How Do You Find a Suitable Secondary Dataset for HSC Science?

Learn how to choose a secondary dataset for your HSC Science investigation by checking its source, variables, units, missing data, sample coverage, and licence. Includes practical examples, a selection checklist, and worked questions with solutions.

You find a spreadsheet containing 12,000 measurements from NSW rivers. Your research question is: Is warmer water associated with lower dissolved oxygen levels? The spreadsheet has columns for temperature and dissolved oxygen, so it looks perfect.

But what if the temperatures were measured at different locations from the oxygen readings? You might have thousands of measurements without a single valid comparison.

To find a suitable secondary dataset for HSC Science, check six things: provenance, variables, units, missingness, sample coverage, and licence. A smaller dataset that passes these checks is often more useful than a huge one that doesn’t.

01Start with the question your dataset must answer

A secondary dataset contains measurements or observations collected by someone else that you can analyse for your own investigation.

You might find one in a government monitoring archive, a university research repository, or a published scientific study.

The important word is measurements. A report saying that Sydney summers are getting hotter is useful background information. A downloadable table of temperature observations from identified weather stations gives you data you can analyse yourself.

Before searching, write your investigation question so that you can identify the measurements required.

For example:

Too broad: How does temperature affect water quality?

More useful: At a monitored freshwater site, is higher water temperature associated with lower dissolved oxygen concentration during summer?

The second question tells you what to look for:

  • Water temperature, measured in degrees Celsius.
  • Dissolved oxygen concentration, measured in milligrams per litre.
  • Measurements taken at the same site, preferably at the same time and depth.
  • Dates covering the summer period.
  • Enough observations to examine a relationship.

You also need to know what your question can establish. Monitoring data may show an association between temperature and oxygen concentration, but it cannot automatically prove that temperature caused the difference. Water movement, biological activity, and other conditions also affect dissolved oxygen.

Why matching observations matters

Imagine a thermometer and an oxygen sensor placed next to each other in a creek. Each time you take a reading, you record both values.

Now imagine measuring the temperature in one creek and oxygen concentration in another, then pairing the numbers because the dates match.

Would those pairs answer the same question?

No. The second arrangement mixes differences between creeks with differences in water temperature.

In data analysis, the unit of observation is what one row represents: perhaps one water sample, one monitoring site on a particular day, or one hour of measurements. Your variables need to belong to compatible observations.

02Find candidate datasets in reliable places

Searching for a topic is less effective than searching for the variables you need.

Instead of searching for “water pollution in NSW”, try phrases such as:

  • NSW dissolved oxygen water temperature monitoring data
  • river water quality CSV monitoring station
  • daily rainfall observations NSW station

Adding terms such as dataset, CSV, monitoring, or download can help you find measurements rather than general articles.

Two useful starting points are:

SourceUseful for
NSW SEED environmental data portalDiscovering NSW datasets relating to waterways, air quality, land, biodiversity, and environmental monitoring.
Bureau of Meteorology Climate Data OnlineFinding historical rainfall, temperature, and other climate observations from weather stations.

A trustworthy portal is a good starting point, not automatic proof that every dataset is suitable.

For example, the Bureau of Meteorology explains that weather records can contain missing observations, quality-control flags, and changes in instruments or observation practices. Some station histories contain substantial gaps.

Similarly, SEED can direct you to datasets held by different organisations. The portal helping you discover a file may not be the organisation that collected its measurements.

You need to inspect the individual dataset.

Open the metadata before downloading everything

Metadata means information about the dataset itself.

Look for a description, data dictionary, methods document, or data quality statement. You want to establish:

  • Who collected or maintains the measurements?
  • How were they collected?
  • Where and when were they collected?
  • What does each column mean?
  • Have the observations been checked, corrected, averaged, or estimated?
  • What conditions apply to downloading, modifying, and republishing them?

A CSV file without those details can be difficult to interpret reliably, even when every cell contains a number.

03Apply the six suitability checks

Use this table as a first screening tool.

