Percentile Ranks and Standard Scores

APPENDIX C

PERCENTILE RANKS AND STANDARD SCORES

PERCENTILE RANKS The percentile rank is the most commonly used indicator of rank. It can be used to indicate the percentage of students in a group who score the same or less than a student. For instance, a percentile rank of 75 would indicate that 75% of a group scored 75 or less. You may not know that percentiles are not evenly spaced. Just one example of this uneven spacing is that the distance from zero to the first percentile is much greater than the distance from the 40th to the 50th percentile. If a student is well above or well below average then he/she needs to improve considerably just to increase their percentile by one or two points.

PERCENTILE T SCORES RANKS 10

1 30 5 10 40 20 30 40 50 60 50 70 80 60 90 95 70

99 80

Figure 80. Percentiles and T-scores (i.e., converted scores)

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This is shown a little clearer in the relationship between percentiles and other scores (see Figure below). Percentiles are used for large scale testing but are not always helpful for classroom tests with small groups. Note also that percentiles cannot be added or averaged.

STANDARD SCORES Scores from tests can be standardised or scaled. Standardised means that they are all converted to the same range or units. It does not change the shape of the distribution of test scores. For instance in the Higher School Certificate in New South Wales, the Board of Studies converted the 2 Unit examination marks so that they had an average of around 60 and a standard deviation close to 11.5. Scaling means that there is a common range of scores, such as making every test have the same range of scores. On the other hand, normalisation means that the actual graph or distribution of the scores is changed. As a result of scaling in the Higher School Certificate, approximately 1% of candidates have marks of 90 or more; 20% of candidates have marks of 70 or more; 80% of candidates have marks of 50 or more; and 1% of candidates have marks of less than 30. Such scaling of performance in different subjects and the standardisation of scores is not straightforward. It has numerous pitfalls. Standardised scores were developed to overcome the problem of scoring systems where the units were so different, such as in the example of the percentiles shown above. There are various options for standardising scores (e.g.,, z-scores) and most rely on norm-referenced comparisons with the mean and standard deviation of test results in a group. These approaches are not considered relevant for classroom testing except when you wish: – to add scores from different tests; or – to compare the performance of a student on different subjects. In order to achieve these learning outcomes you need scores which are on a common scale. The following sections show you how to calculate standard scores and then you are shown how to convert scores to a common scale. These sections are relevant to you when you need to combine scores from different tests, assignments etc.

How to calculate standard scores Using the standard scores for tests puts all your scores on a common scale. You may then add scores together without the problem of worrying about different measurement scales. To compute the standard scores for a group you will need to calculate the mean and the standard deviation of the scores. This can be done easily using a scientific calculator. To find the equivalent z-score, you first subtract the mean from each score and then divide this by the standard deviation. Here is a worked example for you:

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