chapter 16 ppt eval & testing 4e formatted 01.10 kg edits

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Chapter 16Interpreting Test Scores

Oermann & GabersonEvaluation and Testing in Nursing Education4th edition


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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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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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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Characteristics ofScore Distributions♦ Symmetry♦ Skewness♦ Modality♦ Kurtosis

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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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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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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


“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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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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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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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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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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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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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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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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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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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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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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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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