• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Statistics Coursework - Bivariate Data.

Extracts from this document...

Introduction

Bivariate Data                Shahida Jaffer

Statistics Coursework

Bivariate Data

INTRODUCTION

Moving to a new area with so much choice, my parents are skeptical about which middle school my brother should go to.  They want to find a school that doesn’t just do well in one subject at Key Stage 2, but at least two out of the three subjects.  I am going to investigate this by looking at maths and science results for children at Key stage 2 achieving level 5 to see if I can find a school with a positive correlation between them.  This will be shown if a school dos well in maths, and does just as well in science, and if it does badly in maths, does it do equally as badly in science.  

DATA COLLECTION

The data I have used was collected from the ‘Department for Education and Skills’ Website, under the section of performance tables for primary schools at Key Stage 2.  I chose to get the data for schools within 15 miles around my postcode (MK5 8BS), the nearest being printed first.

...read more.

Middle

CORRELATION CO-EFFICIENT

Now I will do a hypothesis test using the Pearson's Product Moment Correlation Co-efficient.  This is calculated using the formula below:image00.png

This is easier than it looks!  The first step is to calculate the following:

image01.png

And then put all of these into the formula to find r (which is always between 1 and -1).  Using programs such as Microsoft Excel, you can highlight the data and the computer can automatically calculate the PPMCC.

Doing this, the PPMCC is 0.8528  - this backs up my thought that my variables have a good positive correlation, as perfect correlation is at 1 or -1.

I will now carry out a hypothesis test on the correlation co-efficient comparing it with ρ (the parent population correlation co-efficient).  This is called a test statistic, and will be a 1-tailed test at a 5% significance level.

Important things to know:

  • The null hypothesis, H0 represents a theory that has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved.
  • The alternative hypothesis, H1, is a statement of what a statistical hypothesis test is set up to establish.
  • The final conclusion once the test has been carried out is always given in terms of the null hypothesis. We either 'reject H0 in favour of H1' or 'do not reject H0'; we never conclude 'reject H1', or even 'accept H1'.
...read more.

Conclusion

So, one can conclude that if a school have a high percentage of students doing well in maths, then they will have a similar high percentage of students doing well at science and achieving level 5.  Similarly, a school that has a poor performance in maths, will have an equally poor performance in science.  

This means that if my parents want to find a good primary school for my brother, then they should choose a school which has a high percentage of students doing well in maths and science.

IMPROVING THE QUALITY OF DATA

There are many different ways I could do this if I was to repeat the investigation.  If my parents decide what type of school they want to send my brother to (eg public or private) than I could sort the data into these categories first, and then sample and test.  Another thing that I could do is remove all the schools that have percentages below the national average to see if this makes a difference to my hypothesis.

Page  of 3

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Probability & Statistics essays

  1. The mathematical genii apply their Statistical Wizardry to Basketball

    However at this stage I will calculate the relevant parameter for this piece of coursework. I will estimate the expected number of shots required by Lee and Dom to score a basket. Expected Mean Values To find out the expected mean value for a geometric distribution it is defined as

  2. Mayfield High School Maths Coursework

    Below are all my samples which I have gathered by using the random formula:- Random Numbers For Year 7 Boys: - 103, 119, 89, 6, 4, 78 For Year 7 girls: - 73, 114, 30, 23, 34, 76 For Year 8 Boys: - 134, 96, 29, 60, 63, 104 For

  1. GCSE Mathematics Coursework: Statistics Project

    For my scatter graph, the average hours of TV watched per week will be on the x-axis, as my hypothesis states that this will determine the weight of a pupil. This scatter graph will test my hypothesis and is placed after my sample of 100 (which is immediately overleaf), so that I can analyse the findings.

  2. "The lengths of lines are easier to guess than angles. Also, that year 11's ...

    This is 0.4cm bigger than the actual length of the line. The actual length of the line is contained in the box, but at the very edge of the lower quartile. This again shows that most people estimated over the length of the line.

  1. Statistics coursework

    Then I will produce a stem and leaf diagram of the year 7's KS2 results against the year 11's KS2 results. Once again this is for the same reasons as when I used the same type of diagram in the beginning.

  2. Anthropometric Data

    A dependent variable is a variable that dependent on another, the independent variable is said to cause an obvious change in the dependent variable. So I' am going to plot the foot breadth (mm) as a dependent against the foot length (mm)

  1. Teenagers and Computers Data And Statistics Project

    to work out, the total was1000 cubes, because it was 10 x 10 x 10. The zero face was accomplished by taking the 2 adjacent cubes away then cubed .The actual sum was 10-2 = 8 x 8 x8 = 512.

  2. Maths Statistics Investigation

    11 6450 665 89.7 67 Seat Ibiza 2003 7200 3 9030 6315 30.1 68 Ford Mondeo 93-96 34000 11 12255 690 94.4 73 Mercedes Cab 93-97 18500 9 51825 14225 72.2 78 Audi 80 Cabriolet 96000 9 19430 4125 78.8 79 Subaru Forester 50000 11 16945 4550 73.1 82 Fiat

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work