The investigation cycle
A statistical investigation follows a cycle that many statisticians call PPDAC:
| Stage | Key tasks |
|---|---|
| Problem | Write a clear research question. |
| Plan | Decide what to measure, who to sample, how to collect data. |
| Data | Collect and clean the data. |
| Analysis | Summarize, display and test. |
| Conclusion | Answer the question; discuss limitations. |
Writing a good research question
| Weak | Strong |
|---|---|
| "What about screen time?" | "Is there a relationship between daily screen time and hours of sleep among Grade 12 students at our school?" |
| "Do people like sports?" | "What proportion of students at our school play at least one organized sport?" |
A good question is specific, measurable and answerable with data.
Data sources
| Type | Description | Examples |
|---|---|---|
| Primary data | you collect it | surveys, experiments, measurements |
| Secondary data | someone else collected it | Statistics Canada, Environment Canada weather records, sports databases |
Secondary data saves time but check how it was collected and whether it fits your question.
Planning data collection
- Define variables precisely ("screen time" = recreational use, hours per day).
- Choose a sampling method (random if possible).
- Decide on sample size.
- Write neutral survey questions and pilot-test them.
- Consider ethics: consent, privacy, anonymity.
Analysis
| Data type | Displays | Summaries |
|---|---|---|
| one categorical | bar or circle graph | proportions |
| one numerical | histogram, box plot | mean, median, SD, IQR |
| two numerical | scatter plot | r, regression line |
| two categorical | two-way table | conditional percentages |
| numerical by group | side-by-side box plots | compare medians and spreads |
Use technology (spreadsheets, Desmos, statistics software) for accuracy.
Writing the report
- Introduction: the question and why it matters.
- Method: sample, data collection, variables.
- Results: graphs and summary statistics, clearly labelled.
- Discussion: answer the question; note patterns and surprises.
- Limitations: sample size, bias, measurement issues, correlation vs causation.
- Conclusion and next steps.
Example summary
"In a random sample of 120 Grade 12 students, daily recreational screen time and nightly sleep showed a moderate negative correlation (r = −0.52). Students with more screen time tended to sleep less. Because this is observational data, we can’t conclude that screen time causes less sleep. Limitations include self-reported data and a single school."
Worked examples
Example 1: Is data from Statistics Canada primary or secondary? Secondary.
Example 2: Improve: "Do you agree that homework is too much?" → "About how many hours of homework do you do on a typical weeknight?"
Example 3: Name a limitation of surveying only your own class. It may not represent the whole school.
Common mistakes
- Vague questions that data can’t answer.
- Collecting data before planning.
- Overstating conclusions or ignoring limitations.
Try it yourself
- Write a research question about student part-time jobs.
- Which display for comparing test scores of three classes?
- Primary or secondary: your own stopwatch timings?
- Name two possible limitations of an online survey.
Answers: 1) e.g. "Do students with part-time jobs average fewer hours of homework per week than students without?" 2) side-by-side box plots 3) primary 4) e.g. voluntary response bias, people without internet access excluded
Quick recap
- A statistical investigation follows Problem → Plan → Data → Analysis → Conclusion.
- Use primary data or secondary data wisely.
- Report clearly and acknowledge limitations.