Your High School Grades Highly Likely Predicts Your KCSE Results
While keeping busy in the COVID lockdown, I stumbled upon my high school exams reports from Form 1 to Form 3. This quickly reminded me of England’s exam scoring algorithm fiasco. Due to coronovirus outbreak in Europe, the exam regulation body in England suspended sit-in exams. A-level students waiting to join universities would receive estimate grades partially computed on school-based exams for previous years.
In effect, the exam regulation body in England created an algorithm that would predict the grade a student is likely acquire if learning had continued uninterrupted. These predictions resulted to about 40% of students receiving lower grades than they had expected — hell broke loose. Before continuing with the woes of the Department of Education in England, I thought about how this phenomenon would apply to Kenya.
The Grades
Unlike England, the Kenyan government opted to postpone the national exams. However, what if that wasn’t the case and Kenya opted for the same mechanism? To get started, I plotted my core subjects grades (marks) distribution for my first three years in high school as shown below.
From the diagram above, I was way above average in chemistry (80% zone) and thus would be expected to score A and I indeed scored an A. In Physics my mean score aggregated to 52% which is a C. However in I scored an A plain in KCSE exams — that’s many grades elevation. This brings us to the point that grades are adjusted for relative score. In Kenya’s 2018 KCSE examination, the English language exam had an A from 80–100%, the Kiswahili exam A from 78–100%, Mathematics A from 70%, Physics A from 60%, Chemistry A from 65% and Geography A from 66%. Using these adjustment, how accurate did my first three years predict my KCSE results? Herein are the results.
To compute the accuracy in prediciting my KCSE grades, we use my median score of for each subject for the three years as my expected/predicted value (adjusted with 2018 redistrubition — PS:I couldn’t find for 2005), then compute the point difference with the actual results. We will the use the Mean Squared Error to measure the prediction error.
Calculating the Mean Squared Error on the point difference results to 0, and 0 means the model is perfect (100% accurate) — the prediction overshot on some subjects and undershot in other subjects, but the averages of the differences comes to zero. This means that your high school grades from form one to form four highly likely predicts your KCSE score — or at least it is true in my case. So what went wrong in the UK version.
The UK version
“All models are wrong, but some are useful”, Statistician George Box coined the expression to recognize that scientific models always fall short of the complexities of realities but can still be useful. The England model of predicting grades introduced more variables into the algorithm, namely;
- The historical grade distribution of schools from the three previous years
- The rank of each student within her own school for a particular subject
- The previous exam results for a student per subject.
The first attribute introduced a great bias. For instance, if no one from your school has gotten the highest grade in the past three years, it’s extremely unlikely — if not impossible — for anyone from your school to attain that grade this year. The second attribute introduced another bias — it meant students at smaller schools were more likely to benefit from grade inflation than those at larger schools. The first two attributes contributed to the low accuracy ofthe prediction model.
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