Chapter 3 Understanding Test Scores Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition

Chapter 3Chapter 3Understanding Understanding

Test ScoresTest Scores

Robert J. Drummond and Karyn Dayle JonesAssessment Procedures for Counselors and Helping Professionals, 6th editionCopyright ©2006 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458All rights reserved.

Test ScoresTest Scores

Imagine that you receive a grade of 60 for Imagine that you receive a grade of 60 for a midterm exam in one of your university a midterm exam in one of your university classes. classes.

What does the score mean, and how What does the score mean, and how should we interpret it? should we interpret it?


Two Methods of InterpretationTwo Methods of Interpretation

Criterion-Referenced InterpretationCriterion-Referenced Interpretation

Norm-Referenced InterpretationNorm-Referenced Interpretation


Criterion-Referenced InterpretationCriterion-Referenced Interpretation

Definition:Definition:– student'student'ss test performance is compared to established test performance is compared to established

criteria rather than to the performance of other students criteria rather than to the performance of other students – the criteria are the basis of evaluating student progress, the criteria are the basis of evaluating student progress,

standards, or competenciesstandards, or competencies

Most useful when test designed for this Most useful when test designed for this purpose: purpose: – set of clearly stated learning objectives set of clearly stated learning objectives – enough items to infer degree of mastery or non-mastery enough items to infer degree of mastery or non-mastery

of that domain of that domain – items selected to actually measure that domain items selected to actually measure that domain


Norm-Referenced InterpretationNorm-Referenced Interpretation

Definition Definition – student’s score relative to other students (in a student’s score relative to other students (in a

norm group) norm group) – norm group is carefully defined norm group is carefully defined – no need to look at level of mastery no need to look at level of mastery

Two of the major forms of norm-Two of the major forms of norm-referenced interpretation:referenced interpretation:– percentiles percentiles – standard scores standard scores


Types of ScoresTypes of Scores Raw scoreRaw score

– Number of points when scored following the scoring directionsNumber of points when scored following the scoring directions– Has no inherent meaningHas no inherent meaning

PercentilesPercentiles– One of the most widely used methods to express the relative position of the test One of the most widely used methods to express the relative position of the test

taker on a norm-referenced test. taker on a norm-referenced test.

Standard Scores (share a common logic; can be translated into each Standard Scores (share a common logic; can be translated into each other) other) – Z scoresZ scores– T scoresT scores– Deviation IQsDeviation IQs– StaninesStanines– Sten scoresSten scores

Developmental ScalesDevelopmental Scales– Age normsAge norms– Grade equivalentsGrade equivalents


PercentilesPercentiles

A percentile is a score that indicates the rank of the student A percentile is a score that indicates the rank of the student compared to others (same age or same grade), using a compared to others (same age or same grade), using a hypothetical group of 100 students. hypothetical group of 100 students.

A percentile of 25 (25A percentile of 25 (25thth percentile), for example, indicates that percentile), for example, indicates that the student's test performance equals or exceeds 25 out of 100 the student's test performance equals or exceeds 25 out of 100 students on the same measure.students on the same measure.

A percentile of 87 indicates that the student equals or A percentile of 87 indicates that the student equals or surpasses 87 out of 100 (or 87% of) students. surpasses 87 out of 100 (or 87% of) students.

Must always refer to a student’s percentile rank as relative to Must always refer to a student’s percentile rank as relative to a a particular norm group.particular norm group.

If you scored at the 80If you scored at the 80thth percentile, what does that mean? percentile, what does that mean?Robert J. Drummond and Karyn Dayle JonesAssessment Procedures for Counselors and Helping Professionals, 6th editionCopyright ©2006 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458All rights reserved.

QuartilesQuartiles

Quartile is another term referred to in percentile Quartile is another term referred to in percentile measure. The total of 100% is broken into four measure. The total of 100% is broken into four equal parts: 25%, 50%, 75% 100%. equal parts: 25%, 50%, 75% 100%.

