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 Post subject: CSSE Standardisation
PostPosted: Sun Dec 27, 2020 3:26 pm 
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Joined: Tue Nov 17, 2020 10:13 pm
Posts: 37
I am starting this thread to discuss mainly the maths behind this, so please refrain from posting unsubstantiated opinions (as happened in a similar thread).

The raw scores for 2019 and 2020 are available from the CSSE website. With these, I applied the standardisation formula to calculate the standardised scores. I worked on the total score, but the same could be done for the individual English/maths score. The age standardisation has not been applied. I then grouped the scores by month, calculated the monthly average and tabulated from September to Aug..

For those of you who want to try it yourself,
get the pdf and open it in word
copy and paste the table into excel.
Use Find & Select to find the blanks, and delete.
create 2 new columns, and calculate the standardised english and maths score.
highlight the data, then File->insert->Pivot table. Select Birth date but remove quarters and years, and the standardised english and maths score. In the values pane, click value field settings and change sum of to average.

For 2019,
Ave English Ave Maths2
Sep 152.7913715 151.6569125
Oct 151.9144324 151.7486512
Nov 152.8071725 150.7909022
Dec 152.2309152 150.4605978
Jan 149.9127088 150.0413259
Feb 147.9201978 149.0174264
Mar 149.8649126 150.4735494
Apr 150.0784295 149.0698706
May 149.8141528 151.6530825
Jun 146.4766114 146.6881987
Jul 147.8867384 148.5094548
Aug 145.1891346 148.3437748
/day 0.013885364 0.006051393

As you can see, there is a gradual decline in scores from Sep to Aug. I haven't drawn a best fit straight line graph, but this is probably what the statistician for DoE has done. There are some anomalies, like Oct in English. I took the sep and aug ave as the 2 points on my best fit straight line, and calculated the change per day. You have to divide it by 1.5, and i got the change per day as above (/day). The CSSE values were 0.0126244 and 0.0068468 but i could easily get that by adjusting my 'best fit straight line'.
Is this How the DoE statistician would have calculated it?

I did the same for 2020, but this time September has a large deviation from the best fit straight line. So for my changes/day, i left out September, and divided it by 335 days.
Ave English Ave Maths2
Sep 151.5257683 150.3311806
Oct 153.9353027 152.9148422
Nov 153.4265587 151.2675363
Dec 151.5110763 150.5269741
Jan 150.510947 150.8919592
Feb 150.6706669 150.2314222
Mar 148.0933386 148.0729864
Apr 148.2807139 148.7186982
May 148.8274281 149.1519432
Jun 147.6167077 148.2414766
Jul 146.78142 149.5193188
Aug 146.7361042 149.4680853
/day 0.014326763 0.006859218

CSSE values were 0.0134943 and 0.0059528.

Here are a list of factors that can affect a candidates CSSE scores (please contribute)
Innate intelligence
memory
schooling
tutoring by tutors/parents
motivation/drive/determination/ambition
hours spent studying
A change (advantage/disadvantage) because you are slightly younger.

With all of the above factors apart from the last one, as your data sample tends to infinity, the differences should even out. The only difference, if it exists, that should remain is if there is a difference caused by being younger.
Now you shall never get an infinite sample number, but the larger the sample, the more 'all other factors' even out.
As you can see in 2019, and 2020, there is a gradual monthly decline in the standardised scores. When the 2021 raw data becomes available, expect the same, and expect the same from historic data from previous years.
From my knowledge of statistics, my opinion is that the CSSE should be taking as much data as possible, and not just do it on a yearly basis. The sample size is only around 5000, and small changes skew the results more than a sample size of say 50000 (10 years worth). Plus, if there is a disadvantage due to age, it is happening in the same way every year, and is not dependant on the year. Th standardisation process is meant to make the scores of any 2 different years comparable, as well as make the english comparable to the maths. So, should CSSE not be using all historic data instead of a yearly basis?


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