Writing a statistics conclusion: Achieved to Excellence
What this lesson covers
- A conclusion answers the investigative question with evidence and says who it applies to.
- Reflecting on the whole enquiry means naming what limits the conclusion and what would improve it.
Where the investigation has got to
- The question, the data and the analysis are done.
- A call has been made from the box plots.
- Now it has to be answered in words.
| Sport and sleep | |
|---|---|
| Question | do sporty Year 11s tend to sleep longer? |
| Sport | median 8.75 h, box 8 to 9.25 |
| No sport | median 7.75 h, box 7.25 to 8.5 |
| Call | yes: 8.75 is above the no-sport box |
Answer the question you asked
- Use the question's own words.
- Back it with statistics and units.
- Say who it is about.
| Part | Sentence |
|---|---|
| Answer | sporty Year 11s here tend to sleep longer |
| Evidence | medians 8.75 h and 7.75 h, 1 h apart |
| Who | Year 11 students at our school |
Who the conclusion covers
- The sample came from one school.
- So the claim is about that school's Year 11s.
- Not all teenagers, anywhere.
| Sample | 60 Year 11s at one school |
| Can claim | Year 11s at this school |
| Cannot claim | all New Zealand teenagers |
Link to what you expected
- The Ministry of Health guideline: 8 to 10 hours.
- The sport median sits inside it.
- The no-sport median sits just below.
| Guideline | 8 to 10 hours for ages 14 to 17 |
| Sport median | 8.75 h, inside the guideline |
| No-sport median | 7.75 h, just below it |
What limits the conclusion
- Name each source of variation in your data.
- Say how it could have affected the result.
- Be specific to this investigation.
| Issue | Variation | Effect |
|---|---|---|
| Self-reported | measurement | students may guess |
| One school night | induced | a match night differs |
| 30 per group | sampling | another 60 would differ |
How it could be improved
- Each limit gets a matching fix.
- A fix you could actually carry out.
- Not just "get more data".
| Limit | Improvement |
|---|---|
| Guessing | sleep tracker or diary for a week |
| One night | mean of five school nights |
| One school | sample several schools |
The question it raises
- Good enquiries end with a new question.
- Is there a relationship between training hours and sleep?
- That is a relationship question: a new cycle.
Reflecting on the whole process
- Was the question clear enough?
- Did the plan measure what it meant to?
- Would you trust the answer? Why?
Achieved, Merit, Excellence
- Each grade includes the one below.
- Merit adds statistics and links between stages.
- Excellence adds context and reflection.
| Grade | The conclusion |
|---|---|
| Achieved | describe features using the graph |
| Merit | justify with statistics, link each stage |
| Excellence | context, variation, reflect on it all |
An Excellence paragraph, spoken
- Claim and evidence.
- Context: the guideline, and a possible reason.
- Reflection: self-reported sleep limits it.
Before you hand it in
- Five checks.
- Every one is a place marks are lost.
- Tick them off.
| Check | Means |
|---|---|
| Answered the question? | in its own words |
| Statistics with units? | medians, IQRs, values |
| Population named? | and no wider |
| Variation named? | with what it did |
| Improvement given? | and a new question |
What to take away
- Answer, evidence, who, context, limits, improvements.
| Answer | the question, in its own words |
| Evidence | statistics, with units |
| Who | the population sampled, no wider |
| Expected? | link to context and what you knew |
| Limits | name the sources of variation |
| Improve | a fix for each limit |
| Next | a new question it raises |
Your turn: four questions
- Walking versus being driven to school.
- Pause here and answer each one.
- Question 2 wants a full sentence.
| Resting pulse, 30 in each group | |
|---|---|
| Data | Walk: median 68, box 62 to 74. Driven: median 76, box 70 to 82. |
| 1 | Can you make a call about resting pulse? Explain. |
| 2 | Write the conclusion sentence, with evidence. |
| 3 | Pulses were taken in period 1. Which variation could that cause? |
| 4 | Suggest one improvement to the investigation. |
Show answer
1. Yes. The driven median, 76, is outside the walking box, which ends at 74. 2. Year 11 students at this school who walk to school tend to have lower resting pulse rates than those who are driven: median 68 compared with 76 beats per minute, 8 apart. 3. Induced variation: walkers may have just arrived after walking, raising their pulse, so the true difference could be even larger. 4. For example: rest for five minutes before measuring, or use a larger sample from several schools.
The answers
- Yes: 76 is above the walking box, which ends at 74.
- Walkers tend to have lower pulses: 68 vs 76.
- Induced: walkers may have just arrived.
- Rest before measuring, or sample more schools.
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