The Meaning of Test Scores

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The Meaning of Test Scores

• Schroeder
• PSY/SPED 572

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Background Statistics

• Scales of Measurement
• Nominal
• LD, ED, OHI
• Ordinal
• 89, 85, 70, 69, 50
• Interval
• Ratio

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Describing Data

• Distributions
• Graphs of scores used to represent how scores
  relate to each other
• Histograms, Frequency Polygons, Curves

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Histogram
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Frequency Polygon
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Curve
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Homework 1

• As a follow-up to the "Everyday Psychometrics"
  section on graphing data, please bring in graphs
  published in newspapers or magazines. We will
  discuss whether the graphs aid in interpreting
  the data or serve to misrepresent the data.

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Symbols

• ?
• X
• N
• f
• X
• S2
• S

• Sum
• Score
• Number of cases
• Frequency
• Mean
• Variance
• Standard Deviation

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Raw Scores

• Based on number of items answered correctly
• Provides basis for all other scores (is
  absolutely necessary)
• Not used in test interpretation because it
  depends on number and difficulty of test items

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Measures of Central Tendency

• 95, 87, 86, 86, 78, 73
• Mean (average)
• Median (score that cuts distribution in half)
• Mode (most frequently occurring score)

• X ?X / N

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Measures of Variability

• 95, 87, 86, 86, 78, 73
• Range
• Highest Score Lowest Score
• Quartiles (p. 79)
• Standard Deviation
• Get from variance

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Homework 2

• Review the evening newspaper and/or weekly news
  magazines and look for news articles or
  advertisements that include references to the
  statistics discussed in this chapter. Bring in
  the articles to discuss during the next class
  session, focusing on the type of statistics
  utilized and whether the appropriate one was
  chosen.

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Skewness

• Describes how scores are distributed not bad or
  abnormal
• Positive skew
• Negative skew

Mo
Md
M
Mo
M
Md
The tail tells the tale
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Question

• You are the union negotiator for a company that
  has a number of very high paid workers who have
  been with the company for a very long time. You
  are trying to negotiate for a substantial raise
  for next year. Which statistic would you want to
  use to summarize the average salary of your
  workers, the mean or median? Why?

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• Discuss the types of distributions of data you
  would expect for the following
• a) IQ test scores from all pupils enrolled in
  Illinois schools
• b) IQ test scores from all pupils enrolled in
  Bayonne, New Jersey schools
• c) test scores from a very difficult test
• d) a series of 1,000 rolls of the die
• e) college professors' salaries in an university
  department in which all of the professors have
  tenure and have been teaching for more than 20
  years
• e) test scores from a very easy test.

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Why norms are important

• Allow us to compare an individuals test score to
  those of others who took the test
• Norms determine percentiles, standard scores,
  grade equivalents, etc.

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Norms

• Standardization
• Norm-referenced
• Sampling

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Within-Group Norms

• Age norms (equivalents)
• Grade norms (equivalents)
• Percentiles (not Percentage Correct)
• 86th percentile ?
• Standard Scores
• z-scores
• t-scores
• Stanines (p. 88)
• Deviation IQ

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Relativity of Test Norms

• Normative Sample
• National Anchor Norms
• Specific Norms
• Fixed Reference Group

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Domain-referenced score interpretation

• Compare individuals performance to a set
  standard (or criterion)
• Best used for testing basic skills, not more
  complex processes
• Create specific objectives and probes for those
  objectives
• Reports what skills a person has
• Need to determine cutoff score

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The Normal Curve

• Many traits are normally distributed in the
  population
• See p. 84 for examples
• Few very extreme, most clustered around average
• Understanding the normal curve
• Shows how scores relate to one another
• Value is in knowing how may cases fall between
  two scores
• What psychological traits would you not expect to
  be normally distributed?

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What is a good test?

• Reliability
• Validity
• Other considerations

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Standards activity

• Standards introduction
• Identify main points of introduction
• Standard 11 Standard 5
• Summarize your standard in everyday language and
  give an example of where it might apply