After I had worked out how many pupils I need for each year by using random stratified sampling I then took my samples from the Mayfield High School database and pasted into a new spreadsheet. As I got the data I firstly sorted it out using the sort option on Microsoft Excel e.g. I set the year group column as ascending this meant that the data would show Yr 7 first then Yr 8 etc. Next I sorted the gender column out this was so that in all the years male and females were separated this helped me as then I could easily take my samples. After I had sorted out my samples I then picked out the amount I needed from each year and gender and but them into a spreadsheet. I also deleted the columns with information that I did not need e.g. the height, weight eye colour etc.
Next I highlighted the data I wanted to make a graph with and then selected the chart wizard button I then selected the chart type I wanted (scatter graph), clicked next and then labelled the axis so it was easy to see what the chart was showing and then finally I clicked OK to create the graph.
After creating the graph I added a line of best fit by clicking on the points of the graph and selecting ‘Add trendline’ next I choose the type of line I wanted (linear) and then clicked OK to finalise the line of best fit.
PMCC (Product Moment Coefficient Correlation)
This is used to calculate how strongly the graphs are correlated
-1 0 +1
Minus 1 showing negative correlation
Plus 1 showing positive correlation
And 0 showing that there is no correlation
After I drew out my graphs I worked out the PMCC for each of the graphs. I did this by using the option on Microsoft Excel were I clicked on the line of best fit and then selected format trendline, next I clicked on the options tab at the top and selected the box stating ‘display r- squared value on chart lastly I clicked OK and this then displayed the R2 value of my graph and after that I square rooted the value to get the PMCC
Analysis
From the line of best fit on this graph I can clearly see the trend that as the IQ of the student increases the Sats result also increases. But this was not always the case as some students scored low on the IQ e.g. 85 and went on to get a level 4 in their English Sats result, in addition some students that scored 100+ in their IQ test got a level 3 in their KS2 Sats English exam.
Also after working out the PMCC value I was able to see how strongly correlated the graph was
-1 0 +1
On this diagram the PMCC value for the KS2 Sats English and the IQ result is approximately here. This also showed me that the graph was positively correlated but also the value 0.810 showed it was very high and close to very strongly correlated.
Overall I have found out that in most cases if a student has a high IQ result they will go on to get a good level (4-5) in their English KS2 Sats result.
Analysis
From the line of best fit on this graph I can clearly see the trend that as the IQ of the student increases the Sats result also increases. But this was not always the case as some students scored low on the IQ e.g. 90 and went on to get a level 3 in their Maths Sats result, in addition some students that scored 100+ in their IQ test got a level 3 in their KS2 Sats Maths examination.
Also after working out the PMCC value I was able to see how strongly correlated the graph was
-1 0 +1
On this diagram the PMCC value for the KS2 Sats Maths and the IQ result is approximately here. This also showed me that the graph was strongly positively correlated as the value 0.823 was very high and suggested strong correlation
Overall I have found out that in most cases if a student has a high IQ result they will go on to get a good level (4-5 or 6) in their Maths KS2 Sats result.
From these graphs I found out that IQ had a similar effect on both subjects English and Maths as they both were strongly positively correlated. But IQ had a greater effect on Maths than English as on maths the PMCC was 0.824 and for English the PMCC was 0.811. Overall IQ only has a tiny difference on the two subjects.
I have proven my first hypothesis and prediction as I said that that IQ will have a greater affect on Maths then English. However the difference between them was only 0.023 which some people may say does not prove my hypothesis as the difference is too small. Therefore to improve my investigation I could use more students from each year and different schools this will give me a larger insight into the investigation
Task Two
Aim: To find out which gender has the best Maths results and why?
Second Hypothesis: The gender with the highest mean IQ and the smallest spread will have the highest KS2 Maths result
To help me prove my second hypothesis I will need to carry out the following calculations:
- Mean of male IQ to show average boy’s IQ
- Mean of female IQ to show average girl’s IQ
- Standard Deviation of male IQ to show how consistent the male IQ data is.
- Standard Deviation of female IQ to show how consistent the female IQ data is.
- Mean of male Maths results to show average boy’s Maths Result
- Mean of female Maths results to show average girl’s Maths Result
Standard Deviation
This is used to measure the spread of data. It is very useful when trying to compare sets of data with the same mean but different ranges e.g. 2,2,3,5,6,8 on one side and on the other I have 4,10,15,26,35 we can see that the second set of numbers have a larger spread and therefore a higher standard deviation
The formula used for standard deviation is:
To find the mean value of the males and females IQ I used this formula:
Added total of each IQ of gender
___________________________ = Mean IQ
Total number of each gender
To get the standard deviation for each set of results I did the following:
Standard deviation for females
4950.5 / 49 = 101.03 > square rooted = 10.051
Standard deviation for males
13801 / 51 = 270.6 > square rooted = 16.445
Analysis
By looking at my results it is clearly visible that the girls had a higher mean IQ (102.9) compared to the boys (98.481) and a higher mean maths result (4.265) compared to the boys (4.078) this clearly shows that the girls are more intelligent. Also the standard deviation shows that the value is much lower for girls (10.051) compared to the boys (16.445) this shows that the girls are consistent and the boys are less consistent as they have a higher standard deviation.
I have proven my second hypothesis to be correct as I predicted the students with the highest IQ and the lowest spread (standard deviation) would have the highest maths Sats result. Clearly from the table above you can see that the girls had a higher IQ result and also a smaller spread and they did get a better Sats maths result compared to the boys.
Conclusion:
Overall, I have found out that having a higher IQ result does generally suggest that the pupil will achieve a higher KS2 Sats score. In addition, I have found out that IQ has a little more affect of 0.023 on Maths than English meaning that pupils who get a higher IQ score are more likely to get a higher level in their Maths Sats Test.
In addition, I have found out that overall girls have the highest IQ levels and also have a less spread (standard deviation) and therefore achieved a better score in their Maths Sats test than boys.
