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Analysing and Evaluating Data » Interpreting and Evaluating Data

What you'll learn this session

Study time: 30 minutes

AQA spec: WS 3.5, WS 3.6, WS 3.7, WS 3.8

How to spot patterns and trends and draw conclusions from data
How to decide whether data supports a hypothesis
The difference between accurate, precise, repeatable and reproducible results
How to spot random errors, systematic errors and anomalies, and how to improve a method

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Finding patterns and drawing conclusions

Once data has been tidied into a table or graph, the real thinking starts. You have to say what the data shows. Results can come in words, diagrams, graphs, symbols or numbers, and you need to be able to read all of them.

Start by looking for a pattern or trend. Is the dependent variable going up, going down, or staying the same as the independent variable changes? Does it level off? Does it go up and then fall? Use numbers from the data when you describe it, for example "the mean height rose from 14 cm to 31 cm as the fertiliser increased from 0 to 3 g".

Key terms:

Trend: the general direction the results move in as the independent variable changes.
Inference: a sensible idea about what is happening, worked out from the evidence.
Conclusion: a statement that sums up what the results show and links back to the aim of the investigation.

Making predictions and drawing conclusions

📈 Using data to predict

If a trend is clear, you can use it to predict what will happen at a value you did not test, such as 2.5 g of fertiliser when you tested 2 g and 3 g. Predictions are safest between the values you measured.

✍ Writing a conclusion

Say what happened to the dependent variable as the independent variable changed, back it up with figures, and then give the scientific reason if you can. Only say what the data allows.

Be careful not to say more than the data shows. If the results only cover temperatures from 10 °C to 40 °C, you cannot say anything about 80 °C.

Worked example

Four groups of tomato plants were given 0, 1, 2 and 3 g of fertiliser. After four weeks their mean heights were 14, 19, 25 and 31 cm.

Pattern: the mean height increased as the fertiliser increased. Figures: it rose by about 6 cm for every extra 1 g. Prediction: with 4 g, the plants might reach about 37 cm, but this is only a prediction because 4 g was not tested.

Does the data support the hypothesis?

A hypothesis is a testable idea. Data can be used to comment on the extent to which it supports the hypothesis. That means you do not just say "yes" or "no". You say how well it fits.

If every result fits the hypothesis, the data supports it strongly.
If most results fit but some do not, the data supports it only partly.
If the results do not fit, the data does not support it.

Sometimes there are two or more hypotheses. You may be asked which one gives a better explanation of the data. Pick the hypothesis that fits all the results, not just some of them.

Worked example

A pond has fewer frogs each year. Hypothesis A: a new road is killing frogs. Hypothesis B: the pond is drying up. Data shows the pond water level has stayed the same for five years, but the road traffic has doubled.

The data fits hypothesis A and does not fit hypothesis B, so A is the better explanation. It does not prove A, because other causes could still exist.

Evaluating data: four key words

To evaluate data you must be objective. That means judging the results fairly, without letting what you hoped to find change your view. These four ideas describe how good a set of measurements is.

Accurate: a measurement that is close to the true value.
Precise: measurements that cluster closely together.
Repeatable: repeating the investigation under the same conditions, by the same investigator, gives similar results.
Reproducible: similar results are obtained by different investigators using different equipment.

A set of measurements can be precise without being accurate. Imagine a thermometer that always reads 2 °C too high. Five readings of 27.1, 27.0, 27.1, 27.2 and 27.1 °C cluster closely, so they are precise, but they are not close to the true value.

Common mistakes

Mixing up repeatable and reproducible. Repeatable is the same person, same equipment. Reproducible is a different person or different equipment. Another mistake is thinking that precise means correct. Precise only means the results are close together.

Errors and anomalies

Every measurement has some uncertainty. Errors are the reasons results differ from the true value. There are two types.

🎲 Random error

Results vary in unpredictable ways, sometimes too high and sometimes too low, for example from reading a measuring cylinder slightly differently each time. These errors can be reduced by making more measurements and reporting a mean value.

⚖ Systematic error

Results differ from the true value by the same amount each time, for example a balance that is not zeroed and always reads 0.5 g too high. Repeating the experiment does not remove it. The equipment or method has to be fixed.

Key terms:

Random error: an error that makes results vary in unpredictable ways.
Systematic error: an error that shifts results from the true value by a consistent amount each time.
Anomalous value: a result that does not fit the pattern of the others.

Anomalous values should always be examined to try to find the cause. If it was a poor measurement, such as a spilt solution or a misread scale, the value is ignored when you work out the mean. If you cannot find a reason, you should say so and be cautious about the result.

Suggesting improvements and communicating

When you evaluate an investigation, link each weakness to a fix. A general phrase such as "be more careful" earns no marks.

Results vary a lot: take more repeat readings and calculate a mean.
Readings are hard to measure exactly: use apparatus with a finer scale, or a digital sensor.
Results are always too high or too low: check and correct the equipment, for example by zeroing a balance.
Few values tested: test a wider range or more values of the independent variable.
Variables not controlled: control them, for example with a water bath.

Finally, scientists must communicate their work clearly. A good report, on paper or on screen, gives the reason for the investigation, the method, the findings and a reasoned conclusion. It should follow a logical order and use the right scientific words, units and symbols. You can use words, diagrams, graphs, numbers and symbols, whichever makes the point most clearly.

Common mistakes

Writing a conclusion that goes beyond the data, or one that ignores anomalous values without saying why. Saying results are "accurate" or "repeatable" without giving evidence for it.

Exam-style question

A student timed how long it took a leaf disc to rise to the surface of a bright, warm solution of sodium hydrogencarbonate. The times in seconds were: 42, 45, 43, 70, 44.

(a) Identify the anomalous result and suggest what the student should do with it. [2 marks]

(b) Calculate the mean time without the anomalous result. [2 marks]

(c) The student's teacher repeats the experiment with a different stopwatch and gets mean times very close to the student's. What word describes these results? [1 mark]

(d) Suggest one way the student could reduce random error. [1 mark]

Model answer

(a) 70 seconds (1). Try to find the cause and, if it was a poor measurement, ignore it (1).

(b) 42 + 45 + 43 + 44 = 174 (1). 174 ÷ 4 = 43.5 seconds (1).

(d) Take more repeat measurements and use the mean (1).

Exam tip

In part (b), say clearly which value you left out. Using the anomalous value in the mean loses both marks.

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