Correlation (AQA Level 3 Mathematical Studies (Core Maths))

Types of Correlation & Conclusions

What is a scatter diagram?

• A scatter diagram is a way of graphing bivariate data

  • You may be asked to plot, or add to, a scatter diagram

  • One variable will be on the  – axis and the other will be on the  – axis

  • The variable that can be controlled in the data collection is known as the independent or explanatory variable and is plotted on the – axis

  • The variable that is measured or discovered in the data collection is known as the dependent or response variable and is plotted on the – axis

• Scatter diagrams allow statisticians to look for relationships between the two variables

  • Some scatter diagrams will show a clear relationship known as correlation

  • Others will not display an obvious relationship

  • If a scatter diagram shows a relationship you may be asked to identify outliers

What is correlation?

• Correlation is how the relationship between the two variables is described

• Perfect linear correlation means that the bivariate data will all lie on a straight line on a scatter diagram

• Linear correlation can be positive or negative and it can be strong or weak

  • Positive correlation describes a data set where both variables are increasing

  • Negative correlation describes a data set where one variable is increasing and the other is decreasing

• When describing correlation you should say whether it is positive or negative and also say whether it is strong or weak

• If correlation exists then there could be outliers, these will be data points that do not fit the pattern seen on the graph

  • There will likely be a maximum of one or two outliers on any scatter diagram

  • You may be asked to identify the outliers

What is the difference between correlation and causation?

• It is important to be aware that just because correlation exists, it does not mean that the change in one of the variables is causing the change in the other variable

  • Correlation does not imply causation!

• If a change in one variable causes a change in the other then the two variables are said to have a causal relationship

  • Observing correlation between two variables does not always mean that there is a causal relationship

  • Look at the two variables in question and consider the context of the question to decide if there could be a causal relationship

  • Observing a relationship between two variables can allow you to create a hypothesis about those two variables

  • For two variables that are correlated but do not have a causal relationship, there may be a third variable (confounder) that forms a link between them

• If the two variables are temperature and number of ice creams sold at a park then it is likely to be a causal relationship

  • An increase in temperature is likely to make people want to buy an ice cream to cool down

• Correlation may exist between rates of skin cancer and exercise but they are unlikely to have a causal relationship

  • It may be that in locations where there there are more hours of daylight, people spend more time exercising, people in these locations may also have greater exposure to the sun and therefore have greater incidences of skin cancer

Outliers of Scatter Graphs

What is an outlier?

• An outlier is a data value that is extreme or does not fit the pattern

  • These are often easy to spot by sight if there is an obvious relationship between two variables on a scatter graph

• Typically an outlier is considered to be

  • greater than 1.5 times the interquartile range above the upper quartile

  • or less than 1.5 times the interquartile range below the lower quartile

Should I exclude outliers from my data?

• The decision to exclude an outlier from a data set should be given careful consideration

• It is reasonable to exclude an outlier from your data set if:

  • it is a result of human error during measurement or faulty equipment,

  • the data value is so extreme that it will significantly affect the results

• If an outlier is excluded then you must state that it has been excluded and the reason why