of all possible split-half correlations, corrected by the Spearman-Brown formula
-Most popular reliability coefficient with psychological research
Calculating Coefficient Alpha
...
Reliability is used to measure how consistent
the results of a test will be
Choice of reliability measure depends on
the type of test you are using
Adding items will typically increase
reliability, but this is not always a practical solution
Typically, adding items to a test will have what effect on the test's reliability?
Reliability will increase
Homogenous vs. Heterogeneous Test Construction
- If a test measures only one construct, then the content of the test is homogenous
- If multiple constructs are measured, the test content is heterogeneous
Dynamic vs. Static
- Static traits do not change much
- Dynamic traits or states are those constructs that can change over time
Restriction of Range
-Sampling procedures may result in a restricted range of scores
-Test difficulty may also result in a restricted range of scores
-If the range is restricted, the reliability coefficients may not reflect the true population coefficient
Power vs. Speed
-Power Test - a test that has items that that vary in their level of difficulty
*Most test-takers will complete the test but will not get all items correct
-Speed Test - a test where all items are approximately equal in difficulty
*Most test-takers will get the answers right, but will not finish the test
Power test
can use the all of the regular reliability coefficients
Speed test
reliability must be based on multiple administrations:
-Test-Retest Reliability
-Alternate-Forms Reliability
-Split-Half (special formula used)
Criterion vs. Norm
- Traditional Reliability methods are used most with Norm-Referenced
- Criterion referenced tests tend to reflect material that is mastered hierarchically
• Reduced variability in scores, which will also reduce reliability estimates
Remember Classical Test Theory:
- Remember Classical Test Theory:
• X=T+ε
• The observed score reflects a hypothetical truce score and the influence of error
Generalizability Theory is an alternative view
Suggests that a test's reliability is a function of the circumstances under which the test is developed, administered, and interpreted
Generalizability Theory
-Developed by Lee J. Cronbach
-in this theory there is no "true" score
-a person's score on a given test will vary across administrations depending upon environmental conditions
-environmental conditions are called facets
Impact of Facets on Test Scores
- Facets include: number of items in the test, training of test scorers, purpose of the test administration
- If all facets in the environment are the same across administrations, we would expect the same score each time
- If the facets vary, then we would expect the scores to vary
Applications of Generalizability Theory
- All possible scores from all possible combinations of environment facets is called the universe score
- This provides more practical information to be used in making decisions:
• In what situations will the test be reliable?
• What are the facets that most impact test reliability?
Generalizability vs. True Score
- True-score theory does not identify the effects of different characteristics on the observed score
- True-Score theory does not differentiate the finite sample of behaviors being measured from the universe of all possible behaviors.
- With generalizability theory, we attempt to describe the conditions (facets) over which one can generalize scores
Standard Error of Measurement
- Important for test interpretation of individual scores
- Provides an estimate of the amount of error inherent in an observed score or measurement
- Based upon True-Score Theory
- Inverse relation with reliability
- Used to estimate the extent to which an observed score deviates from a true score
SEM formula
σ * √(1- α)
σ = SD
α = Cronbach's Alpha; Internal
Consistency
SEM in Relation to Classical Test Theory
- Observed score = True score + Error
- The SEM (σmeas) is a method of estimating the amount of error present in a test score
- is a function of the reliability of the test (rxx) and the variability of test scores (σx)
Test Interpretation
-individual vs. the norm
-test designers use normative data provide an interpretive framework
-test users are not interested in groups scores
-enter the standard error of measurement
Reliability and SEM
-If we have high reliability then we would expect highly consistent results
-Reliability and SEM are inversely related
SEM in Practice
...
Calculating SEM
-Standard Deviation of the distribution of test scores
-Reliability coefficient of the test
True Score Estimates
- The observed score will be the best estimate of the true score
- But because of measurement error, it is not an exact indicator
- The standard error of measurement forces us to think of observed test scores as indicating a potential range of scores for the individual
Standard Error of the Difference
-the SEM is most frequently used in the interpretation of an individual's test scores
-Another statistic, the standard error of the difference (σdiff) is better when making comparisons between scores
-Scores between people, or two scores from the same person over time
Interpreting Differences and Changes
Changes in scores can occur across multiple test administrations for many reasons
-Growth
-Deterioration
-Learning
-Or just good old-fashioned Error
Standard Error of the Difference
A statistical measure to determine how large a difference should be before it is considered statistically significant
Reliability coefficients are influenced by
the same issues as correlation coefficients
The type of test (norm, criterion, power, speed, etc.) determines
which type(s) of reliability measures you can use
SEM and SED allows us to
interpret test scores while taking into account reliability
-Confidence intervals are the preferred way to present test information
Validity is a general term referring to a
judgment regarding how well a test measures what it claims to measure
Validity statements refer to
the degree of appropriateness of inferences
What is Measurement Reliability?
