Analysing: Evaluating Data and Conclusions¶
Syllabus mapping
Working Scientifically outcome — Analysing (part 2 of 2). Covers distinguishing accuracy/precision/reliability/validity, identifying genuine limitations in a method, suggesting targeted improvements, and drawing a conclusion that answers the original hypothesis. See Trends and Relationships for the first half of Analysing.
Outcome codes: CH-11WS-05 (Year 11) and CH-12WS-05 (Year 12) — Analysing data and information. Same outcome wording in both years, with a separate code for each. Wording on this page is paraphrased for teaching use — check the official syllabus before treating any line as verbatim NESA text.
You need to know: four words — accuracy, precision, reliability, validity — that sound interchangeable in everyday speech and are absolutely not interchangeable in a Stage 6 evaluation, plus how to write a conclusion and an improvement that actually says something specific.
Core¶
Accuracy, precision, reliability, validity¶
These four are the single most commonly confused set of terms in Working Scientifically, and "Evaluate" questions frequently hinge on picking the right one.
| Term | What it actually means |
|---|---|
| Accuracy | How close a measured/calculated value is to the true or accepted value. |
| Precision | How close repeated measurements are to each other — regardless of whether they're close to the true value. |
| Reliability | Whether repeating the method (by you, or by someone else) would produce consistent results. |
| Validity | Whether the method actually tests what it claims to test — controlled variables genuinely held constant, no confounding factor sneaking in. |
Worked example — telling them apart
A student's five calorimetry results for the neutralisation of hydrochloric acid all cluster tightly around \(-45\ \text{kJ mol}^{-1}\) (precise), but the accepted value is \(-57\ \text{kJ mol}^{-1}\) — heat was escaping from the uncovered glass beaker every time (inaccurate, specifically because of a systematic error). The method, if repeated exactly as performed, would keep giving the same wrong answer (still reliable — reliability doesn't require being right, just being consistent). If the student had also used a different volume of acid in some trials, the method would have a validity problem too, independent of the heat loss.
It's entirely possible to be precise, reliable, and invalid or inaccurate all at once — which is exactly why an evaluation needs to check all four separately, not treat "the results were consistent" as proof the experiment was good.
Identifying genuine limitations¶
A limitation names a specific weakness in the method and explains how it affected the result — not a vague, generic phrase.
| Weak (avoid) | Strong (specific) |
|---|---|
| "Human error" | "Judging when the cross had 'disappeared' was subjective and varied between trials, giving a spread of about ±0.5 s in the times at each temperature." |
| "Equipment wasn't accurate enough" | "The 10 mL measuring cylinder used for the acid has an uncertainty of about ±0.2 mL — about 4% of the 5 mL measured — which was the largest source of uncertainty in the concentration." |
| "Heat was lost" | "The glass beaker had no lid or insulation, so some heat from the reaction was lost to the surroundings, making the measured temperature rise — and so \(\Delta H\) — smaller than the true value." |
The pattern: name the specific source → explain the mechanism → connect it to the actual effect on the result (including which direction it pushed the result, if you can tell).
Suggesting improvements that match the limitation¶
An improvement should fix the specific limitation just identified, not restate "use better equipment" as a generic close-out line. If the limitation was judging the cross by eye, the improvement is a light sensor that records when the light drops below a set level — not "be more careful." If the limitation was heat loss, the improvement is a polystyrene cup with a lid — not "do more trials", which would just give the same wrong answer more consistently.
Drawing a conclusion¶
A conclusion should explicitly answer the hypothesis stated back in Questioning and Predicting — supported, not supported, or partially supported — and say why, referencing the actual result.
Worked example — a complete conclusion
"The hypothesis — that increasing the temperature increases the rate of the reaction between sodium thiosulfate and hydrochloric acid, because a greater fraction of collisions have at least the activation energy — was supported. The time for the cross to disappear decreased from \(68 \pm 2\) s at 20 °C to \(9.5 \pm 0.6\) s at 50 °C, and a graph of rate (\(\frac{1}{t}\)) against temperature increased more and more steeply (see Trends and Relationships). The rate roughly doubled for each 10 °C rise, consistent with the prediction."
Notice what makes this a strong conclusion rather than a restatement of the hypothesis: it cites actual numbers, references the graph's shape as evidence, and checks the specific prediction ("roughly doubled per 10 °C") — tying together every earlier stage of the investigation.
Advanced
A result that doesn't support the hypothesis is not a failed evaluation. If a hypothesis isn't supported, the strongest response identifies why, distinguishing between "the chemistry is different from what I assumed" and "a limitation in the method hid the real relationship." Concluding "the hypothesis was not supported, most likely due to [specific limitation], rather than because the underlying relationship doesn't hold" is a sophisticated Band 6-level evaluation — it shows you can separate the chemistry from the execution of the experiment.
