Psychometric Tests & Measures
Norms and Percentiles
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Scores
• Raw Score
• Another name for the Observed Score (Remember this?)
• The score you got on the test.
• Does your raw score reflect what you actually know?
• It may or may not!
• Provides the basis for the other scores we’ll discuss.
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Norm-Referenced (N-R) Scores
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Criterion-Referenced (C-R) Scores
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Norm-Referenced (N-R) Scores
• Norm-referenced scores: used to
evaluate one’s relative performance
compared to others in the group.
● Find a partner & discuss these questions:
● What are some examples of
norm-referenced tests you’ve
taken?
● In what contexts did you take
these tests (e.g., school, work, etc.)?
● Examples of norm-referenced scores:
percentile rank, standard scores.
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Norm-Referenced (N-R) Scores
• N-R scores are used to evaluate one’s relative performance.
• We convert raw scores into percentiles or a type of standard score
(e.g., z-scores).
• Developed by administering a test to a large group of reference test
takers (i.e., Norming).
• Valuable in allowing for the comparisons of outcomes with others
in the same group.
• Norm group
• Sample to base Norming process on.
The mean & standard deviation obtained by this group are the
points of comparison for standard scores.
• Norm group examples: age group, people learning the same
material.
•
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Percentile Rank
• Point in a distribution of scores below which a given percentage
of scores fall.
• Example: 45th Percentile (P45) = the score below which 45% of
the other scores fall.
• Example: 60th Percentile (P60) = the score below which 60% of
the other scores fall.
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Percentile Rank
• Point in a distribution of scores below which a given percentage
of scores fall.
• A weakness is the inequality of units (see below).
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Review: The Normal Distribution
• Shape: symmetrical.
• Central tendency: mean (M), that is the average.
• Variability: standard deviation (SD) goes with the mean.
Shape
M
SD
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Standard Scores
• Standard score: raw score standardized on some metric.
• Usually standardized to variability.
• Example: z-scores are standardized to standard deviations
on the normal distribution.
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Standard Scores
• z-scores are the most frequently used standard scores.
• First subtract the mean of the distribution (µ) from an
individual score from the distribution (X).
• Then, divide that amount by the distribution standard
deviation (σ).
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Standard Scores
• z-scores are the most frequently used standard scores.
• Example: Patrick’s dissertation data.
• z-scores below the mean are negative.
• z-scores above the mean are positive.
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Standard Scores
• Let’s talk about IQ scores.
• Most widely implemented,
controversial, & misunderstood
test scores…
• …be aware of the norm
group when interpreting
them!
• Example: one’s score might
compare to the national &
local norms differently.
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Criterion-Referenced (C-R) Scores
• Criterion-referenced scores: based on a predefined set of
performance criteria on which everyone is evaluated.
● Find another partner & discuss these questions:
● What are some examples of criterion-referenced tests you’ve
taken?
● In what contexts did you take these tests (e.g., school, work, etc.)?
● Examples of criterion-referenced scores: percent scores.
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Criterion-Referenced (C-R) Scores
• C-R scores are based on a predefined set of
performance criteria on which outcomes are
evaluated.
• Importance is placed on criteria, NOT on relative
position (i.e., comparison to others in the group) like
norm-referenced scores.
• Calculating a percentage score.
• Example: For females to pass the USCG fitness test, the
criterion is 15 push-ups and 32 sit-ups.
• Becki gets 13 push-ups and 31 sit-ups during her
practice round, what are her percentage scores?
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• 87% for push-ups & 97% for sit-ups.
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