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© 2013 Springer Publishing Company, LLC.
Chapter 16Interpreting Test Scores
Oermann & GabersonEvaluation and Testing in Nursing Education4th edition
© 2013 Springer Publishing Company, LLC.
Interpreting Test Scores
♦ A test produces a score– Number with no intrinsic meaning – Must be compared with something that has
meaning♦ Interpretations can be norm- or criterion-
referenced
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© 2013 Springer Publishing Company, LLC.
Test Score Distributions
♦ Scoring a test produces a collection of raw scores, recorded by student name or number– Difficult to interpret characteristics of the scores
♦ Arrange in rank order, highest to lowest – Reveals range of scores– Still difficult to judge how a typical student
performed on the test or other characteristics of the obtained scores
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© 2013 Springer Publishing Company, LLC.
Test Score Distributions
♦ Frequency distribution – Remove student names or numbers– List each score once– Tally number of times each score occurs– Identify how well the group of students performed on the
exam more easily – Can represent graphically as a histogram or frequency
polygon • Display scores that occurred most frequently, score distribution
shape, range
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© 2013 Springer Publishing Company, LLC.
Characteristics ofScore Distributions♦ Symmetry♦ Skewness♦ Modality♦ Kurtosis
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© 2013 Springer Publishing Company, LLC.
Symmetry
♦ Symmetric distribution or curve – Equal halves, mirror images of each other
♦ Nonsymmetric or asymmetric distribution or curve– Scores cluster at one end, tail toward other end– Most nursing test score distributions
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© 2013 Springer Publishing Company, LLC.
Skewness
♦ Skew—direction in which the tail extends – Positive skew—tail toward the right (in the
direction of positive numbers on a scale)• Positively skewed distribution—cluster of scores at
low end
– Negative skew—tail toward the left (in the direction of negative numbers)• Cluster of scores at the high end• Most nursing test score distributions
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© 2013 Springer Publishing Company, LLC.
Modality
♦ Number of peaks (cluster of scores) in the distribution
♦ Mode– Most frequently occurring score in the distribution
♦ Unimodal—one peak♦ Bimodal—two peaks♦ Multimodal—many peaks
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Kurtosis
♦ Relative flatness or peakedness of the curve ♦ Platykurtic—relatively flat, gently curved ♦ Mesokurtic—moderately curved♦ Leptokurtic—sharply peaked
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“Curving” Grades
♦ Not appropriate if scores lack characteristics of a normal curve– Bell-shaped: symmetric, unimodal, mesokurtic
© 2013 Springer Publishing Company, LLC.
“Curving” Grades
♦ Most score distributions from teacher-made tests not normally distributed
♦ Shape of distribution affected by:– Test characteristics• Difficult test → positively skewed curve
– Ability of students• Nursing content knowledge not normally distributed
– Students admitted to nursing program not representative of general population
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© 2013 Springer Publishing Company, LLC.
Measures of Central Tendency
♦ Ways of indicating the score that is most characteristic or typical of the distribution
♦ “Middle” of a distribution, scores tend to cluster around it
♦ Three measures– Mode– Median– Mean
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© 2013 Springer Publishing Company, LLC.
Mode
♦ Most frequently occurring score in a distribution♦ Must be an actual obtained score ♦ Identified from frequency distribution or graphic
display without mathematical calculation♦ Rough indication of central tendency♦ Least stable measure of central tendency– Can fluctuate considerably among samples drawn from the
same population
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© 2013 Springer Publishing Company, LLC.
Median♦ Point that divides a score distribution into equal halves ♦ 50th percentile—50% of scores are above and 50% are below♦ Does not have to be an actual obtained score
– Even number of scores—median is halfway between the two middle scores
– Odd number of scores—median is the middle score
♦ Index of location—not influenced by the value of each score – Good for skewed distribution
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© 2013 Springer Publishing Company, LLC.
Mean
♦ Mathematical average of all scores– Computed by summing individual scores and dividing by
the total number of scores– Does not have to be an actual obtained score
♦ Value of the mean is affected by every score in the distribution – Influenced by extremely high or low scores– Not the most accurate measure of central tendency in
highly skewed distributions
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Selecting a Measure ofCentral Tendency♦ Relationship between shape of a distribution
and locations of measures of central tendency– Normal distribution• Mean, median, and mode have the same value
– Positively skewed distribution• Mean is highest, mode is lowest
– Negatively skewed distribution• Mode is highest, mean is lowest
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© 2013 Springer Publishing Company, LLC.
Measures of Variability
♦ Used to determine how similar or different the test scores are
♦ Score distributions may have similar measures of central tendency and different degrees of variability
♦ Most common measures– Range– Standard deviation
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© 2013 Springer Publishing Company, LLC.
Range
♦ Simplest measure of variability ♦ Difference between the highest and lowest scores in
the distribution– Sometimes expressed as highest and lowest scores, rather
than a difference score (e.g., 42 to 60)
♦ Can be highly unstable—based on only two values♦ Tends to increase with number of scores– Wider range of test scores from large group of students
because of likelihood of an extreme score
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© 2013 Springer Publishing Company, LLC.
Standard Deviation (SD)
♦ Most common and useful measure of variability♦ Takes every score in the distribution into
consideration♦ Based on differences between each score and the
mean♦ Represents average amount by which scores differ
from the mean– Smaller if scores cluster tightly around the mean– Larger if scores widely scattered over large range
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© 2013 Springer Publishing Company, LLC.
Interpreting an Individual Score
♦ Scores on teacher-made tests– Norm-referenced interpretations• Use mean and SD to interpret individual scores
– Criterion-referenced interpretations• Used in most nursing education settings• Scores are compared to a preset standard• Example: percentage-correct score
– Comparison of a student’s score with the maximum possible score
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© 2013 Springer Publishing Company, LLC.
Percentage-Correct Scores
♦ Derived (not raw) score♦ Often used as a basis for assigning grades♦ Determined more by test item difficulty than by
quality of performance – If test is more difficult than expected, teacher may
want to adjust the raw scores before calculating the percentage correct
♦ Not to be confused with percentile score– Norm-referenced interpretation
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© 2013 Springer Publishing Company, LLC.
Interpreting an Individual Score♦ Scores on standardized tests– Usually used to make norm-referenced interpretations– More relevant to general rather than specific
instructional goals• Should not be used to determine course grades
– Usually reported in derived scores• Percentile ranks• Standard scores• Norm-group scores
(cont’d)
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© 2013 Springer Publishing Company, LLC.
Interpreting an Individual Score
♦ Scores on standardized tests (cont’d)– Important to specify an appropriate norm group
for comparison – User’s manual includes norm tables with
descriptions of each norm group– Teacher should select the norm group that most
closely matches the group of students • Examples: type of nursing program, public or private
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