standardisation score help ?

[ToadMum]

Don't want to sound like Mrs.Wisenose, but checked the statistics textbook:
It's a complicated formula to calculate the standard deviation.

In the example with the candidates A-D:
Candidate A 55
Candidate B 45
Candidate C 60
Candidate D 50

Mean = 52.5
Sd = sqr root of [(55-52.5)^2 + (45-52.5)^2 + (60-52.5)^2 + (50-52.5)^2]/4
= sqr root of [6.25 + 56.25 + 56.25 + 6.25]/4
= sqr root of 31.25
= 5.6

Not sure if this is correct - better leave it to the statistians among us.

You are probably right, it looked rather simplistic when jotting it down

Hopefully conveys some idea of principle, though...

[ToadMum]

Don't want to sound like Mrs.Wisenose, but checked the statistics textbook:
It's a complicated formula to calculate the standard deviation.

In the example with the candidates A-D:
Candidate A 55
Candidate B 45
Candidate C 60
Candidate D 50

Mean = 52.5
Sd = sqr root of [(55-52.5)^2 + (45-52.5)^2 + (60-52.5)^2 + (50-52.5)^2]/4
= sqr root of [6.25 + 56.25 + 56.25 + 6.25]/4
= sqr root of 31.25
= 5.6

Not sure if this is correct - better leave it to the statistians among us.

You are probably right, it looked rather simplistic when jotting it down

Hopefully conveys some idea of principle, though...

[TomPoes]

(not just a pretty face ... )

Tomorrow off to WHSB and maybe Wednesday off to SHSB for open events.

[ToadMum]

(not just a pretty face ... )

Tomorrow off to WHSB and maybe Wednesday off to SHSB for open events.

Only fair to give them both a go; you might be surprised . Lots of building work on the go at SHSB at the moment (it was WHSB's turn last year). DS2 is very excited about the new library which will be part of it.

[TomPoes]

Keep an open mind - see what happens - may be pleasantly surprised ...

Will bring my Bob-the-Builder hat.

[chelmsfordparent]

You can use the function STDEV in excel or compatible spreadsheet to work out the standard deviation of a list of numbers if you want to get a feel for it.

Because it is standardised by the number of candidates you can be confident that a narrower standard deviation means that students are getting more similar performances, it is nothing to do with the number of entries.

(Yes, I am a statistician)

[Victor]

My question is that will the standardised scores achieves mean a similar thing year on year. For example will a score of 330 have the same meaning this year and the next, I am trying to gauge the accuracy of the guidance sheet. I assume that is the point of standardisation.

[sendis]

(not just a pretty face ... )

Tomorrow off to WHSB and maybe Wednesday off to SHSB for open events.

Only fair to give them both a go; you might be surprised . Lots of building work on the go at SHSB at the moment (it was WHSB's turn last year). DS2 is very excited about the new library which will be part of it.

(not just a pretty face ... )

Tomorrow off to WHSB and maybe Wednesday off to SHSB for open events.

Hi
I need a help please

Do you think its worth it to go to the open events for WHSB and SHSB as my son scored 323.56
he is in the orange bar for SHSB

[Victor]

I would ring up SHSB the lady on the reception is helpful.

[chelmsfordparent]

My question is that will the standardised scores achieves mean a similar thing year on year. For example will a score of 330 have the same meaning this year and the next, I am trying to gauge the accuracy of the guidance sheet. I assume that is the point of standardisation.

Yes they will have the same meaning if the distribution of the scores is the same, and the pattern of applicants across schools is the same.

What does this mean in practice... probably best to give an example.

Suppose we have a single paper and only ten students; two places available, only one school, and the marks are as follows:

31, 32, 33, ..... 40

The mean is 35.5 and the standard deviation is 3.028
The standardised scores come out at 77.7, 82.7, .... 117.34, 122.29

Because there are only two places the student who gets 117.34 and the one who gets 122.29 both get in. The cutoff is 122.29

Now suppose the paper gets easier but there is a wider spread of marks:

48.1, 49.4, 50.7, .... 59.8
(I realise decimal marks don't happen in practice but with such a small number of pupils I need to do this to demonstrate everything works properly)

The mean is 53.95 and the std. dev is 3.936
But the scores come out identically at 77.7, 82.7, ... 117.34, 122.29

If you plotted the marks out of 60 on a graph and took away the axis labels they would look identical. This means the scores will be the same.

Now suppose the paper is as hard as before but there is one genius child who gets full marks:

31, 32, 33,.... 39, 60

The mean is 37.5 and the s.d. is 8.320

The scores are different: 88.3, 90.1, .... 102.7, 140.58

The cutoff is now 102.7. It looks like the paper has got a lot easier, but in practice it's just down to that one kid skewing the numbers.

That describes the effect of a change in distribution.

Over the hundreds of kids taking the test rather than just ten this will probably not have too big an effect due to a statistical effect called the central limit theorem. This means the standardised scores can be compared from year to year - the standardisation does a pretty good job.

But the other source of uncertainty is the number of kids applying to each school.

So for example let's assume we have ten kids(child A.... child J) with scores of:

400 (child A), 380 (B), ... 220 (J)

In one year suppose there are two schools, KEGS and Colchester boys (CB), each with two places and no catchments.

Suppose child A and C (and E, G...) have put their preferences as KEGS, CB; and children B and D (and F and H...) as CB then KEGS.

Child A and C will get into KEGS. Child B and D will get into CB. The cutoffs will be 360 and 340 respectively.

Now in the next year suppose the marks are identical but the preferences are slightly different:

Child A KEGS, CB
Child B CB, KEGS
Child C KEGS, CB
Child D KEGS, local non selective
Child E KEGS, CB

Child A and C get into KEGS; Child B and E into CB, child D into a local non selective. The cutoff for KEGS is unchanged at 360, but for CB has fallen to child E's score of 320. This despite the standard scores being exactly the same.

Obviously in reality the permutations are endless, and catchment areas make it even more complicated.

This effect of different application patterns will have a much larger effect on the cutoffs than slight differences in standardisation.