Title: Class 4 Basic Psychometric Characteristics: Variability, Reliability, Interpretability October 9, 20
1Class 4Basic Psychometric CharacteristicsVar
iability, Reliability, Interpretability October
9, 2008
- Anita L. Stewart
- Institute for Health Aging
- University of California, San Francisco
2Overview of Class 4
- Concepts of error
- Basic psychometric characteristics
- Variability
- Reliability
- Interpretability
3Components of an Individuals Observed Item Score
- (Simplistic view)
- Observed true item
score score -
error
4Components of an Individuals Observed Item Score
- Observed true item
score score -
error
score that would be obtained over repeated
testings Nunnally, 1994, p211
5Random versus Systematic Error
- Observed true item
score score -
random systematic
error
6Random versus Systematic Error
- Observed true item
score score -
Relevant to reliability
random systematic
error
Relevant to validity
7Components of Variability in Item Scores of a
Group of Individuals
- Observed true
score score
variance variance - Total variance
- (sum of all observed item scores)
error variance
8Components of Variability in Item Scores of a
Group of Individuals
- Observed true
score score
variance variance - Total variance
- (sum of all observed item scores)
(Random)error variance
9Combining Items into Multi-Item Scales
- When items are combined into a summated scale,
random error to some extent cancels out - Error variance reduced as items increases
- Reducing random error increases amount of true
score variance
10Sources of Error
- Subjects
- Observers or interviewers
- Measure or instrument
11Example Measuring Weight of Children
- Observed score is a linear combination of many
sources of variation for an individual
12Measuring Weight in Pounds (Without Shoes) of One
Child
Amount of water past 30 min
True weight 80 lbs
Weightof clothes
Observed weight
Person weighing childrenis not very precise
Scale ismiscalibrated
13Measuring Weight in Pounds (Without Shoes) of One
Child
Amount of water past 30 min .25 lb
True weight 80 lbs
Weightof clothes .70 lb
Observed weight 82.1 lbs
Person weighing childrenis not very precise 1
lb
Scale ismiscalibrated .1 lb
82.1 80 .25 .70 .1 1
14Sources of Error in Measuring Weight of Children
- Weight of clothes
- Subject source of random error
- Scale is miscalibrated
- Instrument source of systematic error
- Person weighing child is not precise
- Observer source of random error
15Measuring Depressive Symptoms (past 4 weeks) in
an Asian or Latino Man
Hard to choose number on the 1-6response choice
scale
Observed depressionscore
True depression 16
Measure misses 2culturally-bound symptoms
Unwillingnessto tellinterviewer
Poor memory of feelings
16Measuring Depressive Symptoms (past 4 weeks) in
an Asian or Latino Man
Hard to choose number on the 1-6response choice
scale 1
Observed depressionscore 12
True depression 16
Measure misses 2culturally-bound symptoms -2
Unwillingto tellinterviewer -2
Poor memory of feelings -1
12 16 1 -2 -1 -2
17Sources of Error in Measuring Depression
- Hard to choose one number on 1-6 response scale
- Subject source of random error
- Unwilling to tell interviewer, poor memory of
feelings - Subject sources of systematic error (underreport
true depression) - Measure misses culturally-bound symptoms
- Instrument source of systematic error
(underestimate true depression)
18Four Types of Memory Errors From Cognitive
Psychology
- Encoding
- Information inadequately stored in memory
- Storage
- Memory eroded over time
- Retrieval
- Some events/feelings harder to recall
- Reconstruction
- Errors filling in missing pieces
R Torangeau, Chap 3, in AA Stone et al. (eds)The
Science of Self-Report, London Lawrence Erlbaum,
2000
19Memory and Time
- Autobiographical memory memory of things in
time and space - Events not encoded with their calendar dates
- Thus time is a poor retrieval method
- Numerous errors remembering when and how
often something occurred within a particular
time frame
N Bradburn, Chap 4, The Science of Self-Report
20Memory and Emotion
- Tend to remember
- positive more than negative experiences
- more emotionally intense than neutral experiences
- non-threatening events more than threatening,
sensitive events
Kihlstrom et al, Chap 6, The Science of
Self-Report
21Overview
- Concepts of error
- Basic psychometric characteristics
- Variability
- Reliability
- Interpretability
22Variability
- Good variability
- All (or nearly all) scale levels are represented
- Distribution approximates bell-shaped normal
- Variability is a function of the sample
