Understanding cause and effect
This resource list is designed to provide students with the opportunity to:
- use and interpret scatter graphs of bivariate data;
- recognise correlation and know that it does not indicate causation;
- draw estimated lines of best fit;
- make predictions;
- interpolate and extrapolate apparent trends whilst knowing the dangers of so doing.
Visit the secondary mathematics webpage to access all lists.
Correlation
This unit considers the relationship between two quantities, known as correlation. If the two quantities are height of father and height of son, then we often want to know the extent to which 'tall fathers have tall sons'. Two quantities may be correlated quite strongly while another two quantities may be correlated quite weakly.
In this unit students explore how to assess the extent to which two things are correlated. They will be able to use a mathematical formula for deriving a single figure that represents how strong the connection is between two quantities.
More specifically the objectives for this unit are that students will be able to:
- calculate Spearman's rank correlation coefficient from suitable data;
- recognise and distinguish between positive, negative and zero correlation;
- understand that a significant correlation between two variables does not necessarily imply a direct causal relationship between the variables.
The resource is quiet complex but could be used to generate ideas for ways to explore correlation and challenge misconceptions about cause and effect. This resource could be used to challenge more able students.
Let's Compare Feet!
This resource contains a starter activity which explores data analysis and what conclusions can and cannot be drawn from scatter graphs. This can be used to discuss correlation, trends, continuous and discontinuous data, extrapolation and lines of best fit.
Mini-course 5: Scatterplots - Health and Growth
This resource can be used to extend understanding of scatter graphs. Making Sense of Data is about relationships between two, or more, quantities, looked at by plotting graphs of one against the other.
As a result of this mini-course students should:
- look at the shape of the scatterplot before making any calculations
- pay attention in a scatterplot to outlying points, curvature, clustering in one region of the plot and differences across the plot in the variability of a variable
- know that a relationship is not a cause
- understand what different correlations look like on a scatterplot
- know how to fit a resistant straight line
- look at residuals from a fit
- know how to look for a re-expression to straighten a curved plot
- try plotting ranks if either variable is unevenly distributed
- allow for the effect of a variable by fitting and removing it
- know that selecting one group of cases may very much alter the correlation
Health and medical provision forms an introduction to looking at scatterplots, and could be used on its own for that purpose.
Focus Year 10/11 Handling Data Extension
This Handling Data Focus book is aimed at more able students. The content deals with a range of handling data ideas in significant depth. Some of the activities could well be used as extension material for other schemes. Activities are designed to provoke considerable thought and discussion.
The section on Cities of the world includes a range of ideas in which scatter diagrams are used to identify correlation.
Statistics in Your World - Level 4
The unit entitled ‘Smoking and Health’ examines some of the major diseases common among people who smoke. A scatter graph of smoking and birth weight is examined, and students are asked to look at other evidence and consider whether smoking is harmful. Critical appraisal is invited of some conclusions of the Royal College of Physicians report Smoking OR Health (1977). On completing this unit students will have practised reading tables, plotting graphs, drawing and considering inferences, interpreting tables and data, comparing two or more sets of data, describing and assessing trends, plotting and reading bar charts, using and interpreting death rates, reading time series, calculating percentage changes and using them for comparison, interpreting statements using the word ‘average’ and making a critical assessment of other comments based on data. They will be more aware of data sources, the problems of data comparison, the distinction between correlation and causality, the data connecting smoking with various aspects of health and the distinction between conclusions shown from cross-sectional and longitudinal studies.
The unit: ‘Equal Pay’ requires students to investigate whether the Equal Pay Act is working, by applying statistical techniques, and considers some of the inherent problems in making comparisons. The median, cumulative percentages and the interquartile range are covered.
For each unit there are comprehensive teacher's notes giving an overview of the unit, the aims and objectives for that unit, and prior learning or prerequisites and the equipment required.
Correlation
The first activity in this interactive excel file shows a set of data in a scatter plot. The line of best fit can be drawn and a description of the type of correlation can be revealed along with the equation of the trend line. The second activity shows the value of cars at various ages. The scatter plot shows the data and there are a few questions to be answered about the correlation and based on the use of the line of best fit. There are three more sheets of questions which may be suitable for use in the classroom.
