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 Posted: Tue Oct 28, 2014 7:59 am

Joined: Mon Oct 06, 2014 12:18 pm
Posts: 356
So far we have read in the forum various views on this subject, some predicted 15 some predicted 10 as the standard deviation in order to find the total number of student passing the test and the tentative ranking order based on scores of each student.

I was trying to find out which SD looks more probable.

We only have information that 110 is the pass mark this year and maximum score is 130.12.

What I gathered from reading some old post in other forums that usually the pass mark is kept such that around 30% of the cohort pass the test.

If we use Standard Deviation of 15 then NORMDIST(110,100,15,TRUE)*100 yields that 74.75% of total 1203 cohort this year (i.e 304 students) might have got above 110 pass marks. But this also gives 27 students above 130.12 score which we know is not true.

If we use Standard Deviation of 10 then NORMDIST(110,100,10,TRUE)*100 yields that 84.1% of total 1203 cohort this year (i.e 191 students) might have got above 110 pass marks. This now gives 2 students above 130.12 score which though looks more probable but only 84% of cohort passing the test is a bit too low I think .

Whereas if we use Standard Deviation of 12.5 then NORMDIST(110,100,12.5,TRUE)*100 yields that 78.8% of total 1203 cohort this year (i.e 255 students) might have got above 110 pass marks. This gives only 3 students above 130.12 score and 1 student above 141 (which then fits the usual calculator of maximum 141 achieved).

I am quite new to this forum and am just trying to figure out things from other region's forum.

Any expert comment welcome as we all are trying to guess where our DSs stand in the ranking order for Reading Boys.

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 Posted: Tue Oct 28, 2014 8:12 am

Joined: Wed Jan 18, 2012 11:41 am
Posts: 6854
Location: Essex
Sorry, but don't you mean the inverse passing - c.22%, 16% etc?

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 Posted: Tue Oct 28, 2014 9:34 am

Joined: Thu Mar 03, 2011 1:27 pm
Posts: 46
We had an email from the school stating SD is 15 and mean is 100.

The NORMDIST function assumes results are distributed in a standard bell shaped curve. I'm no expert but know enough to say that, in reality, the distribution will not look like this for many reasons such as variations in amount/quality of tuition received by students. Not all 1203 students that set the test will be in catchment and, unlike earlier years, one can no longer move into catchment following result publication. I suspect the number able to apply for day places will be much less than 1203.

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 Posted: Tue Oct 28, 2014 10:54 am

Joined: Sat Dec 28, 2013 3:52 pm
Posts: 853
Good information Kara123.
Wonder if schools give out any information re how many DCs have passed? Was the eligibility 30% or 20% or 10% or any other figure?

Last edited by berks_mum on Tue Oct 28, 2014 11:17 am, edited 1 time in total.

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 Posted: Tue Oct 28, 2014 11:14 am

Joined: Mon Oct 08, 2012 3:25 pm
Posts: 56
I would go with SD 15 because that is the norm many other schools use. However, the distribution only gives you an approximate number, You cannot expect the data to form a perfect bell curve. It will have unpredictable spikes and dents and missing scores at the higher/lower end like between 131 and 141.

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 Posted: Tue Oct 28, 2014 12:53 pm

Joined: Mon Oct 06, 2014 12:18 pm
Posts: 356
kara123 wrote:
We had an email from the school stating SD is 15 and mean is 100.

Sorry was not aware of this. I thought Reading Boys just said so far that the maximum score is 130.12 and nothing more than that.

Ok then that closes any speculation regarding this.

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 Posted: Tue Oct 28, 2014 2:40 pm

Joined: Mon Mar 02, 2009 10:33 am
Posts: 36
Quote:
kara123 wrote:
We had an email from the school stating SD is 15 and mean is 100.

Very likely that Kendrick will be using the same SD in that case?