Refers to stability or consistency of measurement
Messick's Validity
Evidential: face, content, criterion, construct, relevance/utility
Consequential: appropriateness of use determined by consequences of use
Face Validity
Has more to do with the judgments of the test TAKER, not the test user
Content Validity
A judgment of how adequately a test samples behavior representative of the behavior that it was designed to sample
Content Validity: Step 1
Content validity requires a precise definition of the construct being measured
Step 2: Domain Sampling
Used to determine behaviors that might represent that construct
Step 3: Determine Adequacy of Domain Sampling
Experts asked to rate items to determine if the behavior measured by an item is
-essential to the construct
-useful but not essential
-not necessary
Interpreting CVR
- Calculated for each item
-Values range from -1.0 o +1.0
• Negative: less than half indicating "essential"
• Zero (0): half indicating "essential"
• Positive: more than half indicating "essential"
- Items typically kept if the amount of agreement exceeds chance agreement
Criterion-Related Validity
Criterion: the standard against which a test or a test score is evaluated
-No strict rules exist about what can be used, so it could be just about anything
A good criterion is generally
-relevant
-uncontaminated
-something that can be measured reliably
Concurrent Validity
An index of the degree to which a test score is related to a criterion measure obtained at the same time
Predictive Validity
An index of the degree to which a test score predicts scores on some future criterion
Assessing Criterion Validity
- Validity Coefficient - typically a correlation coefficient between scores on the test and some criterion measure (ray)
- Pearson's r is the usual measure, but may need to use other types of correlation coefficients depending on the data scale
Incremental Validity
Does this test predict any additional variance than what has been previously predicted by some other measure?
Construct Validity
Construct Validity is the process of determining the appropriateness of inferences drawn from test scores measuring a construct
Umbrella Validity
construct validity branches into:
-content
-criterion-related
Construct Validation
takes place when an investigator believes that his instrument reflects a particular construct, to which are attached certain meanings
Construct Validation starts with
hypotheses about how that construct should relate to observables
-Also need to hypothesize how your construct is related to other constructs
Evidence for Construct Validity
- The test is homogenous, measuring a single construct
- Test scores increase or decrease as theoretically predicted
- Test scores vary by group as predicted by theory
- Test scores correlate with other measures as predicted by theory
Homogeneity Evidence
- Do subscales correlate with the total score?
- Do individual items correlate with subscale or total scale scores?
- Do all of the items load onto a single factor using a factor analysis?
Change Evidence
- If a construct is hypothesized to change over time or not, those changes should be reflected by either stability or lack of stability (depending on your theory)
- Should the construct change after an intervention
Group Difference Evidence
- Would we expect differences between "normal" people and people hospitalized for schizophrenia?
Convergent validity
Does our measure highly correlate with other tests designed for or assumed to measure the same construct?
Discriminant Validity
Measure should not correlate with measures of dissimilar constructs
Multitrait-Multimethod Matrix
Both convergent and discriminant validity can be demonstrated using the Multitrait- Multimethod Matrix
-multitrait: must include 2+ traitsExpectancy Data
-multimethod: must include 2+ methods
Expectancy Data
Additional information that can be used to help establish the criterion-related validity of a test
-Usually displayed using an expectancy table
Interpretation Depends on
Rates
Base Rate
Extent to which a particular trait, behavior, characteristic, or attribute exists in the population
Hit Rate
proportion of people accurately identified as possessing or exhibiting some characteristic
Miss Rate
proportion of people the test fails to identify as having or not having a particular characteristic
What is a False Positive?
...
What is a False Negative?
...
Tests can be invalid for different reasons
design issues, confounding variables, and inappropriate use
Different measures of validity are used to
address concerns about threats to validity
Choice of validity measure also depends on
the type of test and its purpose
For a norm-referenced test, a good item is one where
people who scored high on the test tended to get it right, and people who scored low tended to get it wrong
For a criterion-referenced test, the items need to
assess mastery of the concepts
Scaling is the process of
selecting rules for assigning numbers to measurement of varying amounts of some trait, attribute, or characteristic
Likert (& Likert-type)
taker presented with 5 alternative responses on some continuum
-generally reliable
-result in ordinal level data
-summative scale
Method of Paired Comparisons
taker presented with two test stimuli and are asked to make some sort of comparison
Sorting Tasks
takers asked to order stimuli on the basis of some rule
-Categorical - placed in categories -Comparative - placed in an order
Guttman Scale
-Items range from weaker to stronger expressions of variable being measured
-Arranged so that agreement with stronger statements implies agreement with milder statements as well
-ordinal data
Thurstone Scaling Method
Process designed for developing a 'true'
Thurstone Scaling Method - start with a large item pool
-Get ratings of the items from experts
-Items are selected using a statistical evaluation of the judges ratings
Test Construction: Choosing Your Item Type
selected or constructed
Selected response items
generally take less time to answer and are often used when breadth of knowledge is being assessed
Constructed response items
are more time consuming to answer and are often used to assess depth of knowledge
Item types: Advantages and Disadvantages
...
Test Construction: Writing Items
Rule of thumb is to write twice as many items for each construct as what will be intended for the final version of the test
An ITEM POOL is a
reservoir of potential items that may or may not be used on a test
Test Construction: Scoring Items
Decisions about scoring of items are related to the scaling methods used when designing the test
options= cumulative, class/categorical/ipsative
Stage 3: Test Tryout
-Should use participants and conditions that match the test's intended use
-Rule of thumb is that initial studies should use five or more participants for each item in the test
Guessing and Faking
-Guessing is only an issue for tests where a "correct answer" exists
-Faking can be an issue with attitudes
Guessing Correction Methods
- Verbal or written instructions that discourage guessing
- Penalties for incorrect answers (i.e., test- taker will get no points for a blank answer, but will lose points for an incorrect answer)
- Not counting omitted answers as incorrect
- Ignoring the issue
Faking Corrections
- Lie scales
- Social Desirability scales
- Fake Good/Bad scales
- Infrequent response items
- Total score corrections based on scores obtained from measures of faking
- Using measures with low face validity
Step 4: Item Analysis
- A good test is made up of good items
• Good items are reliable (consistent)
• Good items are valid (measure what they are supposed to measure)
• Just like a good test!
- Good items also they help discriminate between test-takers on the basis of some attribute.
- Item Analysis is used to differentiate good items from bad items
Item Analysis - Basic Procedures
Procedures used may vary depending upon the goals of the developer
-goals: enhance forms of reliability, certain forms of validity, discrimination
Four indices are used to analyze and select items:
-Indices of item difficulty
-Indices of item reliability
-Indices of item validity
-Indices of item discrimination
Ideally, if we develop a test that has "correct" and "incorrect" answers
we would like to have those takers who are highest on the attribute to get more items correct than those that are not high on that attribute
The proportion of the total number of testtakers who got the item right (pi)
p1 = .90; 90% got the item correct
p2 = .80; 80% got the item correct
p3 = .75; 75% got the item correct
p4 = .25; 25% got the item correc
Ideal Average
Ideal average pi is halfway between chance guessing and 1.0
Item-Total Correlation
A simple correlation between the score on an item and the total test score
Advantages of Item-Total Correlation
-can test statistical significance of the correlation
-can interpret % of variability item accounts for (rit2)
Item-Reliability Index
is the product of the item-score standard deviation and the correlation between the item score and the total test score
-Provides an indication of the tests internal consistency. The higher the index, the higher the consistency
Item-Reliability
Remember, internal consistency is a measure of how well all items on a test are measuring the same construct
-another way is factor analysis
Item-Discrimination Index
If discrimination between those with high and low on some construct is the goal
-we would want items with higher proportions of high scorers getting the item "correct"
-and lower proportions of low scorers getting the item "correct"
Item-Discrimination Index is used to
compare the performance on a particular item with performance in the upper and lower regions of a distribution of continuous test scores
Item-Discrimination Index symbolized by
d - compares proportion of high scorers getting item "correct" and proportion of low scorers getting item "correct"
d = [U - L] / n
Item-Discrimination (Method 2)
...
Empirically Keyed Scales
- Goal is to choose items that produce differences between the groups that are better than chance
- Resulting scales often have heterogeneous content and have a limited range of interpretation
- Used in clinical settings, especially for diagnosis of mental disorders
• Also used in career counseling
Step 5: Test Revision
Modifying the test stimuli, administration, etc., on the basis of either quantitative or qualitative item analysis
Cross-Validation
Re-establishing the reliability and validity of the test with other samples
Item Fairness
-An item is unfair if it favors one particular group of examinees in relation to another
-Results in systematic differences between groups that are not due to the construct being tested
Items can be designed to measure breadth or depth of knowledge
It is difficult to measure both breadth and depth at the same time
Item difficulty and item discrimination are both important considerations for selecting effective items for a test
Optimal item difficulty (from a psychometric standpoint) may be impractical sometimes
Classical Test Theory formula
X=T+E
X= observed score
T= true score
E= error affecting the observed score
Standard Error of Measurement formula
σ√(1-α)
α= reliability of the test
σ= variability of test scores
Error in test construction
Item or content sampling (differences in item wording and how content is selected may produce error)This error is due to variation of items within a test or between different testsMay have to do with how a behavior is sampled or what behavior is sampled
Error in test administration
Anything that occurs during the administration of a test that could affect performance Environmental factorsTest-taker factors Examiner factors
Error in test scoring and interpretation
Subjectivity in scoring is a source of error variance It is more likely to be a problem in non-objective personality tests, essay tests, behavioral observations, computer scoring errors
The higher an item difficulty index is...
the easier the item is
An item difficulty index of .28 means that
28% of the test takers answered the item correctly; an item difficulty index of .73 means 73% of the test takers answered the item correctly. Therefore, the second item would be easier than the first one.
Cronbach's alpha is a measure of the
overall internal consistency of a scale. It is the mean of all possible split-half reliability measures for the scale
Item-total correlations are a measure of the
amount of covariance (overlap in variability) between an item and the rest of the scale
-They're measures of the validity of individual items within a scale.
If an item-total correlation is low
that's a sign that an item should be eliminated
An item will have poor content validity if it is
not measuring the same construct as other items in the scale
Items that measure the same construct as the rest of the scale will have
good content validity and strong, positive item-total correlations
Item difficulty indexes are calculated through
dividing the total number of correct responses by the total number of all responses
Item discrimination indexes are calculated through
dividing the difference between experts and novices by the average number of people in each group
The lower the reliability
the larger the SEM
If the test is reliable the true score will be
higher so that means if a test has high reliability it will have a low SEM and if the test has low reliability it will have a high SEM
a simple way of thinking about reliability is how consistent it is
the best way to see if a test is reliable is to create a trial with different populations to see if you get the results you'd expect. A reliability index could also show a test's internal consistency
One of the simplest ways to tell if a test is reliable is to use the
test-retest method in which the same group of participants takes the same exam twice over a set period of time. If the participants scores for both tests are similiar then the tests demonstrate having reliability
Can you have high reliability and low validity on a test?
Yes, you can have highly consistent results, or highly consistent data/questions, and also have low validity. The questions/results can be reliable, but they can also have nothing to do with what the test is actually trying to measure
Likert Scaling: good for
assessing constructs related to degree or frequency, such as political opinions or prevalence of happy moods
Guttman Scaling: good for assessing
constructs where ideas build on each other, such as attitudes toward how to best treat mental health challenges
Thurstone Scaling: good for assessing
attitude-related constructs that can be adapted to agree/disagree statements, where these statements correspond to an clear level of favorability toward the attitude topic
The observed score will be the best estimate of the
true score
The observed score will be the best estimate of the true score but not
an exact indicator, because of measurement error
SEM forces us to think of observed test scores as
indicating a potential range of scores for the individual
what is validity
how well a test measures what it's trying to measure
Content validity
1. find a precise definition of the construct being measured
2. use domain sampling to determine all possible behaviors that represent that construct
3. determine how well test items sample full domain of those behaviors
concurrent validity
how well results of this test align with other outcomes measured at the same time
predictive validity
how well test scores align with other outcomes measured after the test has been taken
predictive validity - incremental validity
type of predictive validity, does this measure add any predictive power?
convergent validity
does our measure highly correlate with other tests designed to measure the same construct? if so, good
discriminant validity
does our measure correlate with other tests of dissimilar constructs? if so, bad
fairness and bias determine test validity in
practice
bias
problem with the test itself (statistical )
high systematic error that results in inaccurate measurements across groups
means the test cannot possibly be fairly used
fairness
a problem with the way the test is used
regardless of statistical properties, means that test is being used in discriminatory way
item format
form, plan, structure, arrangement and layout of individual test items
selected response
fast, good for breadth of knowledge
more structured (more reliable)
constructed response
slower
good for depth of knowledge
more subjective (less reliable)
discrimination
how well items tell who should do well from people who should not do well
item analysis - differentiating good from bad items
4 indices used
-item difficulty
-item reliability
-item validity
-item discrimination
item reliability and validity
often measured through confirmatory factor analysis
-FA: measure of how many sources of variance there are in a test
-CF: measure of extent to which test variance aligns to theory
item difficulty
proportion of all people who got the question right
# correct answers/total # questions
item discrimination
based on the number of people in two subgroups who got it right
# correct for experts - # correct for novices / average # in each group
item discrimination interpretation
d=.60
positive - more experts than notices answered the item correctly
above 0 - there is a reasonable difference in performance between experts and novices
signs of a bad item
everyone/no one getting it wrong
.
distractors
incorrect answer options on multiple choice test
-item difficulty and discrimination affected
possibilities for validity and reliability are
- low validity, high reliability
- low validity, low reliability
- high validity, high reliability
you cannot have a test with high validity and
low reliability
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