To prove my first hypothesis I am going to plot IQ against the average SATs results on a scatter graph. I am doing this to see any correlation between the two. If my hypothesis is correct, I would expect a positive correlation.
To test the correlation I’m going to input the data into a graphical. I will then use it to calculate Pearsons’ Product Moment Correlation Coefficient. This will give me a value between -1 and 1, where -1 is a perfect negative correlation, 1 is a perfect positive correlation and values near o show no correlation. I would expect a value near 1.
I will then draw two extra scatter graphs to compare boys’ relationship between IQ and average SATs results, to the girls’. I would expect the girls’ correlation to be stronger than the boys’ because girls generally perform better in tests.
Hypothesis 2
Boys have a higher IQ than girls.
To prove this hypothesis I am going to split my sample in to boys and girls. I will then put the boys IQ scores in size order (lowest to highest), and do the same for the girls’ scores. Now they are in size order I will find the median, the lower quartile and the upper quartile for each set of data. I will then use these results to produce two boxplots, one for boys’ IQ scores and one for the girls’ scores.
I will use the fencing method to calculate outliers. This is where I will multiply the inter-quartile range by 1.5, then, subtract this from the lower quartile. Any values lower than the smallest value are outliers at the bottom end. To find the outliers at the top end I will multiply the IQR by 1.5 and then add this answer to the upper quartile. Anything above the highest value are outliers.
Hypothesis 3
IQ increases as age increases
To prove this hypothesis I will put my data in to five separate boxplots. One for year seven, one for year eight, one for year nine, one for year ten and one for year eleven.
I will use these boxplots to compare IQ scores of different age groups.
I will use the fencing method to calculate any outliers.
I will expect the scores to higher in general for year eleven.
Stratified Sample
Year Seven: (30/200) × 80 = 12
Year Eight: (38/200) × 80 = 15
Year Nine: (32/200) × 80 = 13
Year Ten: (53/200) × 80 = 21
Year Eleven: (47/200) × 80 = 19
Results Interpretation
Hypothesis 1
The higher the IQ, the higher the average SATs results. There will be a stronger relationship between the girls’ IQ and average SATs results than the boys’.
The correlation for all the data is a positive one (0.7489830411). This has proved the first part of my hypothesis correct. For the second part of the hypothesis I drew two more scatter graphs, one for boys and one for girls. The correlation for the boys scatter graph is a weak positive one (0.647505017), and the correlation for the girls scatter graph is a strong positive one (0.8937107622). The girls’ correlation is stronger than the boys’, just as I predicted in my hypothesis.
Hypothesis 2
Boys have a higher IQ than girls.
The girls and boys lowest value has a difference of 3.25, with the girls’ value being higher. However, the boys’ lower quartile is larger than the girls’ by 2. Even though this value is small it shows that the boys have started to become cleverer than the girls. Both medians, for boys and girls, are exactly the same (102). The range between the lower quartile and median is greater in the girls than in the boys. The upper quartile’s have a larger difference between them. The girls’ upper quartile is 106 and the boys’ is 109. It is only a difference of 3 but it means the boys’ have become cleverer than the girls. The girls’ highest value is 5 larger than the boys’. There are two outliers at the bottom end for the boys and one at the bottom end for the girls.
I think my hypothesis was incorrect as neither boys nor girls have higher IQ scores.
Hypothesis 3
IQ increases as age increases
All the boxplots in this hypothesis are very similar apart from year 11, in which the IQ scores are generally higher. This is because an IQ test takes in to account the person’s age and changes their score accordingly.
The lowest value for year seven and eight are nearly the same, they are 85.75 and 86, and the lower quartile between these two has a difference of 0.5. The medians have a very slightly larger difference, it is 1.5. The median for year seven is 100.5 and for year eight it is 102. The upper quartile for year seven is 104 and for year eight it is 103, a difference of 1. The highest value for the year seven and eight boxplots are exactly the same (112). There is a bit more of a difference between the year seven and eight boxplots and the year nine one. For year nines the lowest value is only 1 less; however, the LQ is considerably less, by 5. Again the medians are very similar and so are the upper quartiles. The highest value is larger in the year nine boxplot than in the year eight’s; by 9.
In the year ten boxplot the difference between the lower and upper quartile is 21, the LQ is 92 and the UQ is 113. The lowest value is substantially lower. It is 76, where as all the others are around 83. The lower quartile is similar to year nine. Once again the medians are the same. The UQ in year ten is 113, much larger than the others. The highest value is between the two highest values for year eight and nine.
As I mentioned earlier the values in the year eleven boxplot are larger. The LQ is about the same as all the other medians, the median is higher than most of the other upper quartiles and the UQ is larger than all the others. The highest value is 125, this is the higher than all the others by at least 4.
Evaluation
Generally, my coursework went quite easily. I didn’t encounter any problems apart from entering data in to a graphical calculator. I had to repeat this process a number of times due to missing out data.
If I were to repeat the coursework I would use a larger sample size or compare data from different schools to make sure my results are correct for the country or just a few schools in particular.
