How to understand the NPSE results in Sierra Leone

There has been a lot of questions surrounding the new way of calculating NPSE results.

Most parents think that all they need to do is to add up the individual scores to come to a total.

If a child gets 100 in each of the 5 subjects, then they should have a total of 500. Right?

Wrong! This is not the way the results are presented now.

The Ministry of Education in Sierra Leone use the so-called T-Score method to work out the results.

How to work out the T-Score for a test

To show this, I will use a simplified case of marks out of 100.

In a test the following 5 students got these results:

• Vickie — 80
• Edleen — 70
• Ariana — 50
• Kevin — 30
• Wilfred — 20

Step 1: Work out the mean of all the scores

Add all the individual results.

Divide by the number of students

80 + 70 + 50 + 30 + 20 = 250

Mean score = 250/5 = 50

Step 2 — Work out how far the individual scores are from the mean. This is called the standard deviation.

a) To do this you subtract the mean from the individual marks.

• Vickie (80 -50 = 30)
• Edleen (70–50 = 20)
• Ariana (50–50 = 0)
• Kevin (30–50 = -20) (The minus means that Kevin’s score is smaller than the mean)
• Wilfred (20–50 =-30)

b) Now you have to multiply each difference by itself. Ignore the minuses.

• Vickie (30 x 30 = 900)
• Edleen (20 x 20 = 400)
• Ariana (0 x 0 = 0)
• Kevin (20 x 20 = 400)
• Wilfred (30 x 30 = 900)

c) Now add these numbers

900 + 400 + 0 + 400 + 900 = 2600

d) Divide by the number of students

2600/5 = 520

d) Take the square root of this number (this will be hard for the Grammar School students )

Square root of 520 = 22.8

22.8 is the standard deviation.

Step 3- Use the T-Score Formula — Link provided by David Sengeh

a} First work out the difference between the actual score and the mean.

I will do it for Vickie as an illustration

Vickie’s Actual Score = 80

Mean score of all 5 students = 50

80–50 = 30

b) Now divide this answer by the standard deviation

30/22.8 = 1.32

c) Multiply this number by 10

10 x 1.32 = 13.2

d) Add the answer to 50

13.2 + 50 = 63.2

63.2 is Vickie’s T-score

This is different to her original or raw score.

Hence the confusion.

If we do the same for all the other students:

T-Scores for all students

• Vickie — 63.2
• Edleen — 58.8
• Ariana — 50
• Kevin — 41.2
• Wilfred — 36.8

This is done for each subject and added together to get the aggregate score.

Conclusions

• No one will ever get 500 again using this method!
• This method lowers the final scores of the top marks and increases the final scores of the bottom set. Hence the rumours of “mark stealing”. This is not true.

No two years will ever be the same again as the averages (mean) will be different from year to year.

Please recommend our book on Statistics and Probability Worked Examples for Wassce students.

PS: David Sengeh ( @dsengeh )pointed out that this method is not new, so I removed the “new” from the title.