Now I had got both the results for the girls and the boys. I had to find a suitable sampling method. The sampling methods available to me were as follows:-
Systematic Sampling
Purposive Sampling
Opportunity Sampling
Purposive Sampling
Random Sampling
Cluster Sampling
Out of all these Sampling methods I decided to use Random Sampling because I think that is the most appropriate method to use for my secondary data. To get a random set of numbers I am going to go to this is a web site which is made to get a set of numbers out of any sort of a data range it is a very good site. I used to get a set of 20 results from both the girls results and the boys results. I decided to use 20 results from each the Boys set and also the Girls set of data. I chose this amount because it seems suitable. I would not be able to do too many because it would become too hard. If I chosen a little amount like 5 or 10 it might become biased because I might have come across lots of bad results or good ones. I think that 20 is a reasonable number.
Table For Boys KS2 & KS3 SATs result.
Table For Girls KS2 & KS3 SATs result.
Analysis of Results
My first Hypothesis is that Girls on the whole achieve a better mark then the Boys in both their Key Stage 2 and Key Stage 3 Marks. To show this I will have to work out the mean and Standard Deviation out for both the girls KS2 and also KS3 results. Then I will be able to see both the mean of the girls and the boys and compare them. The Standard Deviation will show how accurate my mean is.
Boys Key Stage 2 Mean And Standard Deviation
∑ f x 74
Mean, x = = = 3.7
∑ f 20
279
Standard Deviation = - 3.7² = 0.5
20
Boys Key Stage 3 Mean and Standard Deviation
∑ f x 104
Mean, x = = = 5.2
∑ f 20
557
Standard Deviation = - 5.2² = 0.9
20
Girls Key Stage 2 Mean And Standard Deviation
∑ f x 77
Mean, x = = = 3.85
∑ f 20
307
Standard Deviation = - 3.85² = 0.72
20
Girls Key Stage 3 Mean And Standard Deviation
∑ f x 103
Mean, x = = = 5.15
∑ f 20
547
Standard Deviation = - 5.15² = 0.9
20
The mean Boys Key Stage 2 result for the boys was 3.7 and the Girls Key Stage 2 mean result was 3.85. Girls did better than boys in their Key Stage 2 exams but not by that much. They beat the boys mean mark by 0.15. It is not much of a difference but still means that the Girls did better than the boys.
The mean Boys Key stage 3 result is 5.2 and the mean Girls Key Stage 3 mean result is 5.15. The boys make a bigger improvement than the girls, this causes the boys results to catch up to girls results and is now a nudge ahead. My hypothesis was half correct but I did not think that the boys would make such an improvement that the girls would fall behind. So my hypothesis was half correct.
This also Goes on to prove my third hypotheses which is that “I think by the time Boys get to year 9 their results are catching up to the girls but the Girls Results are still a nudge higher than the Boys Results. I think that in Challney High Schools case the boys make a better improvement than the girls. I also think that this would be the opposite in any other school.” This proves what I thought, that the boys will make a better improvement from their Key Stage 2 to Key Stage 3 mark. I did not think that they would beat the girls in Key Stage 3 marks.
Boys Key Stage 2 Cumulative Frequency
Girls Key Stage 2 Cumulative Frequency
Put cumulative done by hand in
Boys Key Stage 3 Cumulative Frequency
Position No. of Median = n + 1
2
= 21
2
= 10.5th position
As you are able to see 10.5th position comes under the 5 ≤ L < 6 category. It is 2.5 places in the category of level 5
2.5 X 5 = 1.5625
8
1.5625 + 5 = 6.5625 ≈ 6.5 (to 1 dp)
6.5 is the Median Value
Girls Key Stage 3 Cumulative Frequency
∑ f = 20
Position No. of Median = n + 1
2
= 21
2
= 10.5th position
As you are able to see 10.5th position comes under the 5 ≤ L < 6 category. It is 0.5 places in the category of level 5
0.5 X 5 = 0.3571
7
0.3571 + 5 = 5.3571 ≈ 5.3 (to 1 dp)
5.3 is the Median Value.
The Boys Median level which was worked out in a frequency table is:- 6.5
The Girls Median level which was also worked out in a frequency table is:- 5.3
The median level shows me that the boys have a better median level than the girls. This tells me that the boys have made much better of an improvement than the girls because in the Key Stage 2 SATs the girls were ahead.
The median is not always too accurate. To get a better picture on who did better I will also now work out the Modal average.
