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Predicted grades given by subject teachers at the time of Yellis.

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Introduction

Σ2

Aim

The aim of this investigation is to see if the predicted grades given by subject teachers at the time of Yellis, has more correlation to grads achieved by students in there gsce’s then there Yellis predictive grades

Yellis is a test taken in year 9 of schooling; there are 2 parts to the test, a mathematic and vocabulary styles paper, each student has to complete in exam conditions.

The subject teachers predicted grads are based on departmental meetings where all teachers of the student discuses the progress of the child. They take in to consideration the students natural ability, work rate in class, behaviour, quality of work, and test results, these aspect are taken over many weeks so a rounder picture is built up of the student of which a prediction can be based,

Yellis only take in to account the mark achieved on the test, ranks the results all around the country, then assign grand to each percentage, eg top 20% are predicted A.

The population that I will be sampling the data from, is Stoke Dameral community College, but there may be implication outside he given  population, as the trend may be evident over the whole of the examined students, but I can’t say that it will be just with data from the Stoke Dameral as there may be different methods of producing predicted grades.

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Middle

r = Sxy/SxSy

image00.png

Sx = image00.png√((Σx2/n)-x2 )

Sx = square root of the average x squared value subtracted the means squared.

Sx = there average variation from the mean.

Sx is the same as Sy but for the other variable involved. This is always a positive value because of the squaring,

Sxy = image00.png (Σxy/n) –xy

Sxy = the square root of average x multiplied by y value subtract the two means multiplied together.

Sxy = the average difference in the data multiplied together, to the means multiplied. This is what determines if there is positive or negative correlation. If this value is negative then the correlation is too.

 r = is the correlation coefficient for the sample, it with zero being no correlation and 1 or –1 being perfected correlation. The signs say if it is positive or negative, the values in-between are different degrees of correlation. This is only the correlation of the sample, but if the sample is a random sample, like it is, then it can be used for a estimate of the parent populations correlation coefficient (ρ).

ρ can be tested by performing a hypothesis test, using the value n, the number in the sample and by working to a significance level, the significance level I have chosen to use is 5% because the data was integer values, I would have used a smaller significance level if I had raw exam scores.

The hypothesis test gives a critical value, where the justification of the claim that there is correlation in the parent population.  

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Conclusion

On the whole I believe that this data was worth collecting and the analysis was very useful, it shows although Yellis’s predictions do correlate with the GCSE achieved, they are not a accurate as staff predictions.

One of the major sources of error in this investigation was not having raw data, although I tried to counteracted this by taking a large sample, I feel that there would have been greater correlation if I would have used the raw scores. I restricted my self to one year group so one set of results I would have like to expanded the investigation so that I incorporated other years, this would insure that my conclusions are true for all years like I expected.

Another problem I found I could only test students with all of the data, this meant that I didn’t use student that didn’t turn up for the exam, these students where most probably likely to acquire poor grades, so on the whole the average grade was increased. chose  

Although my  parent population is stoke Dameral, the conclusions have implications for all schools that use yellis as a form of predictions, it surely have implications for inner city public schools, with relatively the same standards as Stoke Dameral. I would like to improve this investigation so that the parent population would be the England. To do this I would randomly select 10% of the schools taking part in Yellis, and perform the same statistical analysis as I have already preformed on Stoke Dameral

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