Is there a link between IQ and Key Stage 2 results?

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GCSE Statistics Coursework

Is there a link between IQ and Key Stage 2 results?

Introduction:

        

I intend to investigate whether there are links between your Intelligence Quotient and your Key Stage 2 results. I intend to do this by looking at data from 12 to 16 year olds who attend Mayfield High school.

Lines of Enquiry:

        My lines of Enquiry shall include:

Links between IQ and KS2 results

Links between gender and IQ

Links between gender and KS2 results

Links between age and KS2 results

Hypothesis:

        I predict that Gender will have little effect on both IQ and KS2 results; this is because although females are more mature than boys at adolescence, both IQ and test results depend on the individual. I also predict that IQ will have a strong effect on KS2 results because someone with a higher IQ is able to learn and remember things better so consequently their KS2 results shall be higher than those with a lower IQ. I also predict that someone's KS2 results may be related to what year they took their KS2 exams as learning techniques may be improving as more research is being done in this area. For this reason I would predict that the older you are, the lower your KS2 results shall be.

Data Collection:

        To investigate these links, I tested my questionnaire on a few people first to see if it would work or if improvements were needed. This is called a pilot survey. My survey consisted of questions like ‘what is your age?’, ‘What is your gender?’, ‘How smart do you think you are?’, ‘What is your IQ?’ and ‘What did you get in Key stage 2?’. This questionnaire did not achieve the intended result in the pilot survey. Many people did not give accurate values for their IQ, as many had not taken an IQ test previously. Also, the majority over-rated their smartness and this shows that the question was somewhat subjective and difficult to measure. Consequently, i would introduce bias into my work, which I need to minimize.

As my survey proved unsuccessful I decided to use the data from the Mayfield High School database, which is based on a real school and has been made available by the Edexcel board. This would be a form of secondary data. Secondary data is data which has been gathered by a source other than myself. Primary data is data that has been collected by my own observations. Data that has been collected by my own observations would tend to be more accurate than secondary data. Nevertheless, using secondary data saves time and resources in collection.  There are 1182 pupils in the spreadsheet and I shall base my investigation on a sample of these students in order to save time. A sample is smaller group taken from the population which should represent the population. Sampling saves time but can make the results inaccurate as the sample may not fully represent the population.

The population is the whole group of students from which I am taking my sample; in this case, it would be the students who attend Mayfield High School

        In my sample I shall have to attempt to minimize bias, as this shall distort my findings. Bias is any characteristic that may prevent a sample from truly representing its population. To minimize bias I shall have to ensure that my sample is completely random. To ensure that I can achieve this random sample, I shall list the students alphabetically and give them all a number. I shall then use my random number generator on my calculator. I intend to collect a sample of 30 students as this sample size should allow me to easily handle the data whilst still having a relevant sample size. I intend to put these into several tables; an overall table, one for males, one for females and one sorted by IQ. IQ is a field which was given in the spreadsheet and as I do not know how this was measured, I don’t know how accurate it is. So I shall conduct my investigation assuming that these are accurate figures. I have decided to do this so that it shall be easier to compare the two gender groups and to notice any connections or patterns.

        I shall create histograms to compare the number of grades attained by each group. I shall also use Pie charts to compare the different grades attained in proportion with the total for each group. I intend to use comparative pie charts to compare the age with the grades attained. To do this I may need to group the data which will make me lose individual values making the data lose some accuracy but it also allows me to handle the data easily and emphasizes patterns in a distribution. I shall also attempt to gather some comparative data so as to compare my findings with another population.  

        

Sampling:

        Because I cannot use the whole sample- as this will be too difficult to handle- I shall use a method of taking a sample from my population to draw conclusions from my data. There are several methods of sampling including random sampling, systematic sampling, stratified sampling, quota sampling and cluster sampling.

        In a random sample, every individual from the population has an equal chance of being chosen for the sample. This would require me to give every individual a number and use the random number generator function on my calculator 30 times.

        In a systematic sample, the individuals are chosen from a list at regular intervals. Such a sample may be biased if low or high values occur in a regular pattern throughout the population. I could do this by listing all individuals from my population in alphabetical order by surname and choose every 19th person. In this case it is unlikely to be biased as your surname has little or no effect on your age, IQ and KS2 results.

        As a population may contain separate groups or strata such as gender or age, the sample can be made to represent the groups fairly within the sample. This is done so that the number from each stratum is proportional to the size in the population. Such a sample is called a stratified sample. This would require me to divide the number of individuals in each stratum by the total number of individuals in the population and than multiply that by the necessary population size. I would than have to randomly select the number of individuals needed from each stratum. This would increase the chance of the sample being an accurate representation of the population.

        Quota sampling is used for market research and is entirely dependant on the interviewer as he/she makes the choice of exactly who is asked. It is a very cheap form of sampling but is not very reliable as it depends on the interviewer to choose the sample and this will mean that the sample will consist of people who seem approachable. This would not be suitable for my sample as I shall not be doing any interviews.

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        In cluster sampling, the population is divided into smaller groups called clusters. One or more clusters are chosen at random and this makes up the sample. This form of sampling is also very cheap but can be easily biased if the clusters are not all the same. I shall not be using this form of sampling as it would be very difficult to ensure that the clusters are all the same and so it would be likely that the results are biased.

        I shall use stratified sampling as it is easier to minimize bias when using this method. There shall ...

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