Lower Quartile is the 25th percentile. (0.25)Lower Quartile is the 25th percentile. (0.25) Median Quartile is the 50th percentile. (0.50) Median Quartile is the 50th percentile. (0.50) Upper Quartile is the 75th percentile. (0.75)Upper Quartile is the 75th percentile. (0.75)


Standard ScoresStandard Scores Scores that are based on mean and Scores that are based on mean and

standard deviation standard deviation Transformed standard scores: z scores, T Transformed standard scores: z scores, T

scores, deviation IQ, stanines, stensscores, deviation IQ, stanines, stens


Z ScoreZ Score The standard normal distribution is sometimes called the z The standard normal distribution is sometimes called the z

distribution. distribution. Mean = 0Mean = 0 SD = 1SD = 1 For instance, if a person scored a 70 on a test with a mean For instance, if a person scored a 70 on a test with a mean

of 50 and a standard deviation of 10, then they scored 2 of 50 and a standard deviation of 10, then they scored 2 standard deviations above the mean. standard deviations above the mean.

So, a z score of 2 means the original score was 2 standard So, a z score of 2 means the original score was 2 standard deviations above the mean. deviations above the mean.


Z scores: Handy for thinking Z scores: Handy for thinking about the normal distributionabout the normal distribution

Center a bell curve on Center a bell curve on zerozero

Sign (+) = above the Sign (+) = above the mean, (−) = below the mean, (−) = below the meanmean

Number = standard Number = standard deviationdeviation

• +1/+1/−−1 standard deviation includes about 68% of cases (34% on each side)1 standard deviation includes about 68% of cases (34% on each side)

• +/+/− − 2 standard deviations includes about 95% of cases 2 standard deviations includes about 95% of cases

• +/+/−− 3 standard deviations includes about 99.7% of cases 3 standard deviations includes about 99.7% of cases

• ALL ASSUMING SCORES DISTRIBUTED NORMALLYALL ASSUMING SCORES DISTRIBUTED NORMALLYRobert J. Drummond and Karyn Dayle JonesAssessment Procedures for Counselors and Helping Professionals, 6th editionCopyright ©2006 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458All rights reserved.

T ScoresT Scores T scores are also standardized scores. T scores are also standardized scores. Mean = 50 Mean = 50 SD = 10 SD = 10 A score of 60 is one standard deviation A score of 60 is one standard deviation

above the mean, while a score of 30 is two above the mean, while a score of 30 is two standard deviations below the mean.standard deviations below the mean.


Deviation IQsDeviation IQs

Wechsler Scales (WISC and WAIS) Wechsler Scales (WISC and WAIS) – mean = 100 mean = 100 – SD = 15SD = 15

Stanford-Binet Stanford-Binet – mean = 100 mean = 100 – SD = 16SD = 16


StaninesStanines ““Standard 9’s”Standard 9’s” Range 1 to 9Range 1 to 9 Mean = 5Mean = 5 SD = 1 SD = 1 the largest number of individuals falling in the the largest number of individuals falling in the

middle stanines (3-7), with fewer students falling middle stanines (3-7), with fewer students falling at the extremes at the extremes


Sten ScoresSten Scores A STEN score is a standard score from a A STEN score is a standard score from a

distribution in which most of the scores (almost distribution in which most of the scores (almost 99%) have a range from 1 to 10 (which gives it its 99%) have a range from 1 to 10 (which gives it its name, STEN, meaning Standard Ten). name, STEN, meaning Standard Ten).