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 Posted: Sun Nov 02, 2014 6:12 pm

Joined: Sun Nov 02, 2014 11:59 am
Posts: 10
Hmm, high score 130 with a SD of 15? The rule for a normal distribution is that 95% of all data lie within 2 SD of mean. So 2.5% of the scores should be above 130 or .025x1200=30 scores. So if there are no scores beyond the 130 how do we calculate the percentile rank? Did 30 people score 130? In addition, this would mean that with a1200 test takers some 300 people passed the exam? Why would 300 be allowed to pass for only 100 or so spots? Last year the cutoff was 112 (336/3) and about 150 would have passed the cutoff with a SD of 15 and 700 test takers. This makes sense.

So does the school really know what CEM did? Or what we are asking? Did all 1200 people figure into the statistics? Either 1200 are not used in the statistics as too many passed; the school allowed more than normal amount to pass for they are unsure how many are in catchment or the SD is 15! If someone could include the reply from a qualified official from the school I would like to see it, as I was told this information would be passed on! If we know the amount of test takers and SD we can find the ranks - and this is not to be given out?

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 Posted: Sun Nov 02, 2014 9:13 pm

Joined: Thu Mar 03, 2011 1:27 pm
Posts: 46
OK here is a cut-n-paste of the from Reading School's email:

*** START ***
Every pupil’s score for each test component is then adjusted by a small amount according to their age, so the youngest pupil in the cohort is not disadvantaged on the basis of their age. This creates the age-adjusted raw scores. These are standardised for each component to make the mean standardised score for each component fixed at 100, with a standard deviation of 15. Finally, the Total Weighted Score for each pupil is calculated by adding together the agreed percentage of the Verbal component, Maths component and the Non-Verbal component. The test has no floor- or ceiling-effect, so the standardised scores are not capped.
*** END ***

I think the point to note is that you CANNOT predict the percentile rank as it depends on too many variables. If you create yourself a random set of scores with a mean of 100 and SD of 15 you will be surprised at the variability. There will be peaks and troughs where you may not expect. However, very high scores (120 upwards) should be well within the top 112 and would be a dead cert to get a day place.

In the case of Reading the maximum score is low in comparison what one may expect with a perfect normal distribution. This can and does happen. For example, imagine what happens if you take a perfect distribution and then add 50 extra boys getting 115 and another 50 getting 85. The mean remains at 100 and the standard deviation does not deviate but the distribution is very different to a normal distribution.

If terms of the cut-off for 2015 much depends on how many kids were in catchment and thus able to put Reading on the CAF. We know 1200 or so asked to be included in Reading's standardization but only 630 or so actually sat the test at Reading. My suspicion is that the number of boys in catchment is more like 700 and the cut-off may thus be low-ish.

Can I ask from where did you get the 112 cut-off for last year? The only thread i can see is this one which only goes up to 2013: viewtopic.php?f=10&t=36583

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 Posted: Mon Nov 03, 2014 2:17 am

Joined: Sun Nov 02, 2014 11:59 am
Posts: 10
Cutoff for last year as always was 336, 3 test components added together. So essentially 112 if all three were averaged. I know one person scoring 343 and getting in on the first cut and I believe one person getting in after the waiting list with a 336.

If more people took the test this year over last, why would the cutoff be moved down, to 110. I assume that this qualifies more boys above the cutoff. I also assume that all 1200 are in the stats and deemed eligible at this point, until the school can confirm the catchment. With such a large number of samples the stats would still predict 300 people above the cutoff of 110, and if so why a cutoff of 110?

If 700 take the test and a SD of 15 is used, then 112 (last years cutoff) gives 150 above the cutoff. This seems correct. So this year we are saying that more people took the test, the same SD was used but we lowered the cutoff? No statistical population artifacts can account for this. Perhaps the school let in twice as many above the cutoff to allow for considerable OOC scores?

The e-mail seems to be a cut and paste from the NFER or GL assessment website, I still wonder......

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