Association and causal evidence
An observed association describes how variables vary together. It does not by itself show what would happen if one were deliberately changed
- Language Use “tends to” and identify the observed sample. Avoid guarantees and unsupported “causes” claims
- Alternative explanations A common factor, reverse direction, selection or measurement issues may help explain the pattern
- Study design Appropriate controlled randomised experiments can support causal claims within their conditions and limitations
- Model versus evidence A model illustrates assumptions. It does not prove that the assumed mechanism explains real data
Worked example
Daily ice cream sales and pool entries tend to increase together. Give a supported conclusion and one possible explanation to investigate
\[\text{positive association}\]
- \(\displaystyle \text{observed association}\)On these days, higher ice cream sales tended to occur with more pool entries
- \(\displaystyle \text{possible common cause}\)Hot weather is a plausible common factor, not a cause proved by the association
- \(\displaystyle \text{cause not established}\)An intervention changing sales need not change pool entries. Study design and context matter
Common mistakes
Association proves an intervention
✕\(\displaystyle \text{association}\Rightarrow\text{cause}\)✓\(\displaystyle \text{association}\not\Rightarrow\text{cause}\)
Observational patterns do not isolate a causal mechanismLack of proof means no cause
✕\(\displaystyle \text{unproven}=\text{impossible}\)✓\(\displaystyle \text{unproven}=\text{not established}\)
A causal connection may exist but requires suitable evidenceDifficulty levels
introSelect the observational conclusion supported by a strong positive or negative correlation
standardReject separate causal and intervention claims when the data are observational
challengeIdentify a plausible third factor and reason about a negative strong association
examChoose the conclusion licensed by the reported relationship or study design
Questions about this topic
Can a very strong association still be confounded?+
Yes. A third factor can influence both variables even when their observed association is strong
Does negative association imply a negative causal effect?+
No. Direction describes the observed tendency, not necessarily the effect of an intervention
Is random sampling the same as random allocation?+
No. Sampling concerns selection from a population. Allocation assigns study units to treatments and helps make a causal comparison
Does a simulation prove a real-world cause?+
No. It shows what follows from its assumed mechanism. Check those assumptions against appropriate real evidence
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 5: Statistics
In this chapter
Classify data types5A Data collection and types: Collect data and evaluate biasBuild a frequency and percentage frequency tableBuild a bar chart from a frequency tableGroup numerical data into class intervalsConstruct a histogram from a frequency tableRead values from a histogramDescribe the shape of a distributionChoose an appropriate display for a variableRead values from a frequency table or bar chart5B Frequency tables and histograms: Critique statistical displays and claimsConstruct a dot plot from raw dataConstruct an ordered stem plot from raw data5C Dot plots and stem-and-leaf plots: Compare a numerical variable across groupsMean, mode, median and range of a data listFind the mean and the median, and choose between themFind measures of centre from a frequency displayFind the range, the quartiles and the IQRFind the fences and identify outliers5E Quartiles, interquartile range and outliers: Produce a five-number summary and construct a boxplot5F Box plots: Produce a five-number summary and construct a boxplotRead values and percentages from a boxplot5F Box plots: Compare a numerical variable across groupsPlot, read and classify a basic time-series graphConstruct and read a time series plotIdentify qualitative features in a time seriesIdentify the explanatory and response variablesConstruct a scatterplot from a data tableRead a scatterplotDescribe an association from a scatterplotAssociation is not causationFit a line of best fit by eye and make estimatesCompare categorical groups using two-way tables