117i - Reporting Findings and Acknowledging Uncertainty

Lesson 117 — Reporting Findings and Acknowledging Uncertainty

Strand: Statistics | Descriptor: AC9M8ST04 | Duration: 45 minutes

Block note. Stage 5 (Report) of the investigation. Lesson 116 produced a point estimate: , or about of the Year 8 students, meet the screen-time guideline. Today the class writes and critiques honest, responsible reports of this finding — reports that communicate the result clearly and acknowledge its uncertainty and limitations, ready for the final presentation in Lesson 118.

Learning Intentions

• To communicate statistical findings clearly, precisely and honestly.
• To identify and state the limitations of an investigation, and acknowledge uncertainty appropriately.

Success Criteria

I can:

1. Distinguish appropriately hedged statements from overclaiming statements about a population.
2. Identify specific limitations of our investigation and explain their likely effect on the result.
3. Write a structured report: question, method, result, uncertainty, limitations, conclusion.
4. Critique and improve another report against this structure.

Warmup

(5 minutes — spot the overclaim, pairs)

Sort each statement as overclaiming or appropriately hedged.

1. “Exactly of Year 8 students meet the screen-time guideline.”
2. “Our sample suggests approximately a third of Year 8 students meet the guideline, though the true figure could be somewhat higher or lower.”
3. “All Year 8 students spend far too much time on screens.”
4. “Based on a sample of students, we estimate that roughly – of Year 8 students meet the guideline.”

Answers: 1. Overclaiming — presents an estimate as an exact fact; 2. Appropriately hedged; 3. Overclaiming — a value judgement not supported by the measured variable, and stated as if true of every student; 4. Appropriately hedged — gives a plausible range rather than a single false-precision figure.

Today’s question: how do we write our own findings this honestly?

Activities

Activity 1 — Explicit Instruction: the Anatomy of a Responsible Report (13 min)

A responsible statistical report has five parts:

Part	What it contains	Why it matters
Question	The precise investigation question	Reminds the reader exactly what was measured
Method	Population, sample size, sampling method	Lets a reader judge how trustworthy the result is
Result	The point estimate (proportion and/or count)	The headline finding
Uncertainty	Hedged language — “estimate”, “approximately”, “suggests”	Prevents the result being read as an exact fact
Limitations	Honest weaknesses of the investigation	Shows the boundaries of what can be claimed

I do — modelling a full report for our investigation:

“We investigated what proportion of Year 8 students at our school meet the recommended daily screen-time guideline of hours or less of recreational use on a school day. A stratified random sample of students per class ( selected, responding) was surveyed across all seven classes. Of the responses, met the guideline, giving a sample proportion of . We estimate that approximately of the Year 8 students meet the guideline. This is an estimate based on a sample, not a census, so the true population proportion could reasonably be somewhat higher or lower. One student selected for the sample declined to respond, and all responses relied on students’ own self-reported estimates of their screen time.”

We do — improving a poor report together:

“We found that of Year 8 students meet the screen-time guideline. This proves most students use screens too much.”

(Flaws to draw out: no mention of sample size or method; “proves” and “found that” overclaim certainty; “most students use screens too much” is an unsupported value judgement — the data only measured whether a threshold was met, not whether screen use is a problem; no limitations stated at all.)

You do: Rewrite one sentence from the poor report above, fixing just the overclaiming language, while keeping it brief.

(Sample fix: “Our sample suggests that approximately of Year 8 students meet the recommended screen-time guideline, based on responses.“)

Activity 2 — Guided Practice: Naming and Explaining Limitations (14 min)

Pairs. Complete the table for our investigation.

Limitation	Likely effect on the result	Possible improvement
Self-reported data (students estimate their own screen time)	?	?
One selected student declined ( of responded)	?	?
Sample size ( of )	?	?
Data collected on one school day only	?	?
Ambiguous edge cases in the “recreational” definition	?	?

Circulating prompts:

Prompt	Purpose
Could this limitation push the estimate up, down, or just make it noisier — and can you tell which without more information?	Distinguishes genuine bias (a predictable direction) from ordinary variation (no predictable direction).
Is this limitation something the investigation could have avoided, or something inherent to surveying people honestly?	Separates fixable design flaws from unavoidable real-world constraints.
Would fixing this limitation require a bigger sample, a different method, or neither?	Connects limitations back to the “improvement” ideas already raised in Lesson 116.

(Sample answers: Self-reported data — students may over- or under-estimate their own screen time, possibly in either direction, or answer in a way they think sounds better (social desirability bias), pushing the estimate up; improve by using device screen-time reports where available. One decline — a small loss of data (41 of 42), unlikely to change the estimate much, but if that student’s habits differed systematically from responders, it could introduce a small, undetectable bias; improvement: note the response rate honestly. Sample size — a moderate sample gives a reasonably stable estimate but still carries some sampling variation (Lessons 111–112); improvement: survey more students per class. Single school day — a school day’s screen time may not represent an average day (e.g. a day with a major assignment due); improvement: sample across several different days. Ambiguous “recreational” cases — inconsistent classification by different students could add noise or a slight bias in either direction; improvement: give clearer examples in the survey wording.)

Activity 3 — Inquiry: Writing and Peer-reviewing Our Final Report (8 min)

Pairs, then swap.

Using Activity 1’s five-part structure and Activity 2’s limitations table, write your own complete report of the class investigation, in no more than sentences.

Swap with another pair and check against this list:

1. Does it state the question precisely?
2. Does it state the sample size and method?
3. Does it state the result as an estimate, not a fact?
4. Does it name at least one genuine limitation?
5. Is any sentence overclaiming?

Note one improvement for the report you review, and return it.