- Need to understand variability of a measure in
sample similar to one you are studying - Review criteria
- Adequate variability on the latent variable that
is relevant to your study
23Indicators of Variability
- Range of scores
- Mean, median, mode
- Standard deviation (or standard error)
- Skewness statistic
- at floor (lowest possible score)
- at ceiling (highest possible score)
24Range of Scores Possible and Observed
- Especially important for multi-item measures
- Example
- CES-D possible range is 0-30
- Wong et al. study of mothers of young children
observed range was 0-23 - missing entire high end of the distribution (none
had high levels of depression)
25Mean, Median, Mode
- Mean - average
- Median - midpoint
- Mode - most frequent score
- In normally distributed measures, these are all
the same - In non-normal distributions, they will vary
26Mean and Standard Deviation
- Most information on variability is from mean and
standard deviation - Can envision how measure is distributed on the
possible range - Mean 1 SD 64 of the scores
27Skewness
- Positive skew - scores bunched at low end, long
tail to the right - Negative skew - opposite pattern
- Skewness coefficient ranges from - infinity to
infinity - the closer to zero, the more normal
- Scores 2.0 are cause for concern
28Ceiling and Floor Effects Similar to Skewness
Information
- Ceiling effects substantial number of people get
highest possible score - Floor effects opposite
- More helpful for single-item measures or coarse
scales with only a few levels
29 to what extent did health problems limit you in
everyday physical activities (such as walking and
climbing stairs)?
49 not limited at all (cant improve)
30SF-36 Variability Information in Patients with
Chronic Conditions (N3,445)
All on 0-100 scales, higher is better
McHorney C et al. Med Care. 19943240-66.
31Evidence of Floor and Ceiling Effects in One
SF-36 Scale
24 37
All on 0-100 scales, higher is better
McHorney C et al. Med Care. 19943240-66.
32Reasons for Poor Variability
- Low variability in construct being measured in
that sample (true low variation) - Items not adequately tapping construct
- If only one item, especially hard
- Items not detecting variation at one end
- What to do
- If developing measures, add items
- If selecting measures find another one
33Advantages of Multi-item Scales Revisited
- Using multi-item scales minimizes likelihood of
ceiling/floor effects - Even if items are skewed, multi-item scale
normalizes the skew
34Percent with Best Score on 5 Items in the MOS
MHI-5
- 6-level response scale - all of the time to
none of the time
Stewart A. et al., Measuring Functioning and
Well-Being, 1992
35Percent with Best Score on 5 Items in the MOS
MHI-5
- 6-level response scale - all of the time to
none of the time
5-itemscale 5had highestscore
Stewart A. et al., Measuring Functioning and
Well-Being, 1992
36Overview
- Concepts of error
- Basic psychometric characteristics
- Variability
- Reliability
- Interpretability
37Reliability
- Extent to which an observed score is free of
random error - Produces the same score each time it is
administered (all else being equal) - Population-specific - reliability affected by
- sample size
- variability in scores (dispersion)
- a persons level on the scale
38Back to Components of Variability in Item Scores
of a Group of Individuals
- Observed true
score score
variance variance - Total variance
- (Variation is the sum of all observed item
scores)
error variance
39Reliability Depends on True Score Variance
- Reliability is a group-level statistic
- Reliability
- Reliability 1 (error variance)
- OR
- Proportion of variance due to true score
Total variance
40Reliability Depends on True Score Variance
- Reliability of .70 means 30 of variancein
observed scores is due to error - Reliability total variance error variance
- .70 1.0 .30
41Reliability Coefficient
- Typically ranges from .00 - 1.00
- Higher scores indicate better reliability
42Importance of Reliability
- Necessary for validity (but not sufficient)
- Low reliability (or high measurement error)
attenuates correlations with other variables - May conclude that two variables are not related
when they are - Greater reliability greater power
- The more reliable your scales, the smaller sample
size you need to detect an association
43Reliable Scale?
- NO!
- There is no such thing as a reliable scale
- We accumulate evidence of reliability in a
variety of populations in which it has been tested
44How Do You Know if a Scale or Measure Has
Adequate Reliability?
