Context
Correlation output
A pupil investigates the relationship between weekly revision hours and assessment score.
Simulated output
> cor(study$hours, study$score) [1] 0.82
Which conclusion is best?
Choose an option, then check the feedback.
Back to Statistics and Probability
Higher Applications of Mathematics
Scatter graphs and correlation
Describing relationships between variables.
Statistics reference
Check probability, diagrams, averages, regression, intervals and tests.
Mixed revision quiz
Review Statistics and Probability with adaptive feedback.
Before you start
- Be confident reading values from tables and graphs.
- Check units, sample size and what each variable represents.
- Use context in written answers, especially when interpreting results.
Method chooser
Which statistics method do I use?
Are there stages or repeated chance events?
Use a tree diagram.
Do categories overlap?
Use a Venn diagram.
Do you need a typical value?
Calculate an average.
Do you need to compare consistency?
Compare spread using standard deviation or IQR.
Are you comparing distributions?
Use box plots or histograms.
Are you checking a relationship?
Use scatter graph and correlation.
Do you need a prediction line?
Use linear regression.
Are you estimating a population value?
Use a confidence interval.
Are you judging evidence against a claim?
Use a hypothesis test.
Are the same people measured twice?
Use a paired t-test.
Are you comparing two proportions?
Use a z-test for two proportions.
Key idea
- This topic focuses on describing relationships between two numerical variables without overclaiming causation. In Higher Applications, the aim is to use statistical methods to make careful decisions from real data.
- Good statistical work has three parts: choose a suitable method, carry it out accurately, then explain what the result means in the situation.
- When writing conclusions, use cautious language such as 'this suggests' or 'there is evidence to suggest'. Data can support a conclusion, but it rarely proves it completely.
Key formulae, definitions and methods
- Positive correlation means both variables tend to increase together.
- Negative correlation means one variable tends to decrease as the other increases.
- Pearson's correlation coefficient is appropriate for a roughly linear relationship between two numerical variables; outliers can affect it.
- Correlation does not prove causation, and a confounding variable may help explain an observed relationship.
Technology output practice
Interpreting statistical output
Read the simulated output, pick out the key value, then turn it into a written conclusion. This is a learning preview, not a real RStudio environment.
Worked examples
Worked example 1
Choose the method
A sports club records training hours and 5 km run times for members.
- Plot each pair of values accurately.
- Look for direction, strength and unusual points.
- Describe the pattern in context.
A scatter graph shows whether a relationship is visible before using calculations.
Worked example 2
Carry out and interpret
A sports club records training hours and 5 km run times for members.
- Estimate whether the relationship is positive, negative or none.
- Comment on strength using the closeness of points.
- Avoid saying one variable definitely causes the other.
The interpretation should say what the relationship means in context.
Worked example 3
Check the conclusion
A sports club records training hours and 5 km run times for members.
- Use the graph to make a cautious prediction inside the data range.
- State that extrapolation outside the range is less reliable.
- Include units in the prediction.
Predictions from scatter graphs should be cautious and within the data range.
Watch out
- Choosing a method because it is familiar rather than because it matches the data.
- Giving a numerical answer without explaining what it means in context.
- Mixing up sample evidence with certainty about the whole population.
- Ignoring outliers, skewness, units or the scale on a graph.
- Using causal language when the data only shows association.
Technology connection
Related RStudio and Spreadsheet topics
Next step
Move into practice
Use the learning notes to choose suitable summaries and conclusions, then try varied data sets, tables, p-values and interpretation prompts.