Scatter Diagrams & Correlation (Edexcel GCSE Statistics)

Scatter Diagrams & Correlation Basics

What is correlation?

• Correlation describes how two quantities are related to each other

  • Positive correlation is when one quantity increases and the other quantity also increases

    • For example, as temperature increases, sales of cold drinks increase

  • Negative correlation is when one quantity decreases while the other quantity increases

    • For example, the value of a car decreases as its age increases

  •  Zero (no) correlation is where there is no apparent relationship

    • For example, the masses of snails and students' scores in an exam

• If there is a relationship between two quantities then we say that the quantities have an association (or that the quantities are associated)

  • Temperature and sales of cold drinks are associated

  • Masses of snails and scores in an exam are not associated

What does the phrase "correlation does not imply causation" mean?

• If two quantities correlate, it does not mean that one causes the other one

• For example, each day you record the height of a sunflower and the weight of a puppy

  • As the height of the sunflower increases, the weight of the puppy increases
    

    • This is a positive correlation

  • But you cannot claim that:

    • 'If you want your puppy to weigh more, make your sunflower taller!'

    • or 'Sunflowers grow better when puppies are heavier!'

  • Both quantities may be increasing due to another reason

    • In this case, time

• You should also be aware that multiple factors may interact and cause two quantities to change

  • For example a study may find correlation over time between rising carbon dioxide levels in the atmosphere and rising levels of obesity

    • But carbon dioxide in the atmosphere doesn't cause obesity

    • Instead populations have become richer over time

    • And richer populations tend to emit more carbon dioxide and have higher levels of obesity

What are scatter diagrams?

• Scatter diagrams (or scatter graphs) are used to plot pairs of data

  • For example, students' Maths grades against their Physics grades

• The vertical and horizontal axes represent the two quantities being measured

  • In an experiment where it is suspected that one variable is affecting the other variable

    • the explanatory (or independent) variable should be plotted on the x-axis (horizontal axis)

    • the response (or dependent) variable should be plotted on the y-axis (vertical axis)

• Points are plotted as crosses, ×

  • They are not joined up

• The general shape formed by the points shows the type of correlation

  • Positive correlation goes from bottom left to top right

    • A positive gradient

  • Negative correlation goes from top left to bottom right

    • A negative gradient

  • No (zero) correlation looks like a cloud of points

• You should also be able to talk about the strength of a correlation

  • There is strong correlation if the points are close to lying along a straight line

  • There is weak correlation if the points are not close to lying along a straight line