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Deriving Grading Scale Scores for VoCATS Tests

Deriving Grading Scale Scores for VoCATS Tests. Lorin W. Anderson Purveyor of Common Sense February, 2008. “Purveyor”. 1. One that furnishes provisions, especially food ( in my case, food for thought ).

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Deriving Grading Scale Scores for VoCATS Tests

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  1. Deriving Grading Scale Scores for VoCATS Tests Lorin W. Anderson Purveyor of Common Sense February, 2008

  2. “Purveyor” • 1. One that furnishes provisions, especially food (in my case, food for thought). • 2. One that promulgates something: a purveyor of lies (in my case, a purveyor of truths that we should, as educators, hold self-evident).

  3. Group “A” Students “B” Students “C” Students “D” Students “F” Students TOTAL No “Anticipated Grade” GRAND TOTAL Frequency 521 (25.3%) 549 (26.6%) 495 (24.0%) 317 (15.4%) 180 (8.7%) 2,062 366 2,428 Step 1: Divide Students into Five “Anticipated Grade” Groups

  4. Group “A” Students “B” Students “C” Students “D” Students “F” Students Mean (SD) 75.57 (15.09) 62.15 (16.11) 57.16 (14.18) 53.13 (13.69) 44.18 (18.53) Step 2: Compute mean and standard deviation of raw scores for each group

  5. Step 3: Compare the mean raw scores for the five anticipated grade groups • The mean scores should DECREASE from the “A” to the “F” students. If they do not, this approach does not work. • The differences among the mean scores of the five groups should be statistically significant. • For the 106 “regular” and “field” tests I examined last fall, all but 6 (94.3%) followed the descending pattern of mean scores. All but 11 (89.6%) had statistically significant differences.

  6. Step 4: Use a bar graphs to display the score distribution for each anticipated grade group and fit a curve to each bar graph.

  7. Step 5:Overlay the raw score distributions of adjacent anticipated grade groups (e.g., A vs. B, B vs. C, and so on)

  8. Step 6: Use the contrasting group method to determine the cut-score between adjacent anticipated grade groups • The cut-score is the score at which the two raw score distributions overlap. • In the previous example, the cut-score is 72. • Reference:Cizek, G. J. & Bunch, M. B. (2006). Standard Setting: A Guide to Establishing and Evaluating Performance Standards on Tests. Thousand Oaks, CA: Sage Publications, Inc.

  9. Grade Group Comparison A vs. B B vs. C C vs. D D vs. F Cut-Score 72 63 54 42 Cut-Scores for Anticipated Grade Group Contrasts

  10. Note • Because the raw score distributions for the various anticipated grade groups will be different from each course, the cut-scores will be different for different courses.

  11. Cut-Score 72 63 54 42 Lowest Grading Scale Score 93 (lowest A) 85 (lowest B) 77 (lowest C) 70 (lowest D) Step 7:Set the cut-scores as the lowest grading scale score for each letter grade. In other words, a raw score of 72 is equivalent to a grading scale score of 93, a raw score of 63 is equivalent to a grading scale score of 85, and so on.

  12. Step 8: Prepare a table connecting raw scores with grading scale scores.

  13. The “Mapping” of Raw Scores onto Grading Scale Score • Because the range of raw scores is larger than the range of grading scale scores, different raw scores can map onto the same grading scale scores. • In our example this is particularly clear for raw scores linked with grading scale scores falling into the “A” range. In terms of the uniform grading scale, numerical grades associated with a letter grade of “A” range from 93 through 100 (a range of 8 points). In terms of raw score points, the range for a letter grade of “A” is from 72 through 100 (or 29 points).

  14. The Performance of “Top” Students on the VoCATS Test Q: How many of the 2,428 students who took the test received a perfect score? A: Zero Q: If we used a raw score of 93 on VoCATS to determine our “A” students, how many “A” students would there be based on their VoCATS scores? A: 64 of 2,428 (or 2.6%). To put this in perspective, remember that approximately one-fourth of the students were expected by their teachers to receive “A” grades in the course.

  15. Why the Discrepancy Between Anticipated Grades and VoCATS Scores? • Even with a uniform grading system, letter grades mean different things to different teachers. In the words of the philosopher, Paul Simon, one man’s ceiling is another man’s floor. • Some of the items included on the end-of-course test assess students’ mastery of objectives taught very early in the course. If these were “memory” or “recall” objectives, that is long time to retain information. • Across all states and all subject areas, state tests tend to be more difficult than teacher-made tests and other assessments used by teachers to assign grades.

  16. A Friendly Reminder • The “mapping” of raw scores onto grading scale scores is course-specific since the mapping is based on the cut-scores that are derived from the “anticipated grade” group raw score distributions for every course. • Stated somewhat differently, there are not uniform cut-scores associated with “A’s” “B’s,” and so on. There is, however, a uniform procedure that yields reasonable and defensible cut-scores for the vast majority of CTE courses.

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