CheckWhat to establish
1. ProvenanceThe original data custodian, collection method, measurement dates, and any processing are identifiable.
2. VariablesThe dataset measures the quantities required by your question, with observations that can be matched appropriately.
3. UnitsUnits, measurement definitions, and time intervals are stated and compatible.
4. MissingnessMissing values and quality flags can be identified, and enough usable observations remain.
5. Sample coverageThe measurements cover the relevant places, times, conditions, and range of values.
6. LicenceThe terms permit your intended use, including any publication or adaptation of the data.

These aren’t six equally important marks to award a dataset. They’re six ways a dataset can become unusable.

A missing citation may be fixable by locating the original source. Missing measurements of your main variable usually aren’t.

Check 1: Can you trace where the measurements came from?

This is provenance: the origin and history of the data.

A useful dataset should identify the organisation responsible for it and provide enough information about how observations were obtained.

Suppose a website offers a graph of river oxygen concentrations but doesn’t identify the monitoring stations, measurement methods, or original provider.

You might be able to describe the graph, but you cannot confidently assess whether the measurements are comparable.

Try to locate the original dataset and its metadata.

Also distinguish between the date a webpage was updated and the dates measurements were collected. A dataset updated yesterday might still contain observations from ten years ago.

Check 2: Are the variables actually what you need?

Suppose you’re investigating whether warmer water has lower dissolved oxygen concentration.

A dataset containing air temperature and dissolved oxygen does not directly provide water temperature.

Air temperature may help explain changes in water temperature, but the two quantities are not interchangeable.

The same problem appears in Physics. Energy generated by a solar panel, measured in kilowatt-hours, is not the same quantity as its instantaneous power output, measured in kilowatts.

Ask:

  • Is each variable directly measured, calculated, or estimated?
  • Do both variables refer to the same location and relevant time?
  • Does the dataset contain other measurements needed to interpret the relationship?

If the key variable is absent, decide whether a justified calculation is possible. Don’t simply rename a convenient column.

Check 3: Are the units and measurement definitions compatible?

Consider these two oxygen measurements:

  • Dissolved oxygen concentration: \(8.0\ \mathrm{mg\,L^{-1}}\)
  • Dissolved oxygen saturation: \(85\%\)

They describe related properties, but they are not the same measurement.

Concentration reports the mass of dissolved oxygen per unit volume. Percentage saturation describes how close the water is to its equilibrium oxygen concentration under specified conditions.

Converting between them requires additional information, including temperature and the conditions affecting oxygen solubility. You cannot compare the two numbers directly.

Time intervals matter just as much.

A daily rainfall total, a rainfall rate in millimetres per hour, and a monthly rainfall average do not mean the same thing.

Check the data dictionary rather than guessing from a column heading.

Check 4: What is missing, and why?

A blank cell may indicate an instrument failure, an uncollected sample, or a value excluded during quality control.

Don’t automatically replace missing measurements with zero.

A recorded oxygen concentration of \(0\ \mathrm{mg\,L^{-1}}\) would describe an anoxic sample. A missing oxygen measurement tells you nothing about the concentration.

Some datasets use codes such as NA, -999, or BDL (below detection limit). Their meanings must come from the dataset documentation.

Missingness becomes especially important when it follows a pattern.

For example, if a river sensor stops recording during floods, the missing measurements may be concentrated precisely when water conditions are most unusual.

Deleting those rows could make the remaining data look more stable than the river really is.

Check 5: Does the sample cover the conditions in your question?

A dataset can contain thousands of valid measurements and still have poor coverage.

Suppose your question concerns temperature changes across an entire year, but your downloaded data cover only January and February.

That dataset may be useful for a summer investigation, but it cannot establish the full annual relationship.

Inspect:

  • Time: Which dates and seasons are included?
  • Place: Which sites are represented?
  • Frequency: Are measurements hourly, daily, monthly, or irregular?
  • Conditions: Were unusual events, high values, and low values captured?
  • Comparability: Did sites, methods, or instruments change?

The total number of rows is not the same as the number of useful observations.

Check 6: Can you legally use and share the data?

Being able to download a spreadsheet doesn’t automatically mean you can republish its contents or graphs.

Look for the dataset’s licence.

