Methods of Mark Adjustment in Educational Assessment

In educational assessment, methods like Z-score normalization, quadratic scaling, and piecewise linear scaling are used to adjust marks based on Gaussian distribution assumptions. Z-score normalization helps to adjust both mean and standard deviation, impacting the distribution of marks. Quadratic scaling allows for adjusting marks by setting desired values, either increasing or reducing, with candidates falling on the line of equality before adjustments. These methods aim to fine-tune marks to better reflect the performance of cohorts in assessment modules.

• Educational Assessment
• Mark Adjustment
• Z-score Normalization
• Gaussian Distribution
• Quadratic Scaling

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1. Methods of mark adjustment 28 May 2019

2. Methods of mark adjustment Z-score normalisation Quadratic scaling Piecewise linear scaling #uniofsurrey 2

3. Z-score Based on the assumption that the marks obtained by a cohort in a module or unit of assessment broadly follows a normal or Gaussian distribution. ps://en.wikipedia.org/wiki/Normal_distribution #uniofsurrey 3

4. Z-score With z-score normalisation one can Frequency Mark #uniofsurrey 4

5. Z-score increase the mean Frequency Mark #uniofsurrey 5

6. Z-score .reduce the mean Frequency Mark #uniofsurrey 6

7. Z-score Or alternatively one can Frequency Mark #uniofsurrey 7

8. Z-score reduce the standard deviation Frequency Mark #uniofsurrey 8

9. Z-score or increase the standard deviation Frequency Mark #uniofsurrey 9

10. Z-score One can adjust both the mean and standard deviation, as in this example: Frequency Note how the lowest marks have increased dramatically: Mark #uniofsurrey 10

11. Quadratic scaling Before any adjustment, all candidates fall on the line of equality (A=R): A = R Adjusted mark Raw mark #uniofsurrey 11

12. Quadratic scaling Pick an Actual point A = R Adjusted mark Raw mark #uniofsurrey 12

13. Quadratic scaling and set its Desired value, which can be an increase or (as shown here) a reduction: A = R Adjusted mark Raw mark #uniofsurrey 13

14. Quadratic scaling A curve is then fitted that goes through the Desired point and the end points (0% , 100%) A = R Adjusted mark The end points are preserved (anyone on 0% or 100% stays there). The biggest adjustment is felt in the middle of the distribution. Raw mark #uniofsurrey 14

15. Quadratic scaling This is what an upward adjustment might look like .. A = R Adjusted mark The end points are preserved (anyone on 0% or 100% stays there). The biggest adjustment is felt in the middle of the distribution. Raw mark #uniofsurrey 15

16. Piecewise linear scaling This method allows adjustment to be carried out in different parts of the mark distribution A = R Adjusted mark Raw mark #uniofsurrey 16

17. Piecewise linear scaling Establish scaling points at normal boundaries (e.g. Pass, Merit, and Distinction at Level 7): A = R Adjusted mark P M D Raw mark #uniofsurrey 17

18. Piecewise linear scaling Adjust one or more points up or down in value (e.g. move Pass to 40%): A = R Adjusted mark P M D Raw mark #uniofsurrey 18

19. Piecewise linear scaling Kink the line of equality to pass through the new point (or points, if more than one adjusted): A = R Adjusted mark P M D Raw mark #uniofsurrey 19

20. Piecewise linear scaling Note that P, M, D are in the original locations (e.g. 50, 60 and 70) on the Adjusted scale: A = R Adjusted mark D M P P M D Raw mark #uniofsurrey 20

21. Piecewise linear scaling Here is another example in which Distinction is moved to 80%: A = R Adjusted mark P M D Raw mark #uniofsurrey 21

22. Piecewise linear scaling Again, kink the line of equality to pass through the new point: A = R Adjusted mark P M D Raw mark #uniofsurrey 22

23. Piecewise linear scaling Again, note that P, M, D are in the original locations (e.g. 50, 60 and 70) on the Adjusted scale A = R Adjusted mark D M P P M D Raw mark #uniofsurrey 23

24. Piecewise linear scaling For Levels 4-6, four scaling points are required, at Pass, Lower 2nd, Upper 2nd and First: A = R Adjusted mark P L U F Raw mark #uniofsurrey 24

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