Calculating the Key Stage 2 Boys Modal Average
Calculating the Key Stage 2 Girls Modal Average
Calculating the Key Stage 3 Boys Modal Average
Calculating the Key Stage 3 Girls Modal Average
Girls and Boys Key Stage 2 Results shown in a Multiple Bar chart
Girls and Boys Key Stage 3 Results shown in a Multiple Bar chart
The girls again achieve more high results but the boys achieve more levels 5 to 6 and 6 to 7. That is the reason why boys by this time have a better average than the girls.
In conclusion my first hypothesis and my third one was more or less correct. You have seen that the girls beat the boys in their Key Stage 2 exams but the boys beat the girls in the Key stage 3 exams. I did predict that the girls would beat the boys in their Key Stage 2 exams but they did not in their KS3 exams. I did not think that the boys would beat them I thought that they will still be a nudge under.
Hypothesis Three
Now I will look at my second hypothesis which is that
“I think that the Boys will have a better gain in their results from Key Stage 2 too Key Stage 3 than the girls. I have Predicted this because the girls who come with high results from Junior School to High School do make an improvement but not better than the Boys in Our School. Where as the majority of boys come with normal and below average results and make a better improvement than the Girls. I think that this is because our school is an all Boys school, if it was a mixed school I do not think that the boys would have made a better improvement than the girls.”
I predicted this because if the high school was mixed one the boys attention would bee all of the work and on the girl sitting in front. This would be the case for most of the students, I am sure that would be the case for me! This can be proved as well if you were to take a look at our schools Results and another mixed school boys results, I think that our results would be a considerable amount higher than the Boys from a mixed school. I think that the girls would come with good results because they are more intellectually clever at the age of 11 than boys. This being because the girls have already started growing up physically and mentally. The boys start at a much later age. This would be another factor of why boys catch up by the time they are in year 9.
I will try to prove my hypothesis by looking at the last column in my results table which are on pages 11 and 12. The last column is the results gain column. I got the results gain by taking away the KS2 results average with the KS3. I will work out the mean and the standard Deviation for both the Girls and the Boys results.
Result Gain for Boys Results.
∑ f x 34
Mean, x = = = 1.7
∑ f 20
65
Standard Deviation = - 1.7² = 0.5
20
Result Gain for Girls Results.
∑ f x 32
Mean, x = = = 1.6
∑ f 20
57
Standard Deviation = - 1.6 = 0.5
20
The Boys mean improvement is 1.7 and the Girls improvement is 1.6. This shows that the boys make a better improvement than the girls not by much. So in conclusion my 2nd hypothesis is correct. So I was right, when boys don’t have girls to look at the work is better.
In conclusion my hypothesis was correct. Boys did make a better improvement then the Girls.
Hypothesis Four
My fourth hypothesis is as follows: “The higher the Key stage 2 Mark Achieved, for any subject, the higher the Key Stage 3 mark will be. I think that this counts for both girls and boys.” To prove this I will use a correlation graph and also spearman’s Rank Correlation.
Girls Correlation for KS2 and KS3.
Boys Correlation for KS2 and KS3.
So Far my Hypothesis is correct, the better the results for KS2 the better the Results for KS3. Now I am do the rank correlation.
Boys Results:
∑ d²=278.25
6 ∑ d²
Correlation coefficient = 1-
n (n -1)
= 1- 1669.5
7980
= 1- 0.2092
=0.8908
My hypothesis was again correct.
Conclusion
In my hypotheses at the beginning I had 4 predictions, these being
- Girls on the whole achieve a better mark then the Boys in both their Key Stage 2 and Key Stage 3 Marks.
- I think that the Boys will have a better gain in their results from Key Stage 2 too Key Stage 3 than the girls. I have Predicted this because the girls who come with high results from Junior School to High School do make an improvement but not better than the Boys in Our School. Where as the majority of boys come with normal and below average results and make a better improvement than the Girls. I think that this is because our school is an all Boys school, if it was a mixed school I do not think that the boys would have made a better improvement than the girls.
- I think by the time Boys get to year 9 their results are catching up to the girls but the Girls Results are still a nudge higher than the Boys Results. I think that in Challney High Schools case the boys make a better improvement than the girls. I also think that this would be the opposite in any other school.
- The higher the Key stage 2 Mark Achieved, for any subject, the higher the Key Stage 3 mark will be. I think that this counts for both girls and boys.
The first hypothesis was proved half correct because the girls beat the boys in the KS2 mark but the girl lost to the boys in the KS3 mark. So my prediction was half correct. My second hypothesis was correct because the boys made a better improvement then the girls. My third hypothesis was half correct boys did make an improvement but the girls fell behind the results in KS3. I thought that the girls will stay a nudge ahead. My fourth hypothesis was correct because there was a positive correlation.
This coursework has been enjoyable, now I will be able to prove my sisters wrong! Overall I am pleases with the work I have produced.