For example, a Creative Commons Attribution 4.0 (CC BY 4.0) licence generally permits reuse and adaptation, provided you give appropriate credit, link to the licence, and indicate changes where required.

Other datasets may have additional restrictions, approval requirements, or conditions concerning sensitive information.

Check the terms attached to the actual dataset, not just a general statement on the hosting website.

For your investigation record, save the source URL, original custodian, dataset title, licence, version or download date, and any required attribution.

04Test a small sample before committing

You don’t need to process an entire archive to find its basic weaknesses.

Download a small, relevant section and inspect the actual rows.

Worked example: Which water-quality dataset is usable?

You want to investigate whether higher water temperature is associated with lower dissolved oxygen concentration at one NSW creek monitoring site during summer.

Two hypothetical datasets are available. All details and numbers below are invented to demonstrate the selection method.

Dataset A: Contains 140 water-temperature measurements and a separate table of monthly oxygen averages from several other sites. There is no way to match the measurements by individual sample.

Dataset B: Contains six scheduled visits to the same site, with paired water-temperature and dissolved oxygen measurements at 09:00, from the same depth of \(0.5\ \mathrm{m}\). Its source, units, measurement methods, and permission for reuse are documented.

Here is Dataset B:

DateWater temperature (\(^{\circ}\mathrm{C}\))Dissolved oxygen (\(\mathrm{mg\,L^{-1}}\))
5 Jan198.9
12 Jan218.4
19 Jan23Missing
26 Jan247.9
2 Feb208.6
9 Feb228.2

Which dataset is more appropriate, and how much usable information does it contain?

Step 1

You need matched temperature and oxygen measurements from the same creek, not unrelated measurements from different sites.

Dataset A has more records but lacks the matching observations required.

Dataset B is the stronger candidate.

Step 2

Dataset B has six scheduled observations, but one dissolved oxygen reading is missing.

There are five complete pairs.

Step 3

Let \(C\) represent the percentage of scheduled observations containing both variables.

\[ \begin{aligned} C &= \frac{5}{6}\times100\%\\ &=83.3\% \end{aligned} \]

The dataset has approximately \(83\%\) completeness for the required pairs.

Step 4

Among the five complete observations, oxygen concentration tends to be lower at higher temperatures.

For example, at \(19\,^{\circ}\mathrm{C}\), the recorded concentration is \(8.9\ \mathrm{mg\,L^{-1}}\), while at \(24\,^{\circ}\mathrm{C}\), it is \(7.9\ \mathrm{mg\,L^{-1}}\).

The observed difference is:

\[ \begin{aligned} \Delta D &= 7.9-8.9\\ &=-1.0\ \mathrm{mg\,L^{-1}} \end{aligned} \]

Here, \(\Delta D\) is the change in dissolved oxygen concentration between those observations.

This is consistent with a negative association. It does not prove that temperature alone caused the change.

Step 5

Dataset B is more suitable for an exploratory investigation at this site during the sampled summer period.

However, five observations provide limited evidence, and the missing reading should be acknowledged. The dataset cannot support claims about every NSW creek or every season.

The lesson isn’t to prefer small datasets. It’s to prefer measurements that actually answer your question, while being clear about what they cannot establish.

Worked example: Can you compare solar irradiance with panel output?

A student wants to investigate whether greater solar irradiance is associated with higher average electrical power output from the same rooftop solar installation.

The archive contains half-hourly solar irradiance measurements and the electrical energy generated during each corresponding half-hour interval.

The following figures are hypothetical.

IntervalMean irradiance (\(\mathrm{W\,m^{-2}}\))Energy generated (kWh)
10:00-10:306000.45
10:30-11:008000.65
11:00-11:30Missing0.70
11:30-12:0010000.85

The metadata confirms that irradiance is measured in the plane of the panels, the energy measurements cover the stated intervals, and the equipment configuration is unchanged. The original provider and reuse terms are documented.

Can this dataset answer the question?

Step 1

Irradiance is incoming solar power per unit area, measured in watts per square metre (\(\mathrm{W\,m^{-2}}\)).