- Adequacy of reliability judged according to
standard criteria - Criteria depend on type of coefficient
45Types of Reliability Tests
- Internal-consistency
- Test-retest
- Inter-rater
- Intra-rater
46Internal Consistency Reliability Cronbachs
Alpha
- Requires multiple items supposedly measuring same
construct to calculate - Extent to which all items measure the same
construct (same latent variable)
47Internal-Consistency Reliability
- For multi-item scales
- Cronbachs alpha
- for scales using ordinal items (e.g., 1-5)
- Kuder Richardson 20 (KR-20)
- for scales using dichotomous items
48Minimum Standardsfor Internal Consistency
Reliability
- For group comparisons (e.g., regression,
correlational analyses) - .70 or above is minimum (Nunnally, 1978)
- .80 is optimal
- above .90 is unnecessary
- For individual assessment (e.g., treatment
decisions) - .90 or above (.95) is preferred (Nunnally, 1978)
49Internal-Consistency Reliability Can be Spurious
- Based on only those who answered all questions in
the measure - If a lot of people are having trouble with the
items and skip some, they are not included in
test of reliability - Important to compare sample size in reliability
calculation to total sample
50Internal-Consistency Reliability is a Function of
Number of Items in Scale
- Increases with the number of items
- Very large scales (20 or more items) can have
high reliability without other good psychometric
properties
51Example 20 item Beck Depression Inventory (BDI)
- BDI 1978 version (asks about past week)
- Internal consistency reliability .86
Beck AT et al. J Clin Psychol. 1984401365-1367
52Example 20 item Beck Depression Inventory (BDI)
- BDI 1978 version (asks about past week)
- Internal consistency reliability .86
- BUT 3 items correlated lt .30 with other items in
the scale
Beck AT et al. J Clin Psychol. 1984401365-1367
53Reliability Varies by Level on Measure
- Reliability can be poorer for those scoring at
one end of the scale - Example Number of visits to doctor in past 12
months - More reliable for those with fewer visits
54Test-Retest Reliability
- Repeat assessment on individuals not expected to
change - Time between assessments should be
- Short enough so no change occurs
- Long enough so subjects dont recall first
response - Only reliability test for single item measures
- Coefficient correlation between 2 measurements
55Appropriate Test-Retest Coefficients by Type of
Scale
- Continuous scales (ratio or interval scales,
multi-item Likert scales) - Pearson
- Ordinal or non-normally distributed scales
- Spearman or Kendalls tau
- Dichotomous (categorical) measures
- Phi or Kappa
56Minimum Standards for Test-Retest Reliability
- Magnitude of a test-retest correlation is
important, not significance - Criterion similar to that for internal
consistency - gt.70 is desirable
- gt.80 is optimal
57Observer or Rater Reliability
- Inter-rater reliability (across two or more
raters) - Consistency (correlation) between two or more
observers of the same subjects (one point in
time) - Intra-rater reliability (within one rater)
- Consistency within one observer
- Correlation among repeated values obtained by the
same observer (over time)
58Observer or Rater Reliability
- Sometimes Pearson correlations are used scores
on a group of individuals obtained by one
observer correlated with scores obtained by
another observer - Assesses association only
- .65 to .95 are typical correlations
- gt.85 is considered acceptable
McDowell I et al. Measuring Health, 2006, p. 45.
59Association vs. Agreement When Correlating Scores
from Two Times or Ratings
- Association degree to which scores of one rater
linearly predict scores of 2nd rater - Agreement extent to which same score obtained
on 2nd measurement (retest, 2nd rater) - Can have high correlation and poor agreement
- If second score is consistently higher for all
subjects, can obtain high correlation - Need second test of mean differences
60Hypothetical Scores on 4 Subjects by 2 Observers
61Example of Association and Agreement
- Scores by observer 1 are exactly 2 points above
scores by observer 2 - Correlation (association) would be perfect
(r1.0) - Agreement is poor (no agreement on score in all
cases - a difference of 2 between scores on each
subject
62Intraclass Correlation Coefficient (Kappa) for
Testing Inter-rater Reliability
- Coefficient indicates level of agreement of two
or more judges, exceeding that which would be
expected by chance - Appropriate for dichotomous (categorical) scales
and ordinal scales - Several forms of kappa
- e.g., Cohens kappa 2 judges, dichotomous scale
- Sensitive to number of observations, distribution
of data
63Interpreting Magnitude of Kappa Level of
Reliability
- lt0.00
- .00 - .20
- .21 - .40
- .41 - .60
- .61 - .80
- .81 - 1.00
Poor Slight Fair Moderate Substantial Almost
perfect
.60 or higher is acceptable (Landis, 1977)
64Reliability Often Poorer in Lower SES or Low
Literacy Groups
- More random error due to
- Reading problems
- Difficulty understanding complex questions
- Unfamiliarity with questionnaires and surveys
65Advantages of Multi-item Scales Revisited
- Using multi-item scales improves reliability
- Random error is canceled out across multiple
items
66Overview
- Concepts of error
- Basic psychometric characteristics
- Variability
- Reliability
- Interpretability
67Interpretability What does a Score Mean?
