I want to find out if there is a connection between people's IQ and their average KS2 SATs results.

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Radojka Radulovic

10SML

Maths Statistics Coursework

Aim:  I want to find out if there is a connection between people’s IQ and their average KS2 SATs results. I have gotten my data from the internet and I will take what I need to use in my coursework.

Hypothesis 1:  I predict that the higher someone’s IQ is, the higher their average KS2 SATs results will be.

Plan and Analysis: 

I found a sheet of data put onto Microsoft Excel on the internet for a fictional school called Mayfield High School. Even though the school is made up, the data is based on real people and there are 1183 students in all. The data is details of male and Female students in years 7 to 11 e.g. Height, Weight or favourite colour. This data is a secondary piece of data, I had not collected the information myself, and it was already on and Excel worksheet ready for me. Also the data for each individual student that I have is mixed, some information is discrete (favourite TV program or IQ), but some pieces of information are continuous (height or weight).

        I had decided to see the connection between students IQ and her average KS2 SATs results. To do this I had to take a sample of students out of all the data that I had, for I could not sample the whole population, as there are too many students. I decided that a sample of 50 students was big enough to get a decent and fairly accurate result, but small enough not give me too much unnecessary work. As it is my first sample and that it is quite small, I will pick the student sample by random sampling. I knew that there were different ways of random sampling, such as using a number grid, but I decided to use my calculator to come up with random numbers. I programmed my calculator to random pick, I did this by pressing the random key and then multiplying it by the total amount of data that I had, 1183 pupils.

        Once I had got my random numbers from the calculator, I found the matching pupil number on Excel, then copied and pasted their details onto a separate sheet. I did this until I had 50 different pupils information on my sheet, this was my first sample.

        I averaged out the samples KS2 results. This made it easier for me to find out my aim, as I could tackle the results for the three subjects (maths, english and science) in one go. I found the average easily as all I had to do was highlight the columns I needed in Excel and type in a formula.

=AVERAGE(M2:O2)

This gave me an average for the first person in my sample, then I dragged the little box down which copied and pasted my formula into the other boxes and gave me the average for other people.

        The problem with a random sample is that the information is bias.  For example, there could be more boys than girls in my sample or more year 9 children than any other year.  This biasness could tip my findings and make my results inaccurate or untrustworthy.  

        I wanted to get a graph of all my sampled data; it would be very useful to me, as it would put all my selected information into a picture form.  A scatter graph would be best as it would be easier and clearer for me to see any connections and the correlation of the IQ and the average KS2 SATs results.  Microsoft Excel drew my graph for me quickly and accurately on the computer.  All I had to do was select the two columns from the data that I wanted – IQ and average KS2 SATs results and the graph was drawn.  

As you can see from my scatter graph, nearly all the points are bunched up, very near the trend line on the lower middle part of the graph. This shows and proves that the higher the IQ, the higher the average KS2 SATs results are. The correlation of the points on the graph is positive and quite strong, as the points are slanting from the top right to the bottom left of the graph and are close together.

        If you notice on my graph there are points that do not fit in with any of the others. One person had a high SATs Result but a very low IQ; the other person had a low SATs result but a very high IQ. These two points are called outliers. I will change the two outlying pieces of data with two more fitting pieces of data, and see if this changes anything. Also I can see how my scatter graph has changed and where my line of best fit will be. I want to change the outliers because they distort my sample and I want to see if my hypothesis is correct with the average persons data – the outlier people are only a few and have very unusual data.

        As you can see from my new sample that I have made, I swapped my two outliers with two pieces of data that fitted better with the other pieces of data. I randomly chose my bits of data with a calculator. I will continue using my new sample for the rest of my coursework.

        For my new sample, I have drawn a new scatter graph (without the outliers). I have put a trendline onto my graph, this helps me see where the mean results are and I can find other pieces of data from it easily. The trendline looks like it has changed on my second graph, it looks steeper, but this might just be because the scale on the axis has changed, there are fewer numbers on it and the trendline might just be more stretched. As you can see the points are mainly bunched up near the trend line in the middle to right, top part of the graph. The correlation is still positive and very strong though, but this time ALL of the points are near the trend line, instead of just SOME of them. To check that I am correct with my correlations, I have calculated some things on Excel.

        First I calculated the Product Moment Correlation Coefficient (PMCC). When I was researching this, I found that PMCC could be found in two ways. Pearsons Product Moment Correlation Coefficient (Pearsons) and Spearmans Rank Correlation Coefficient (Spearmans). Pearsons takes all the points on the graph and measures how far away from the trendline they are. It measures both ways from the trendline, horizontally and vertically, Average KS2 SATs results and IQ. Spearmans ranks all the data for IQ and Average KS2 SATs result and then finds the difference of the rank, then finds the correlation. The scale that they both use is from 1 to –1, the closer the number is to 1, the more positive and strong it is. The closer the number is to –1, the more negative and strong the correlation is, and 0 means no correlation.

=PEARSON(L12:L61,M12:M61)

My Pearsons PMCC for my graph was 0.88. This shows that my correlation is positive and is very strong as 0.88 is very close to 1. Now I will calculate my Spearmans.

=CORREL(L12:L61,M12:M61)

My Spearmans Rank for my sample was 0.88. This again shows that my correlation is positive and very strong as 0.88 is very close to 1 on the scale. These calculations both mean that my data is really close together, and that the higher the IQ, the higher the KS2 SATs results will be. You can see this on my graph.

You might notice as well that the points on my graph are positioned in lines going downwards.  This is because I was not given the raw scores of the KS2 SATs results; the maths, english and science results were rounded up to a whole number.  I had to find the average of the three results to make my data little more spread out and accurate for the whole picture.  Because I calculated the average, the scores were divided by three (for the subjects) and the decimals of the averages are in thirds.  The thirds used are the same for each SATs level and this can be seen on the graph.  

Join now!

        To help me get a better picture I have calculated some more things on the average KS2 SATs results and IQ.  First of all I calculated the mean, I did this on Excel using a simple equation.

         =AVERAGE(L12:L61)    and

=AVERAGE(M12:M61)

I can see where the mean result and IQ would be on my scatter graph.  Quite a few students are around that point and it looks as if there are an equal amount of students on either side of the mean.  This shows that my scatter graph is right and has the same pieces of ...

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