Statistical enquiry: PPDAC and investigative questions
What this lesson covers
- A statistical enquiry moves through problem, plan, data, analysis and conclusion, and each stage depends on the one before it.
- An investigative question names the variable, the group and the kind of answer it wants: a summary, a comparison or a relationship.
Five stages, one question
- A statistical enquiry answers a question with data.
- PPDAC: problem, plan, data, analysis, conclusion.
- Each stage hands something to the next.
| Stage | You | You end with |
|---|---|---|
| Problem | pose the question | an investigative question |
| Plan | decide what to measure | variables and a method |
| Data | collect or source it | a clean data set |
| Analysis | graph and calculate | features and statistics |
| Conclusion | answer the question | a statement in context |
Three kinds of investigative question
- Summary: what is typical for one group?
- Comparison: does one group tend to be higher?
- Relationship: do two variables change together?
| Kind | About | Display |
|---|---|---|
| Summary | one variable, one group | dot plot or box plot |
| Comparison | one variable, two groups | box plots, one scale |
| Relationship | two numerical variables | scatter plot |
A summary question, taken apart
- It names one variable, with units.
- It names the population it is about.
- Its wording says what kind of answer it wants.
| Part | In this question |
|---|---|
| Variable | hours of sleep on a school night |
| Population | Year 11 students at our school |
| Answer type | typical value, so a summary |
| Wording | "What is the typical...?" |
Numerical or categorical?
- Numerical variables are measured or counted.
- Categorical variables sort people into groups.
- The mix of types decides the question and the graph.
| Variable | Type | Values |
|---|---|---|
| Hours of sleep | numerical | 6.5, 8, 9.25 |
| Plays a team sport | categorical | yes, no |
| Arm span (cm) | numerical | 152, 168, 175 |
| Way to school | categorical | walk, bus, car |
A comparison question
- One numerical variable, split by a categorical one.
- "Tend to" is deliberate: not every sporty student.
- At least 30 in each group.
| Comparison | |
|---|---|
| Question | Do Year 11s who play sport tend to sleep longer? |
| Numerical | hours of sleep |
| Groups | plays team sport: yes or no |
| Needs | at least 30 in each group |
A relationship question
- Two numerical variables, measured on the same people.
- The one that might explain the other goes across.
- At least 30 pairs.
| Relationship | |
|---|---|
| Question | Is there a relationship between screen time and sleep? |
| Across (x) | screen time, the explanatory variable |
| Up (y) | hours of sleep, the response |
| Needs | at least 30 pairs |
Two more kinds of enquiry
- A time series follows one variable over time.
- A probability enquiry repeats an experiment.
- Same cycle, same care with the question.
| Enquiry | Looks at | Minimum |
|---|---|---|
| Time series | one variable over time | at least 5 full cycles |
| Probability | an experiment, repeated | at least 30 trials |
Fixing weak questions
- No variable: there is nothing to measure.
- No population: there is no one to measure.
- Opinion or one person: data cannot answer it.
| Weak | Problem | Fix with |
|---|---|---|
| Do boys like sport? | no variable to measure | hours of sport a week |
| How tall are people? | no population | Year 11s at our school |
| Is sleep good? | an opinion, not data | typical sleep of Year 11s |
| Who is the fastest? | about one person | typical 100 m time |
One rewrite, step by step
- "Do boys like sport?" Like is not measured.
- Measure hours of sport a week instead.
- Add groups and a population: a comparison.
Population and sample
- The question is about the whole population.
- You usually only measure a sample of it.
- So the conclusion says what the sample suggests.
| Word | Means |
|---|---|
| Population | everyone the question is about |
| Sample | the part you actually measure |
| The question | is about the population |
| The answer | is worked out from the sample |
Before you commit to a question
- Can you actually get the data?
- Is it fair and safe to collect?
- Will there be enough of it?
| Check | Means |
|---|---|
| Can the data be got? | measured, surveyed or sourced |
| Is it fair to ask? | consent, privacy, no harm |
| Is there enough? | 30 per group or 30 pairs |
| Is the variable clear? | units and how it is measured |
Where the question earns marks
- Achieved: explain where the data came from.
- Merit: connect each stage to the question.
- Excellence: reflect on the whole process.
What to take away
- Get the question right, and the rest has a direction.
| PPDAC | problem, plan, data, analysis, conclusion |
| Summary | one variable, one group |
| Comparison | one variable, two groups, "tend to" |
| Relationship | two numerical variables, scatter plot |
| Every question | names variable and population |
| Weak question | no variable, no population, or opinion |
| Enough data | 30 per group, 30 pairs, 30 trials |
Your turn: four questions
- Pause here. For 1 and 2, name the kind of question.
- Name the variables and their types too.
- For 3, write a whole new question.
| Question | |
|---|---|
| 1 | Is there a relationship between height and 100 m time for Year 11s? |
| 2 | Do Year 11s who walk to school tend to have lower pulse rates? |
| 3 | Improve this question so data can answer it: "Are phones bad?" |
| 4 | Drawing box plots and finding medians is which PPDAC stage? |
Show answer
1. A relationship question. Two numerical variables, height and 100 m time, for Year 11 students, shown on a scatter plot with at least 30 pairs. 2. A comparison question. Numerical variable: resting pulse rate. Categorical variable: walks to school or not, which makes the two groups. 3. Any question with a measurable variable and a population, for example: Is there a relationship between daily phone use and hours of sleep for Year 11 students at our school? 4. Analysis.
The answers
- Relationship: height and time, both numerical.
- Comparison: pulse rate, split by walking or not.
- A variable and a population, e.g. phone use and sleep.
- Analysis.
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