Mean = 5.5 Mean = 5.5 SD = 2SD = 2


Norm Score DistributionNorm Score Distribution


Grade Equivalent ScoresGrade Equivalent Scores

DescriptionDescription Definition: the grade level at which the typical Definition: the grade level at which the typical

student obtains that raw scorestudent obtains that raw score Sample interpretation: “student had the same Sample interpretation: “student had the same

raw score that was average for students in grade raw score that was average for students in grade 5.6 in the average school”5.6 in the average school”

Typical score is determined for each month in a Typical score is determined for each month in a grade: 5.0-5.9grade: 5.0-5.9

Widely used, especially in elementary schoolWidely used, especially in elementary school


Grade Equivalent ScoresGrade Equivalent ScoresWidely Misinterpreted!Widely Misinterpreted! Don’t confuse GE norms with standards that all students should attain Don’t confuse GE norms with standards that all students should attain Don’t interpret a GE as an estimate of the grade a student should be Don’t interpret a GE as an estimate of the grade a student should be

placed in placed in Don’t expect all students to gain 1.0 GE each year (the average). Not a Don’t expect all students to gain 1.0 GE each year (the average). Not a

realistic goal realistic goal Don’t assume that the units are equal at different parts of the scale Don’t assume that the units are equal at different parts of the scale

(the same difference can mean “just above” or “vastly above” average) (the same difference can mean “just above” or “vastly above” average) Don’t assume that scores on different tests are comparable Don’t assume that scores on different tests are comparable

– Different publishers test fuller ranges of students than others Different publishers test fuller ranges of students than others – Patterns of growth (variance in scores) may differ across subjects Patterns of growth (variance in scores) may differ across subjects

Don’t interpret extreme scores as dependable estimates of student’s Don’t interpret extreme scores as dependable estimates of student’s performance (usually extrapolated) performance (usually extrapolated)

UsefulnessUsefulness Most useful in reporting growth in basic skills in elementary school Most useful in reporting growth in basic skills in elementary school Least useful for comparing performance on different tests Least useful for comparing performance on different tests Inequality in grade units will muddle interpretation if you don’t keep it Inequality in grade units will muddle interpretation if you don’t keep it

clearly in mind clearly in mind


Norm-referenced TestsNorm-referenced Tests

Compare an individual child's performance to Compare an individual child's performance to that of his or her classmates or some other that of his or her classmates or some other larger group. larger group.

Tells how one child compares to similar Tells how one child compares to similar children on a given set of skills and children on a given set of skills and knowledge, but does not provide information knowledge, but does not provide information about what the child does and does not know.about what the child does and does not know.

Scores on norm-referenced tests indicate the Scores on norm-referenced tests indicate the student's ranking relative to that group.student's ranking relative to that group.


NormsNormsThe specific group of test takers upon which the test scores were The specific group of test takers upon which the test scores were

checked for validity and reliabilitychecked for validity and reliability

Criteria for Judging Norms:Criteria for Judging Norms: RelevantRelevant

– Is this particular norm group appropriate for (a) the decision you want to Is this particular norm group appropriate for (a) the decision you want to make, make, andand (b) the set of test takers involved? (b) the set of test takers involved?

RepresentativeRepresentative – Was the norm group created with a random sample or stratified random Was the norm group created with a random sample or stratified random

sample? Does it match census figures (by race, sex, age, location, etc.) sample? Does it match census figures (by race, sex, age, location, etc.) for the general population being considered? for the general population being considered?

Up-to-dateUp-to-date – Don’t rely on the copyright date of the test manual. Read the manual to Don’t rely on the copyright date of the test manual. Read the manual to

see how old the norms are. see how old the norms are. – Beware of Lake Wobegon effect (the tendency to treat all members of a Beware of Lake Wobegon effect (the tendency to treat all members of a

group as above average—a statistical impossibility).group as above average—a statistical impossibility).


In summary, when evaluating test norms, In summary, when evaluating test norms, check for the following:check for the following:

Does the norming group include the type of person Does the norming group include the type of person with whom the test takers should be compared?with whom the test takers should be compared?

What was the size of the norming group?What was the size of the norming group?

Does the manual include information regarding Does the manual include information regarding differentiated norms (differences among gender, differentiated norms (differences among gender, ethnic, grade, or age groups)?ethnic, grade, or age groups)?


Documents

Chapter 3 Understanding Test Scores Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition