Chapter 3. Reliability:

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Chapter 3. Reliability

• As my grand pappy, Old Reliable,
• used to say . . .
• Who is this famous bloodhound?
• What was he noted for saying?

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What CU?
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Reliability Topics

• The Basic Notion of Reliability
• Factors Affecting Reliability
• Methods of Determining Reliability
• Methods Used by Professional Test Makers
• Method Suggested for Your Own Tests
• Standard Error of Measurement
• Confidence Bands

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Basic Notions of Reliability

• Reliability refers to the reliability of a test
  score or set of test scores, not the reliability
  of the test.
• Reliability questions ask Are the scores
  consistent? Are they stable?
• Reliability is a matter of degree it is NOT
  all-or-none.
• Reliability is not the same as validity
  validity asks Does a test measure what is
  suppose to? (reliability is necessary for, but
  not a sufficient condition for, validity) .
• Reliability deals with unsystematic error in
  assessment. Systematic error (examples, I test
  well because I am test-wise or I do not test
  well because English is not my first language)
  will not be uncovered through tests of reliability

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Factors Affecting ReliabilitySources of
Unreliability

• Test Scoring
• difference between two scorers judgments
• one scorer over time (fatigue) and/or halo effect
  
• Test Content
• the sample of test items is too small
• the sample of test items is not evenly selected
  across material
• Test Administration
• noise, time limits not consistent, physical
  conditions
• Personal Conditions
• temporary ups and downs
• (chronic test anxiety would be a systematic error
  and thus undetectable through measures of
  reliability)
• Note None of these factors automatically result
  in unreliability, but as we build our
  assessments, we hope to reduce the impact of
  these factors. The extent to which these factors
  may be affecting test scores is an empirical
  question and we can and will address this as we
  continue.

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A Bit of Theory (True/Observed)

• The perfect test would be unaffected by the
  sources of unreliability and on this perfect test
  each examinee should get his or her true score.
  Unfortunately, we know the observed score we get
  was likely affected by one or more of the sources
  of unreliability.
• So, our observed score is likely too high or to
  low. The difference between the observed score
  and the true score we call the error score and
  this score can be positive or negative.
• We can express this mathematically as
• True Score Obtained Score /- Error
• T O /- E (or, looking at it another way, O T
  /- E)
• Theory Time If we could re-administer a test to
  one person an infinite number of times, what
  would expect the distribution of their scores to
  look like? Answer The Bell Shaped Curve. We
  will return to this concept when we discuss the
  standard error of measurement.

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Determining Reliability by Usingthe Concept of
Correlation

• I can use my understanding of correlation (how
  two things are related) to come up with a
  mathematical calculation that will suggest the
  strength (or lack of strength) regarding one or
  more of the sources of unreliability that I have
  identified.
• I will be calculating what will be called the
  reliability coefficient (since it is a
  correlation coefficient measuring a type of
  reliability). This value will range -1 to 1.
• For example, lets consider rater reliability.
  That is, do different scorers rate equally or,
  another concern, does one scorer rate differently
  over time. We express that as either
• Inter-rater reliability among raters
  (international many nations)
• Intra-rater same rater (intramural sports
  within 1 school)
• Note the hyphen after inter- and intra- may not
  be used by some authors
• Compute using Spearman Rank Correlation

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Some History . . . Karl Pearson (1857-1936)

• Pearson was a Galton protégé and was appointed
  the first Galton Professor or Eugenics (1911) at
  University College of London .
• Introduced a new science  "Biometrics" which
  integrated statistics with evolutionary theory.
• Advocated social imperialism "superior" races
  and countries should produce more offspring than
  those considered to be less developed.
• In the United States, Indiana was the first to
  pass a pioneering statute (1907) allowing state
  officials to sterilize those deemed unfit to
  breed. California enacted an even stricter
  eugenics law.  California made it legal for state
  officials to asexualize those considered
  feeble-minded, prisoners exhibiting sexual or
  moral perversions, and anyone with more than
  three criminal convictions. 

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More Reliability Approaches to Consider

• Test-retest (impractical for you important in
  standardized tests)
• Alternate Forms (again, impractical for you but
  important in standardized tests)
• Internal Consistency (not appropriate for speeded
  tests)
• Kuder-Richardson (really a series of formulas
  based on dichotomously scored items)
• Coefficient alpha - Cronbachs (most widely used
  as can be used with continuous item types)
• Split-half odd-even w/Spearman-Brown
  correction to apply to full test (easiest for you
  to do and understand)

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Reliability of Your Classroom Tests

• I would recommend doing Split-Half Reliability.
• Step 1 Split your test into two parts (odd
  even).
• Step 2 Use Pearson Product Moment Correlation
  - Ungrouped Data to determine rxy (rxy
  represents the correlation between the two halves
  of the scale). By doing the split-half we reduce
  the number of items which we know will
  automatically reduce the reliability, SO
• Step 3 To estimate reliability of whole test
  then use the Spearman Brown correction formula
• rsb 2rxy /(1rxy)
• where rsb is the split-half reliability
  coefficient

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As a Teacher, What Do I Need to Know Most About
Reliability

• For tests I create myself
• Increasing number of items increases reliability.
• Moderate difficulty level increases reliability.
• Having items measuring similar content increases
  reliability.
• For standardized tests I use
• Look for each tests published reliability data.
• Use the published reliability coefficient to
  determine the Standard Error of Measurement
  (abbreviated SEM) found in the data
• See the following illustration

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Standard Error of Measurement

• The SEM is the standard deviation of a
  hypothetically infinite number of obtained scores
  around a persons true score.

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SEM and Confidence Bands

• The SEM is a standard deviation of a distribution
  assumed to be normal .
• So computing the SEM can help me better interpret
  scores
• Formula SEM SD ? 1 - r
• I can take the computed SEM and build a
  Confidence Band around my score.
• Confidence Band
• 68 Confidence Band /- 1 SEM
• 95 Confidence /- 1.96 SEM
• 99 Confidence /- 2.58 SEM
• I can also do percentiles (a bit harder).
• Many professional test makers give me this
  information

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Final Thoughts Advice

• Use multiple sources of information.
• Find and Use a published tests SEM to help
  interpretation.
• Standard Error of Measurement is distinct from
• Standard error of mean (samples/populations)
• Standard error of estimate (prediction)
• Reliability for Criterion-referenced Items may
  use techniques already covered but sometimes
  require special treatment.
• Worry about scorer reliability when score depends
  on judgment.

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More Final Words . . .

• Reliability for Sub Scores is problematic since
  small clusters are usually quite unreliable.
• For important decisions, get reliability gt.90.
• Be wary of short tests. To increase reliability,
  increase number of items, exercises, or
  observations.
• Occasionally check reliability of your classroom
  tests.
• Be able to distinguish between reliability and
  validity.

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Terms/Concepts to Review andStudy on Your Own (1)

• alternate form reliability
• coefficient alpha (Cronbachs)
• confidence band
• error score
• internal consistency
• inter-rater reliability
• intra-rater reliability
• observed score

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Terms/Concepts to Review andStudy on Your Own (2)

• odd-even reliability
• reliability coefficient
• Spearman-Brown correction
• split-half reliability
• standard error of measurement
• test-retest reliability coefficient
• true score