Checks for Understanding

(5 minutes — exit ticket, collected)

1. Name the five parts of a responsible statistical report.
2. Rewrite this overclaiming statement responsibly: “The data proves students don’t meet the guideline enough.”
3. State one limitation of our investigation and explain its likely effect.
4. Why should a report state the sample size, not just the result?
5. Reasoning. Explain why “our sample suggests approximately ” is more honest than ” of Year 8 students”, even though both are based on the same data.

Answers: 1. Question, method, result, uncertainty, limitations; 2. E.g. “We estimate that approximately of the Year 8 students do not meet the guideline, based on our sample.”; 3. Any from Activity 2’s table, with a correctly reasoned effect; 4. The sample size lets a reader judge how much sampling variation to expect, and therefore how much to trust the result — the same from and deserve very different levels of confidence; 5. The first correctly signals that the figure is an estimate drawn from a sample and could differ from the true population value, while the second states it as if it were a certain, exact fact about every one of the students.

Common Misconceptions

Misconception	How to pre-empt it
Reporting only the headline percentage, with no mention of sample size or method.	Insist all five report parts are present; use the peer-review checklist.
Using “proves” or “shows” for a sample-based estimate.	Ban these words explicitly in Activity 1; model “suggests” and “estimates” instead.
Treating “limitation” as an admission of failure rather than a mark of honest reporting.	Frame limitations as expected and professional — even large, well-funded studies report them.
Drawing an unsupported value judgement from a measured fact (e.g. “students use screens too much” from a guideline-met/not-met statistic).	Activity 1’s “We do” example, dissected explicitly.
Believing acknowledging uncertainty weakens a report.	Contrast: a report with no uncertainty acknowledged is less trustworthy to an informed reader, not more.

Enrichment — Competition-Style Problems

E1 (Kangaroo style). A report states: ” out of people surveyed prefer Option A, so exactly of the population prefers Option A.” Identify the specific overclaiming word and rewrite the sentence responsibly.

Answer

The word “exactly” overclaims — the survey establishes the sample proportion precisely (), not the population’s true value. Rewrite: ” out of surveyed prefer Option A, so we estimate that approximately of the population prefers Option A.”

E2 (AMC Junior style). Two reports on the same population state: Report 1 (n=): ” support the proposal.” Report 2 (n=): ” support the proposal.” A reader concludes support has “clearly grown” from Report 1 to Report 2. Explain the flaw.

Answer

The two reports are not two points in time — they are two different samples, of very different sizes. Report 1’s small sample () could easily land percentage points away from Report 2’s more reliable estimate purely by ordinary sampling variation, with no real change in support at all.

E3 (Challenge). A student writes: “We surveyed students, so our estimate of students is definitely correct to the nearest person.” Explain what is wrong with this claim, referencing the ideas of sample size and estimation from this block.

Answer

No sample-based estimate — regardless of size — can be claimed “definitely correct to the nearest person”; only a full census of all students could establish the exact count. A larger sample (like versus ) makes the estimate more reliable, but never removes uncertainty altogether, exactly as established in Lessons 111–112 and 116.

E4 (Investigation). Write two versions of the same one-sentence finding from our investigation: one that would pass a strict “no overclaiming” check, and one that would fail it. Explain the exact wording difference that separates them.

Answer

Student’s own; e.g. Pass: “Based on our sample of students, we estimate that approximately of Year 8 students meet the screen-time guideline.” Fail: ” of Year 8 students meet the screen-time guideline.” The difference is the explicit sourcing (“based on our sample”) and hedging (“we estimate”, “approximately”) versus a bare, unqualified statement of the figure as fact.

Homework

1. List the five parts of a responsible statistical report.
2. Rewrite responsibly: “The survey proves that of customers want the new flavour.”
3. Name two limitations a report about self-reported exercise habits should acknowledge.
4. Explain, in one sentence, why “estimate” is a more honest word than “fact” when describing a sample-based result.
5. A report states a result but never mentions the sample size. Explain what a reader cannot judge as a result.
6. Rewrite this statement to correctly acknowledge uncertainty: ” Year 8 students meet the screen-time guideline.”
7. Reasoning. Explain why two honest reports of the same investigation, written by two different students, might use slightly different numbers (e.g. “about ” versus “about ”) without either being wrong.
8. Reasoning. A classmate says acknowledging limitations makes an investigation “look bad.” Explain why the opposite is closer to the truth.
9. Challenge. Using the five-part structure from this lesson, write a complete report (in your own words, – sentences) of a different finding: that Class D had the highest class-level proportion (, ) of any class in the sample. Your report must include a limitation explaining why this single class’s high figure should not be over-interpreted.

Answers: Q1 — question, method, result, uncertainty, limitations. Q2 — e.g. “Our survey suggests that approximately of customers surveyed prefer the new flavour.” Q3 — e.g. participants may over- or under-report their own activity; the sample may not represent everyone (e.g. only active volunteers respond). Q4 — “estimate” correctly signals the figure is a best approximation from incomplete data, while “fact” wrongly implies certainty about the whole population. Q5 — a reader cannot judge how much sampling variation to expect, and therefore cannot judge how much to trust the reported figure. Q6 — e.g. “We estimate that approximately of the Year 8 students meet the screen-time guideline, based on a sample of responses.” Q7 — both are reasonable roundings of the same underlying estimate (), and reasonable people can round or phrase an approximate figure slightly differently without either being incorrect, as long as both are clearly presented as estimates. Q8 — acknowledging limitations is a mark of a careful, trustworthy investigation; hiding them does not make the underlying data any more reliable, it only misleads the reader into false confidence. Q9 — student’s own; must state the specific finding ( from Class D, ), the method (stratified sample, per class), and explicitly note the limitation that with only responses, ordinary sampling variation (Lessons 111–112) could easily produce a result this high even if Class D’s true rate were no different from any other class.