1. Chapter 3 Understanding Test Scores Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

2. Test Scores  Imagine that you receive a grade of 60 for a midterm exam in one of your university classes.  What does the score mean, and how should we interpret it? Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

3. Two Methods of Interpretation  Criterion-Referenced Interpretation  Norm-Referenced Interpretation Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

4. Criterion-Referenced Interpretation  Definition: –student's test performance is compared to established criteria rather than to the performance of other students –the criteria are the basis of evaluating student progress, standards, or competencies  Most useful when test designed for this purpose: –set of clearly stated learning objectives –enough items to infer degree of mastery or non-mastery of that domain –items selected to actually measure that domain Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

5. Norm-Referenced Interpretation  Definition –student’s score relative to other students (in a norm group) –norm group is carefully defined –no need to look at level of mastery  Two of the major forms of norm- referenced interpretation: –percentiles –standard scores Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

6. Types of Scores  Raw score –Number of points when scored following the scoring directions –Has no inherent meaning  Percentiles –One of the most widely used methods to express the relative position of the test taker on a norm-referenced test.  Standard Scores (share a common logic; can be translated into each other) –Z scores –T scores –Deviation IQs –Stanines –Sten scores  Developmental Scales –Age norms –Grade equivalents Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

7. Percentiles  A percentile is a score that indicates the rank of the student compared to others (same age or same grade), using a hypothetical group of 100 students.  A percentile of 25 (25 th percentile), for example, indicates that the student's test performance equals or exceeds 25 out of 100 students on the same measure.  A percentile of 87 indicates that the student equals or surpasses 87 out of 100 (or 87% of) students.  Must always refer to a student’s percentile rank as relative to a particular norm group.  If you scored at the 80 th percentile, what does that mean? Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

8. Quartiles Quartile is another term referred to in percentile measure. The total of 100% is broken into four equal parts: 25%, 50%, 75% 100%. Quartile is another term referred to in percentile measure. The total of 100% is broken into four equal parts: 25%, 50%, 75% 100%.  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) Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

9. Standard Scores  Scores that are based on mean and standard deviation  Transformed standard scores: z scores, T scores, deviation IQ, stanines, stens Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

10. Z Score  The standard normal distribution is sometimes called the z distribution.  Mean = 0  SD = 1  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 standard deviations above the mean.  So, a z score of 2 means the original score was 2 standard deviations above the mean. Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

11. Z scores: Handy for thinking about the normal distribution  Center a bell curve on zero  Sign (+) = above the mean, (−) = below the mean  Number = standard deviation +1/−1 standard deviation includes about 68% of cases (34% on each side)+1/−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 NORMALLY Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

12. T Scores  T scores are also standardized scores.  Mean = 50  SD = 10  A score of 60 is one standard deviation above the mean, while a score of 30 is two standard deviations below the mean. Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

13. Deviation IQs  Wechsler Scales (WISC and WAIS) –mean = 100 –SD = 15  Stanford-Binet –mean = 100 –SD = 16 Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

14. Stanines  “Standard 9’s”  Range 1 to 9  Mean = 5  SD = 1  the largest number of individuals falling in the middle stanines (3-7), with fewer students falling at the extremes Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

15. Sten Scores  A STEN score is a standard score from a distribution in which most of the scores (almost 99%) have a range from 1 to 10 (which gives it its name, STEN, meaning Standard Ten).  Mean = 5.5  SD = 2 Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

16. Norm Score Distribution Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

17. Grade Equivalent Scores Description  Definition: the grade level at which the typical student obtains that raw score  Sample interpretation: “student had the same raw score that was average for students in grade 5.6 in the average school”  Typical score is determined for each month in a grade: 5.0-5.9  Widely used, especially in elementary school Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

18. Grade Equivalent Scores Widely Misinterpreted!  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 placed in  Don’t expect all students to gain 1.0 GE each year (the average). Not a realistic goal  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)  Don’t assume that scores on different tests are comparable –Different publishers test fuller ranges of students than others –Patterns of growth (variance in scores) may differ across subjects  Don’t interpret extreme scores as dependable estimates of student’s performance (usually extrapolated) Usefulness  Most useful in reporting growth in basic skills in elementary school  Least useful for comparing performance on different tests  Inequality in grade units will muddle interpretation if you don’t keep it clearly in mind Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

19. Norm-referenced Tests  Compare an individual child's performance to that of his or her classmates or some other larger group.  Tells how one child compares to similar children on a given set of skills and knowledge, but does not provide information about what the child does and does not know.  Scores on norm-referenced tests indicate the student's ranking relative to that group. Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

20. Norms The specific group of test takers upon which the test scores were checked for validity and reliability Criteria for Judging Norms:  Relevant –Is this particular norm group appropriate for (a) the decision you want to make, and (b) the set of test takers involved?  Representative –Was the norm group created with a random sample or stratified random sample? Does it match census figures (by race, sex, age, location, etc.) for the general population being considered?  Up-to-date –Don’t rely on the copyright date of the test manual. Read the manual to see how old the norms are. –Beware of Lake Wobegon effect (the tendency to treat all members of a group as above average—a statistical impossibility). Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

21. In summary, when evaluating test norms, check for the following:  Does the norming group include the type of person with whom the test takers should be compared?  What was the size of the norming group?  Does the manual include information regarding differentiated norms (differences among gender, ethnic, grade, or age groups)? Robert J. Drummond and Karyn Dayle Jones Assessment Procedures for Counselors and Helping Professionals, 6 th edition Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.