- What are the endpoints?
- What does a high score mean? (direction of
scoring) - Compared to norms - is score low or high?
- Single items, more easily interpretable
- Multi-item scales, no inherent meaning to scores
68Endpoints
- What is minimum and maximum possible?
- Enable interpretation of mean score
- When scores are added, endpoints depend on number
of items number of response choices - 5 items, 4 response choices 5 to 20
- 3 items, 5 response choices 3 to 15
69Compare Results to Norms
- Comparing your means to published norms helps
interpret the mean of your sample - SF-36 has numerous norms, e.g.
- General population
- By age group, gender, and chronic disease
70SF-36 in MOS versus Norms
JE Ware et al, SF-36 Health Survey Manual
andInterpretation Guide, The Health Institute,
1993.
71Direction of Scoring
- What does a high score mean?
- Where in the range does the mean score lie?
- Toward top, bottom?
- In the middle?
72Descriptive Statistics for 3,000 Women
Med Care, 2003411262-1276
73Descriptive Statistics for 3,000 Women
Activity no measure mentioned Stress Perceived
stress scale (Cohen, 1983)
Med Care, 2003411262
74Perceived Stress Scale (Cohen 1983) Hard to Find
- Available in JSTOR
- Can print one page at a time
- Searched article on line
- Could not find scoring information other than
reverse 7 of the 14 items and sum them - Possible score range of 0-56
- Could not find response choices
75Another Example Mean Scores in a Sample of Older
Adults
Mean
Physical functioning 45.0 Sleep
problems 28.1 Disability 35.7
76Making it Easier to Interpret
Mean
Physical functioning 45.0 Sleep problems
28.1 Disability 35.7
All scores 0-100
77Making it Easier to Interpret
Mean
Physical functioning () 45.0 Sleep problems
(-) 28.1 Disability (-) 35.7
All scores 0-100 () indicates higher score is
better health (-) indicates lower score is
better health
78Confusion Introduced by Labels
- SF-36 Bodily Pain scale
- Higher score is no pain or limitations due to
pain - Rationale so 8 subscales scored in same
direction - Social Adjustment Scale (Weissman)
- Functional Status Index (Jette)
79Mean Has to be Interpreted Within Possible Range
- M SD
- Parents harsh discipline practices
- Interviewers ratings of mother 2.55
.74 - Husbands reports of wife 5.32
3.30 -
- Note high score indicates more harsh practices
80Mean Has to be Interpreted Within Possible Range
(Add Range)
- M SD
- Parents harsh discipline practices
- Interviewers ratings of mother (1-5)
2.55 .74 - Husbands reports of wife (1-7)
5.32 3.30 -
- Note high score indicates more harsh practices
81Mean Has to be Interpreted Within Possible Range
- M SD
- Parents harsh discipline practices
- Interviewers ratings of mother (1-5)
2.55 .74 - Husbands reports of wife (1-7) 5.32
3.30 - Interviewer 1 2 3
4 5 - Husband 1 2 3 4
5 6 7 - Note high score indicates more harsh practices
2.55
5.32
82Transforming a Summated Scale to a 0-100 Scale
- Works with any ordinal or summated scale
- Transforms it so 0 is the lowest possible and 100
is the highest possible - Eases interpretation across numerous scales
(observed score - minimum possible score)
100 x
(maximum possible score - minimum possible score)
83Homework
- Complete rows 9-20 on matrix for both measures
- Interpretability, scale characteristics,
variability, reliability