In assessment, scores can be reported in different ways to better reflect student performance and provide meaningful insights.
In this blog, Carmen Lim, Senior Researcher at Cambridge, explores the difference between standardised and normalised scores, explaining why understanding these scoring methods is important for accurate assessment interpretation.
Are grades the only way to measure student achievement?
Grades are not the only way to report student performance in assessments.
Another widely used, but perhaps less understood, reporting score apart from grades is the scaled score.
Two of the most common forms of these are standardised scores and normalised scores. These are specific types of scaled scores based on the method in which the raw number of marks achieved on a test are converted to a new numerical scale. This conversion process is generally known as “score scaling,” which is analogous to “grading” when raw marks are transformed into grades.
To be clear, there are other types of scaled scores that are not standardised or normalised scores. The reporting scores of Cambridge English Qualifications are one example.
What are standardised scores in assessment?
The process of converting assessment scores to standardised scores is known as standardisation.
Standardised scores tell us how candidates performed in a test relative to a particular, defined group.
The group of candidates against which the scores are benchmarked is typically a nationally representative sample, but it could be any population of interest depending on the target candidates of the test. More commonly, you’ll see them referred to as the norm group or the reference group.
For example, in the US SAT —a test commonly used for university admission—the reference group is a representative sample of 11th and 12th-grade students (about 16 to 18 years old) in the United States. Learn more about the SAT scoring system.
The process of converting assessment scores to standardised scores is known as standardisation. It involves producing a score for each candidate that reflects the positioning of their assessment scores within the score distribution of the reference group.
Continuing with the US SAT as an example, the standardised score for this test ranges from 400 to 1600, with the mean score of the reference group typically represented by the value 1010. Therefore, a candidate who demonstrated a performance level lower than the average of the reference group would have a standardised score less than 1010, and those who performed better than the average of the reference group would have a standardised score above 1010.
Exactly how high or low the standardised score would depend on their distance from the average.
Note that in standardisation, the score distribution of the reference group might be taken as given. This score distribution can be normally distributed or not.
If a test is intentionally designed to be harder (e.g., selection tests) or easier (e.g., diagnostic tests) for its targeted candidates, then the assessment score distribution is unlikely to be normally distributed.
In cases where the assessment score distribution of the reference group is not normally distributed, the standardised score will not be either. In other words, standardisation might not change the underlying shape of the score distribution.
What are normalised scores in assessment?
Normalised scores allow us to infer the relative position of a candidate based on their reported score.
In some cases, it might be desirable for the standardised score to follow a normal distribution. This is because a normal distribution has some attractive properties that can help us more easily interpret candidates’ performance.
One way to achieve this is to transform the assessment scores of the reference group so that it resembles a normal distribution as closely as possible before being used in the standardisation process. Standardised scores that are normally distributed can be more precisely known as normalised scores. Visit this resource to understand more about the normal distribution.
Normalised scores allow us to infer the relative position of a candidate based on their reported score, in ways that wouldn’t have been possible with non-normalised standardised scores.
For example, a student with a normalised score that is one standard deviation above the mean is scoring better than roughly 84% of the candidates in the reference group, and those with two standard deviations above the mean are among the best 2% scoring candidates.
In summary, standardised scores can be normalised or non-normalised scores, and normalised scores are a specific case of standardised scores.
Standardised scores vs. grades
One potential benefit standardised scores have over grades is that they can differentiate between candidates more finely and provide a better picture of their relative standing.
Similar to grades, when properly maintained, the interpretation of standardised or normalised scores should remain consistent over time so we can meaningfully and fairly compare candidates’ scores from different years, cohorts, or even versions of a test.
One potential benefit standardised scores have over grades is that they can differentiate between candidates more finely and provide a better picture of their relative standing. This is particularly useful for assessments where it is necessary to draw fine distinctions between candidates, such as for university applications.
This does come with potential downsides. If every single mark on an assessment potentially impacts your comparative ranking with other candidates, it will likely further increase the ‘high-stakes’ element of the assessments, potentially leading to greater exam anxiety.
If you want to learn more about normalisation and standardisation you can take our online course which covers these topics and much more in the area of assessment data and statistics. Find out more.