The boxes below are optional, tertiary-level statistical tools for a more rigorous evaluation — beyond this syllabus, but useful in a depth study. See also the standard error and t-test boxes on Trends and Relationships, which these build on.
Extension — Standard deviation and the 68–95–99.7 rule
Beyond the syllabus for this course — won't appear in the HSC, included for interest / depth study inspiration.
📎 Depth study idea
For data whose random error is roughly symmetric, standard deviation lets you judge how unusual a particular reading is:
- About 68% of readings fall within \(\pm 1\sigma\) of the mean
- About 95% fall within \(\pm 2\sigma\)
- About 99.7% fall within \(\pm 3\sigma\)
This turns "is this reading an anomaly?" (see Conducting) into a checkable statement rather than a gut feeling.
Worked example
Five disappearing-cross times at 30 °C: mean \(\bar{t} = 35.1\) s, \(\sigma \approx 0.32\) s. A sixth trial reads \(41.0\) s — how unusual is that?
That reading is about \(18\sigma\) from the mean — far outside the \(\pm 3\sigma\) range that contains 99.7% of genuine random variation. Strong grounds to treat it as an anomaly worth investigating, not a legitimate result.
Extension — Confidence intervals: how sure, precisely?
Beyond the syllabus for this course — won't appear in the HSC, included for interest / depth study inspiration.
📎 Depth study idea
A confidence interval combines the standard error with a critical t-value (see Trends and Relationships) to give a range you can attach an actual confidence level to:
Worked example
Using the five calorimetry results from Trends and Relationships: \(\bar{x} = -54.0\), \(SE = 0.71\), \(df = 4\), \(t_{crit}(95\%) = 2.776\).
So: "We are 95% confident the true value from this method lies between −56.0 and −52.0 kJ mol⁻¹." Since the accepted −57 kJ mol⁻¹ is outside that range, the method has a systematic error.
Extension — Type A and Type B uncertainty
Beyond the syllabus for this course — won't appear in the HSC, included for interest / depth study inspiration.
📎 Depth study idea
Professional labs report uncertainty using Type A and Type B evaluation (from the international Guide to the Expression of Uncertainty in Measurement): Type A comes from the statistical spread of repeated measurements, while Type B comes from everything else — the tolerance printed on a pipette or volumetric flask, a balance's calibration certificate, the purity stated on a chemical's label. A depth study that explicitly separates its uncertainties into Type A and Type B is a genuinely university-level treatment of this section's content.
Video/visual resources¶
- 🎥 Khan Academy — TODO: source an accuracy vs precision explainer, ideally covering reliability and validity too (the dartboard analogy is the standard way this is taught).
Check yourself¶
-
A group's five masses of dried precipitate are 1.52 g, 2.95 g, 1.50 g, 1.49 g, 1.51 g. What does the 2.95 g result suggest about that particular trial, and what does it not tell you about accuracy?
Answer
The one very different value suggests something went wrong on that trial (perhaps the precipitate wasn't fully dried, or the filter paper wasn't subtracted) — worth flagging as an anomaly (see Conducting). The other four are tightly clustered, so they're precise. But that doesn't tell you they're accurate: even the ~1.5 g values could all be wrong in the same direction if there's a systematic error (e.g. some precipitate passing through the filter paper every time).
-
Rewrite this limitation to make it specific: "There was human error in reading the volumes, which affected the results."
Answer
E.g. "Reading the measuring cylinder from above rather than at eye level with the bottom of the meniscus (parallax error) could make each volume reading slightly too high, by up to about 0.5 mL — around 5% of the 10 mL measured." — names the specific mechanism, its direction and its likely size.
-
A student's conclusion reads: "My results proved my hypothesis was correct." Identify two things wrong with this as a scientific conclusion.
Answer
(1) Experiments support a hypothesis — they don't "prove" it; it stays open to being disproven by future evidence. (2) It doesn't reference any actual data, graph, or comparison with a prediction or accepted value — a strong conclusion shows how the results support the hypothesis.
-
(Stretch — uses the Extension boxes above.) A data set has mean \(50.0\) and \(\sigma = 2.0\). Using the 68–95–99.7 rule, state the range within which about 95% of readings should fall, and whether a new reading of \(53.5\) would be unusual.
Answer
95% should fall within \(\pm 2\sigma\): between \(46.0\) and \(54.0\). A reading of \(53.5\) (\(1.75\sigma\) from the mean) is inside that range, so it's not unusual — consistent with normal random variation.