The electrical meter reports energy generated during an interval, measured in kilowatt-hours (kWh).

The question asks about average electrical power, not energy.

Step 2

Average power is:

\[ P=\frac{E}{\Delta t} \]

where:

  • \(P\) is average electrical power, in kilowatts (kW).
  • \(E\) is electrical energy generated, in kilowatt-hours (kWh).
  • \(\Delta t\) is the measurement interval, in hours (h).

Each interval lasts 30 minutes, or \(0.5\ \mathrm{h}\).

For the first interval:

\[ \begin{aligned} P &= \frac{0.45\ \mathrm{kWh}}{0.5\ \mathrm{h}}\\ &=0.90\ \mathrm{kW} \end{aligned} \]

For the second interval:

\[ \begin{aligned} P &= \frac{0.65\ \mathrm{kWh}}{0.5\ \mathrm{h}}\\ &=1.30\ \mathrm{kW} \end{aligned} \]

For the final interval:

\[ \begin{aligned} P &= \frac{0.85\ \mathrm{kWh}}{0.5\ \mathrm{h}}\\ &=1.70\ \mathrm{kW} \end{aligned} \]

These are the average electrical power outputs during the respective half-hour intervals.

Step 3

One interval is missing an irradiance measurement.

Three of the four intervals contain both required values.

\[ \begin{aligned} C &= \frac{3}{4}\times100\%\\ &=75\% \end{aligned} \]

The completeness is \(75\%\). The missing interval cannot be used for a paired comparison without additional justified information.

Step 4

The three complete observations show higher average output power alongside higher mean irradiance.

The units and time intervals are compatible after converting energy into average power.

However, the dataset contains only three usable intervals. It does not isolate other influences such as panel temperature, shading, or inverter behaviour.

The defensible decision is to retain this dataset as a possible source, then investigate whether a longer period with adequate coverage is available.

05Decide whether to use, revise, or reject the dataset

After inspecting the sample, there are three reasonable outcomes.

Use it

Choose the dataset when its measurements, definitions, coverage, and reuse conditions support your question.

Record any limitations before analysing it.

Revise your question

Sometimes the data are reliable but cover a narrower situation than you originally intended.

For example:

Original question: How does dissolved oxygen vary with water temperature throughout NSW?

Revised question: What association between water temperature and dissolved oxygen is observed at this monitored creek during summer?

That’s a legitimate adjustment when the narrower question matches the available evidence.

Don’t broaden your conclusions again after finishing the analysis.

Reject it and continue searching

Reject a candidate when a fundamental problem prevents the investigation:

  • The origin or measurement method cannot be established.
  • The necessary variable is absent.
  • Measurements cannot be paired or compared meaningfully.
  • Critical conditions are missing.
  • The intended reuse is not permitted, and permission cannot be obtained.

You may be able to resolve some problems by finding additional metadata or another compatible dataset. Others require choosing a different source.

A practical dataset selection checklist

Before settling on a file, work through these actions:

  • [ ] Write the question with its required variables, location, and time period.
  • [ ] Find the original custodian and measurement method.
  • [ ] Confirm units, timestamps, site identifiers, and relevant measurement definitions.
  • [ ] Download a sample and inspect missing values and quality flags.
  • [ ] Count usable observations for the conditions you want to compare.
  • [ ] Check geographic, seasonal, and measurement coverage.
  • [ ] Read the specific licence and any access conditions.
  • [ ] Record the source, version, download date, and reasons for accepting or rejecting it.

A useful final note might be:

Dataset selected because it provides paired water-temperature and dissolved oxygen measurements from the same site and depth. Five of six observations are complete. Its principal limitations are the small sample, summer-only coverage, and one missing oxygen measurement.

That’s much stronger than writing, “I chose this dataset because it was from a reliable website.”

06What does NESA require?

NESA’s science syllabuses include opportunities for students to work with secondary-source information and data. Dataset selection is part of applying Working Scientifically skills, not simply finding a spreadsheet.

The applicable syllabus depends on your cohort.

As at 10 November 2026:

Earlier cohorts continue under the relevant 2017 syllabuses.

