Test scores: Know what they really mean


IN THE old days when I was a secondary school boy in a Chinese school, the passing mark was 60. For my friends who attended the then English schools, the passing mark was 40. When our two schools merged, the pass mark was changed to 50.

Was this a compromise between 40 and 60? Nobody really knows. But the real question is not how this pass mark was decided but what the mark tells you about the performance of your child.


Anatomy of a test score

An examination score by itself has no meaning; to understand or interpret the marks meaningfully, you need other related information such as

  1. (a). how other students fared, or
  2. (b). how many questions the students answered correctly.

In short, you need a frame of reference.

  • If you have information (a), then you know how your child fared when compared with his classmates; for instance, he is better than 80% of them (at the 80th percentile). This is termed as the norm-referenced interpretation of examination results.
  • If you have information (b), then you can tell that your child has spelled 32 out of 40 words correctly for a spelling test, and assuming that these words have been chosen to suit the class level, then he is 80% correct. This is termed as the criterion-referenced interpretation of test results.


Reason to have a passing mark

A pass mark represents the expectation of the examination system. First, the test has to be pitched at a suitable level. This ensures there is not much deviation from the past years' scores, which can be misleading to both parents and examiners. The passing rate is controlled by maintaining the difficulty levels of questions and the proportion of students who pass.

testscores_3_normalcurve.jpgWhen scores are represented as a normal distribution curve, a typical bell-curve, the number of students scoring the pass mark (be it 40, 50, 60 or 200) should be as low as possible to minimise errors.



An example

Take the passing mark of 50 for instance. If 60 out of 300 students scored close to this passing mark, then for administrative convenience, those who scored 50 will get a pass and those who scored 49, a fail grade. Assuming that half of the 60 students scored 50 and the other half 49, there is then an error rate of 20%, because those who failed may pass if they are to take the test a second time and vice versa.

If the number of students scoring around the passing mark is only 10 (5 passed and 5 failed), the error rate is only 3.3%. Thus, only a small proportion may swap places (from pass to fail and vice versa). Such errors are almost inevitable due to limitations of the test setting methods. In fact, research on setting the passing mark is still underway at the Educational Testing Service at Princeton, USA.

Educational Testing Service (ETS) is a US-registered non-profit organization created in 1947 by three non-profit educational institutions and testing services: the American Council on Education, The Carnegie Foundation for the Advancement of Teaching, and The College Entrance Examination Board. Located just outside Princeton in the US state of New Jersey, ETS is the world's largest private educational testing and assessment nonprofit organization.


What goes on at examinations?

For most general purpose-examinations, the objective is to gauge students' performance. Thus the results would yield a normal curve. However, for situations such as scholarship selection tests, the error rates should be low to select the right candidates.

Thus the pass mark remains an important parameter that helps school administrators and teachers make correct decisions.


Is a score of 100 a good grade?

You may think so. Well, it depends. It depends on the level of difficulty of the test and whether it was pitched at the academic level of the student. As a parent, think about three likely questions that you may ask:

  • Any Improvement?

Albert scored 75 for his Mathematics test in March. In May, he obtained 75 for Mathematics again. His mother
was disappointed because she expected him to show improvement after all that coaching from his private tutor.

  • Did he slip?

Benny's mark for the first English test was 70 and he scored 65 for his second test. His mother was horrified
as she had expected a better grade after she spent much time tutoring him.

  • Time for celebration?

Calvin scored 10 marks more for the recent Chinese test, compared to his previous results. His mother was
rather pleased.

BUT all three mothers may be wrong! Why? 

When we compare two scores, it is easy to be misled. Tests cover different topics of different standards and
usually the syllabus lists easier topics earlier.

  • So, though Albert scored 75 for both tests, he may have in fact made an improvement if the later one was more difficult. However, such gains are not reflected in the marks.
  • This same principle works for Benny and Calvin. An increase in scores may not reflect improvement. Conversely, a decrease may not signify lack of progress either. The crucial factor is the relative difficulty levels of the two examinations.


Parental support and child self-esteem

In recent times, examination results' times have become highly emotional events for students and parents. Perhaps it is important to know that every score is relative to other factors which are essential for the correct interpretation of results. Sometimes such pertinent information is not available to you as a parent. So what is critical remains your child's self-esteem. Encourage and support your child in his or her progress and not be overly concerned about absolute scores.

Reproduced with permission: absolutelyparents.com

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