11plus

Standardised Scores - An Explanation

One of the most common causes of confusion about the 11 Plus are the terms “standardised score” and “age standardisation”. Parents struggle to understand how, when a paper may have 80 questions on it, the final score they are given can be a figure of, say, 130.

What follows here is a very simplified explanation of the process of standardising scores. There is a more technical explanation below for those who wish to learn more on the subject, along with links to further information.

Standardisation is a statistical process that is designed to take account of two factors:

  • Firstly, the number of questions on a test paper and the time allowed for it can differ. If a Verbal Reasoning test has 80 questions and takes 50 minutes, while a maths paper has 100 questions and takes 45 minutes, simply adding the “raw scores” of the two together will not give equal weight to the results of both tests, and nor will an average. Standardisation is a way of giving equal value to the results of each test, regardless of the number of questions and the time allotted for completing them.
  • Secondly, and possibly of more concern to parents, the test scores have to be adjusted to take account of their age at the time they take the 11+. One child taking the test might be born on the first day of the school year (September 1st) while another might be born on the last day (August 31st). With what amounts to a whole year’s difference in their ages, the older child is clearly at an advantage: as just one example they will have a whole additional year’s vocabulary, which the younger child will not. As children are exposed to new vocabulary at the rate of more than 1,000 words per year, the difference can be very significant for the 11+ tests. In order to remove this unfairness, the marks are adjusted to make them “standard” for all children, regardless of their age.

If both children in this example – the oldest one and the youngest one – achieve the identical “raw score”, the youngest child’s final 11+ score will be higher than that of the oldest child. The standardisation process has “awarded” extra marks to the younger child to compensate for their younger age. Every test paper is unique in the factors that go into standardising it but if both children achieved a raw score of 75/80, a very rough outcome could be that the older child’s standardised score might be approximately 133, while the younger child’s score could be around 136. (Please note that these figures are given as examples only and do not represent actual marks.)

There are two myths that are frequently expounded about the standardisation prcoess. Firstly, the myth that older children have marks deducted because they are older. That is not the case. Secondly, there is the myth that boys 11+ scores are standardised differently to those of girls because boys tend to develop more slowly than girls. That is not only untrue, but it would be illegal under the terms of the Sex Discrimination Act.

So, how does the raw score of 75/80 become 133 or 136? The methods used vary, but there are two factors that can be applied, singly or together, in the standardisation process. Firstly the company setting and marking the test may apply statistical information about how difficult the paper is, based on tests that they conduct among a sample of children either nationally, or more usually in the 11+ area. (An example of the latter is the “equating test” that takes place in Buckinghamshire each year, whereby a sample of children who have taken the 11+ are then asked to take one of the papers from the previous year. The results are then compared with their real 11+ papers and the overall results for the cohort adjusted depending on whether the children found the real papers easier or more difficult than the previous year’s paper.) The second factor taken into account is the age of all the children taking the test.

From this information an average will emerge, and that is usually around 100 (although in certain areas the average can be as high as 111). The lowest score will usually be 69 or 70 and the highest score is usually stated to be 140 or 141. This “highest score” is actually a cut-off point rather than the maximum mark possible, and it is possible for children to achieve higher scores, although they become increasingly statistically unreliable beyond 141, which is why a cut-off point is often used.

In some areas where places are allocated in descending order by score the cut-off point is not used and therefore scores above 141 have been reported in the past. These exceptionally high scores are really irrelevant because so few children achieve them and the great majority of school places will still be allocated to children achieving scores below the cut-off of 141 used in other areas. However they are still recorded because, in the most unlikely event that more children scored above 141 than there were places available, the score would be needed to ensure that places were allocated in the correct order.

To bring this all back down to basics, standardisation removes variable elements from test scores and allows children to be compared equally. It is fair to say however that very few people fully understand the process! There are too many factors that are unknown to the general public – the relative difficulty of the paper, the ability of the cohort, and so on – to allow you to calculate a standardised score directly from a raw score.

You will find information about past “minimum standardised scores” (i.e. pass marks or qualifying marks) required for entry to schools in your area on the regional pages of this site. On our 11+ Forum you will find that in many areas information is available about the approximate raw scores required to achieve the minimum standardised score. That is all the information you need to be able to judge whether your child is on target to qualify in the 11+.

Standardised Scores – more information

In order to calculate a standardised score the company producing and marking the tests will create a reference table – called a “look-up table” – for each test paper that is written, and the table is specific to that test paper, because it takes account of the difficulty of the paper. (For illustration purposes only, one of these “look-up” tables is shown below.)

The minimum standardised score is derived from the look-up table and the actual number will vary depending on the average score of all those taking the test and the number of applicants. As an example, in north-west London in 2003 the minimum standardised score was said to be 124, whilst in Buckinghamshire the figure has been 121 for several years.

In the example look-up table below the vertical axis is the “raw score”, i.e. the number (percentage) of actual questions that a child gets right on a paper. The horizontal axis represents the age of the child at the time of taking the exam, shown as years + months.

  10y0m 10y1m 10y2m 10y3m 10y4m 10y5m 10y6m
               
72 109              
73 110              
74 111 110 110 109 109 108 107  
75 112 111 110 110 109 108 108  
76 113 113 112 112 111 109 109  
77 114 114 113 112 111 110    
78 115 115 113 113 112 111 110  
79 116 116 114 113 112 111 111  
80 117 117 116 115 113 112 111  
81 118 117 116 115 114 113 112  
82 119 119 118 117 117 115 114  
83 120 120 120 118 118 118 117  
84 121 121 120 119 118 118 117  
85 122 122 121 121 120 119    
86 123 122 121 121 120 119    
87 124 123 122 121 120 120    
88 125 124 123 123 122 121    
89 126 126 125 124 124 123    
90 127 127 126 125 125 124    

So, in the illustration above, if the child needed to attain a standardised score of 124, a child who is exactly 10 years old will need to attain a raw score of 87 percent in order to qualify, while a child who is 10 years and 5 months old will need to achieve 3 extra marks and get a raw score of 90 percent in order to qualify.

Please note that this is only an illustration, and this “look-up” table will be different for every test.

For those who are still hungry to learn more about standardisation there is a helpful visual guide to the issue of scores and ages in a post from our 11+ Forum Moderator “WP”, which can be viewed here, and an even more detailed explanation of the whole process here

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