NESA establishes syllabus and assessment requirements, while schools set their assessment tasks within the applicable rules. Check your school’s task notification for requirements such as permitted data sources, source approval, referencing, and submission format.

The six checks in this article are a practical selection method, not a separate NESA-mandated marking rubric.

If you’re still deciding how your dataset fits into an investigation, see What Is a Depth Study in HSC Science?. For the broader skills involved in processing and evaluating evidence, see What Is Working Scientifically in HSC Physics and Chemistry?.

07Questions and solutions

The following questions use invented datasets. Assume the sources are accessible and their reuse is permitted unless a question states otherwise.

The difficulty increases from basic source selection to problems where apparently convincing data can support the wrong conclusion.

Question 1

A student investigates whether the pH of creek water differs between an upstream site and a downstream site on the same day.

Two datasets are available:

Dataset A: Six sampling days, with upstream and downstream pH measured on each day using the same calibrated probe and sampling procedure. All readings are complete.

Dataset B: Four hundred downstream pH measurements collected over several months. No upstream measurements are available.

Which dataset is more suitable? Explain two reasons for your choice.

Solution 1

Dataset A is more suitable because it provides paired measurements from both locations on the same six days.

The investigation requires a comparison between upstream and downstream pH. Dataset A measures both quantities under a consistent procedure, allowing the student to examine differences for each sampling day.

Dataset B contains more observations, but it cannot establish the difference between upstream and downstream pH because it has no upstream measurements.

The tempting mistake is to assume that 400 readings must be stronger evidence than six pairs. The larger sample is irrelevant if it lacks one of the required comparisons.

Dataset A still has limited sample coverage, so any conclusion should be restricted to the sampled conditions.

Question 2

A monitoring station records weekly river turbidity and whether heavy rainfall occurred during the preceding 24 hours.

Turbidity describes how much suspended material scatters light in the water. The station uses consistent units and measurement methods.

Over 16 scheduled weeks:

  • Six weeks are classified as wet, with at least \(20\ \mathrm{mm}\) of rain.
  • Ten weeks are classified as dry.
  • Turbidity is missing for five of the six wet weeks.
  • Turbidity is missing for one of the ten dry weeks.

The station’s metadata indicates that its equipment sometimes fails during high-flow conditions.

A student removes the missing rows, compares the remaining readings, and concludes that heavy rainfall has little relationship with turbidity.

Calculate the overall percentage of complete observations and the percentage for each rainfall category. Explain whether the conclusion is justified and identify a better next step.

Solution 2

The conclusion is not justified because the missing turbidity measurements are concentrated in the wet conditions the student wants to investigate.

There are 16 scheduled observations and six missing turbidity values.

The overall completeness is:

\[ \begin{aligned} C &= \frac{16-6}{16}\times100\%\\ &=62.5\% \end{aligned} \]

For wet weeks, only one of six observations is complete:

\[ \begin{aligned} C_{\mathrm{wet}} &=\frac{1}{6}\times100\%\\ &\approx16.7\% \end{aligned} \]

For dry weeks, nine of ten observations are complete:

\[ \begin{aligned} C_{\mathrm{dry}} &=\frac{9}{10}\times100\%\\ &=90\% \end{aligned} \]

Here, each \(C\) represents the percentage of observations with usable turbidity measurements for the specified group.

The overall completeness of \(62.5\%\) hides a serious imbalance: almost all dry observations are available, but only one wet observation remains.

Equipment failures during high flow may also be connected to unusually high turbidity. If so, deleting those observations systematically removes important conditions rather than a random selection of weeks.

The student should look for a monitoring record with reliable turbidity measurements during rainfall events, or investigate whether the missing measurements can be recovered from the provider.

The trap is treating every missing observation as equally harmless. The pattern of missingness can matter more than the overall percentage.

Question 3

A Physics student investigates whether a rooftop solar system produces more average electrical power during hours with greater mean solar irradiance.

The solar system’s electricity meter reports cumulative energy generated:

TimeCumulative energy (kWh)
10:0012.4
11:0013.5
12:0014.8

Two irradiance datasets are available for the same location.

Dataset X reports instantaneous irradiance:

TimeIrradiance (\(\mathrm{W\,m^{-2}}\))
10:00650
11:00800

Dataset Y reports mean irradiance over complete one-hour intervals:

IntervalMean irradiance (\(\mathrm{W\,m^{-2}}\))
10:00-11:00650
11:00-12:00800

Both irradiance datasets are properly documented and use the same plane of measurement as the panels.

Calculate the average electrical power output for each hour. Which irradiance dataset is more suitable for the question, and why would pairing the raw electricity meter readings with the instantaneous irradiance values be misleading?

Solution 3

The average electrical powers are \(1.1\ \mathrm{kW}\) and \(1.3\ \mathrm{kW}\), and Dataset Y is more suitable because its irradiance measurements cover the same complete hourly intervals as the calculated power values.

The meter reports cumulative energy, so the energy generated during each hour must be calculated from differences between successive readings.

For 10:00-11:00:

\[ \begin{aligned} E_1 &=13.5-12.4\\ &=1.1\ \mathrm{kWh} \end{aligned} \]

For 11:00-12:00:

\[ \begin{aligned} E_2 &=14.8-13.5\\ &=1.3\ \mathrm{kWh} \end{aligned} \]

Using average power \(P=E/\Delta t\), where \(E\) is interval energy and \(\Delta t\) is interval duration:

\[ \begin{aligned} P_1 &=\frac{1.1\ \mathrm{kWh}}{1\ \mathrm{h}}\\ &=1.1\ \mathrm{kW}\\[4pt] P_2 &=\frac{1.3\ \mathrm{kWh}}{1\ \mathrm{h}}\\ &=1.3\ \mathrm{kW} \end{aligned} \]

Dataset Y gives mean irradiance over exactly those intervals, allowing the student to compare hourly mean irradiance with hourly average electrical power.

Dataset X gives instantaneous readings. Irradiance could fluctuate significantly between those moments, so an instantaneous value is not necessarily representative of the entire preceding or following hour.

The cumulative meter readings are also not the energy produced during individual hours. The \(12.4\ \mathrm{kWh}\) at 10:00 includes energy generated before the investigation period.

The student would make two errors by pairing the raw tables directly: comparing cumulative energy with power-related measurements and treating instantaneous irradiance as an hourly mean.

Even with Dataset Y, two hourly comparisons cannot establish a general relationship or isolate all influences on the system.

Question 4

A Chemistry student investigates whether the concentration of a dissolved contaminant in a lake decreased between 2019 and 2025.

The same compound is measured in both years, in \(\mathrm{mg\,L^{-1}}\), at the same location and season.

The archive contains the following information:

2019:

  • Twenty samples collected.
  • Eighteen samples reported as \(0.10\ \mathrm{mg\,L^{-1}}\).
  • Two samples reported as below the detection limit of \(0.02\ \mathrm{mg\,L^{-1}}\).

2025:

  • Twenty samples collected.
  • Every result appears as 0 in the downloaded spreadsheet.
  • The metadata explains that 0 means below the reporting limit of \(0.20\ \mathrm{mg\,L^{-1}}\), not a measured concentration of zero.

A student claims that the contaminant was completely eliminated by 2025.

Can the dataset establish that concentrations decreased? Explain how the changing reporting limit affects the conclusion, give two possible interpretations of the 2025 results, and state what comparison remains defensible.

Solution 4

No. The dataset cannot establish that concentrations decreased, and the claim of complete elimination is unsupported.

The main problem is that the 2025 reporting limit is ten times higher than the 2019 detection limit:

\[ \frac{0.20}{0.02}=10 \]

Both limits are expressed in \(\mathrm{mg\,L^{-1}}\), so the ratio is dimensionless.

A reported 2025 value of 0 represents an unknown concentration below \(0.20\ \mathrm{mg\,L^{-1}}\). It is not a measured concentration of \(0\ \mathrm{mg\,L^{-1}}\).

Two possible situations fit the 2025 observations:

  • The true concentrations could all be approximately \(0.01\ \mathrm{mg\,L^{-1}}\), indicating lower values than the \(0.10\ \mathrm{mg\,L^{-1}}\) measurements in most 2019 samples.
  • The true concentrations could all be approximately \(0.15\ \mathrm{mg\,L^{-1}}\), indicating higher values than those measurements.

Both are consistent with results below the 2025 reporting limit.

A defensible common-threshold comparison is possible at \(0.20\ \mathrm{mg\,L^{-1}}\).

In 2019, all 20 samples were below this threshold, including the 18 reported at \(0.10\ \mathrm{mg\,L^{-1}}\).

In 2025, all 20 were also reported below this threshold.

Therefore, both years had \(100\%\) of samples below \(0.20\ \mathrm{mg\,L^{-1}}\), but this does not reveal whether their average concentrations differed.

The student should investigate whether archived measurements with a lower reporting limit or a comparable analytical method are available.

The tempting mistake is to treat a reporting code as a physical measurement. Once the reporting limit changes, the apparent reduction may reflect the measurement system rather than the lake.

Question 5

Two freshwater lakes, Fern Lake and Ridge Lake, are monitored during cooler and warmer conditions.

A student asks:

At each lake, is dissolved oxygen concentration lower during observations at \(20\,^{\circ}\mathrm{C}\) than during observations at \(16\,^{\circ}\mathrm{C}\)?

The archive contains the following summary of valid measurements:

LakeWater temperatureValid observationsMean dissolved oxygen
Fern\(16\,^{\circ}\mathrm{C}\)8\(7.0\ \mathrm{mg\,L^{-1}}\)
Fern\(20\,^{\circ}\mathrm{C}\)2\(6.0\ \mathrm{mg\,L^{-1}}\)
Ridge\(16\,^{\circ}\mathrm{C}\)2\(11.0\ \mathrm{mg\,L^{-1}}\)
Ridge\(20\,^{\circ}\mathrm{C}\)8\(10.0\ \mathrm{mg\,L^{-1}}\)

All values are hypothetical. The methods, depths, units, and measurement periods are documented and comparable within each lake.

The original monitoring schedule reveals one further detail: six additional warm-condition visits occurred at Fern Lake, but their oxygen measurements are missing. The reason is not documented.

A student pools all valid observations, ignoring lake identity, and claims that warmer water is associated with higher dissolved oxygen concentration.

Another student compares the two temperatures separately within each lake and claims the opposite.

  1. Calculate the pooled mean oxygen concentration at each temperature, using valid observations.
  2. Calculate the change in mean oxygen concentration within each lake between \(16\,^{\circ}\mathrm{C}\) and \(20\,^{\circ}\mathrm{C}\).
  3. Explain how the two students can obtain opposite results from the same valid measurements.
  4. Decide which comparison better answers the original question. Explain how the six missing Fern Lake observations affect the strength of the conclusion, and whether the dataset can establish that temperature caused the differences.

Solution 5

The pooled measurements show higher mean dissolved oxygen at \(20\,^{\circ}\mathrm{C}\), but each individual lake shows lower mean oxygen at that temperature. Both calculations are correct; they answer different questions.

The six missing warm observations at Fern Lake also mean that the measured within-lake difference may not accurately represent all the warm conditions sampled there.

Part 1: Calculate the pooled means.

For \(16\,^{\circ}\mathrm{C}\), there are eight valid Fern observations with a mean of \(7.0\ \mathrm{mg\,L^{-1}}\), and two Ridge observations with a mean of \(11.0\ \mathrm{mg\,L^{-1}}\).

The pooled mean must account for the number of observations contributing to each site mean.

Let \(\bar D_{16}\) represent the pooled mean dissolved oxygen concentration at \(16\,^{\circ}\mathrm{C}\).

\[ \begin{aligned} \bar D_{16} &=\frac{8(7.0)+2(11.0)}{10}\\ &=7.8\ \mathrm{mg\,L^{-1}} \end{aligned} \]

At \(20\,^{\circ}\mathrm{C}\), two valid observations come from Fern and eight come from Ridge.

\[ \begin{aligned} \bar D_{20} &=\frac{2(6.0)+8(10.0)}{10}\\ &=9.2\ \mathrm{mg\,L^{-1}} \end{aligned} \]

The pooled difference is:

\[ \begin{aligned} \Delta\bar D &=9.2-7.8\\ &=+1.4\ \mathrm{mg\,L^{-1}} \end{aligned} \]

In the pooled valid observations, the warmer group has a higher mean dissolved oxygen concentration.

Part 2: Compare temperatures within each lake.

For Fern Lake:

\[ \begin{aligned} \Delta D_{\mathrm{Fern}} &=6.0-7.0\\ &=-1.0\ \mathrm{mg\,L^{-1}} \end{aligned} \]

For Ridge Lake:

\[ \begin{aligned} \Delta D_{\mathrm{Ridge}} &=10.0-11.0\\ &=-1.0\ \mathrm{mg\,L^{-1}} \end{aligned} \]

In both lakes, the mean dissolved oxygen concentration is \(1.0\ \mathrm{mg\,L^{-1}}\) lower in the measured warmer condition.

Part 3: Resolve the apparent contradiction.

The contradiction disappears when you examine where the observations come from.

Fern Lake has lower oxygen concentrations than Ridge Lake at both temperatures.

However:

  • Most of the valid cooler observations come from low-oxygen Fern Lake.
  • Most of the valid warmer observations come from high-oxygen Ridge Lake.

When the student pools the measurements, the change in the proportion of observations from each lake becomes mixed with the temperature comparison.

The pooled result is influenced by which lake supplied the observations, not just their temperature.

This is an example of a statistical reversal often called Simpson’s paradox: a pattern observed within separate groups can reverse when the groups are combined because their relative weights differ.

The arithmetic is not wrong. The interpretation is wrong if the pooled result is treated as evidence about the temperature relationship within each lake.

Part 4: Decide what the dataset can establish.

The separate within-lake comparisons better answer the original question because they retain lake identity.

For valid recorded observations at both sites, the warmer group has a lower mean dissolved oxygen concentration.

But the six missing warm observations at Fern Lake are a serious limitation.

Only two of its eight scheduled warm observations have valid oxygen results:

\[ \begin{aligned} C_{\mathrm{Fern,warm}} &=\frac{2}{8}\times100\%\\ &=25\% \end{aligned} \]

The completeness for Fern Lake’s warm observations is only \(25\%\).

If the missing readings occurred under systematically different oxygen conditions, the two recorded values could give a misleading estimate of the lake’s usual oxygen concentration at \(20\,^{\circ}\mathrm{C}\).

For example, if equipment failed more often during very low-oxygen conditions, the observed warm mean could be too high. A different missingness mechanism could create a different bias. The available metadata do not establish which, if either, occurred.

There is also insufficient information about variability in the measurements to assess the statistical strength of the observed differences.

Finally, neither comparison proves causation. Other conditions may vary with water temperature, and the lakes may differ in mixing, biological activity, and water chemistry.

The most defensible conclusion is:

Within the valid observations from each monitored lake, mean dissolved oxygen was lower at 20°C than at 16°C. However, missing warm observations at Fern Lake and the observational design limit how confidently this relationship can be generalised or attributed to temperature.

The deepest trap is assuming that more pooled observations must produce the best conclusion. Pooling can actually remove the distinctions needed to answer the question.

08What should you do once you’ve found a suitable dataset?

Before making your final graph or drawing a conclusion, write down exactly what one observation represents, which variables can be compared, and what conditions your sample covers.

Keep the original data unchanged. Make a separate working copy for conversions, filtering, and analysis, and record any observations excluded and why.

Then choose a graph or calculation that answers your actual question. A scatter plot may be suitable for paired temperature and dissolved oxygen measurements, while a time-series graph may help investigate changes at one monitoring station.

The next skill is interpreting that evidence without claiming more than the measurements support.

A suitable dataset doesn’t need to be perfect. It needs to have a traceable origin, meaningful measurements, enough relevant observations, and known limitations. Most importantly, it needs to answer the question you are actually asking.