A.1 Handling data

Significant figures communicate the precision supported by a measurement or calculation. Zeros between non-zero digits count; leading zeros only locate the decimal point.

Keep guard digits during working, then round the final result to match the least precise relevant measurement. State a value such as 2.40 to show its precision.

A mean based on readings recorded to 0.1 s should not be reported as 2.437891 s; 2.4 s or 2.44 s may be appropriate depending on the data.

More digits do not make a result more accurate, and exact counted quantities are not limited by instrument precision.

The arithmetic mean is the total of the observations divided by their count. It summarises repeated measurements when they represent the same quantity and are on the same scale.

Inspect the raw values first, calculate the mean with full precision and report spread or anomalous values rather than hiding them.

Rates 9, 10 and 11 units min⁻¹ have mean 10; if one reading was taken at a different temperature, combining it may be misleading.

A mean is sensitive to outliers and does not prove that the system is stable or normally distributed.

Tables keep exact values visible; bar charts compare categories; histograms show how continuous measurements are distributed; diagrams clarify structure or process.

Label axes and units, choose equal scales, include a key when needed and make the display match the variable type. Keep raw data available behind any summary.

Use a histogram for a distribution of cell diameters, but a bar chart for separate treatment groups; joining category bars can falsely imply continuity.

A polished graph cannot repair missing units, selective data or a misleading scale.

Probability lies between 0 and 1 and describes how often an outcome is expected under stated conditions. Define the event and the sample space before calculating.

For equally likely outcomes, divide favourable outcomes by total outcomes; for repeated independent events, multiply their probabilities only when independence is justified.

If 3 of 12 sampled cells meet a criterion, the observed proportion is 0.25; it is evidence from that sample, not a guarantee for every future cell.

A low probability is not proof that an event is impossible, and “at least one” is not the same as “exactly one”.

A sample should represent the population relevant to the question. Random, systematic or stratified choices can reduce selection bias when their use is justified.

Define the population, sampling frame, sample size and inclusion rule; record non-response and avoid replacing inconvenient observations without explanation.

Sampling plants only beside a path may over-represent tolerant individuals; spread quadrats across the habitat and use a stated random rule.

A larger biased sample can be less informative than a smaller representative one.

The mean uses every value, the median is the middle after ordering, and the mode is the most frequent value. The best summary depends on the measurement and its distribution.

Use the median when an outlier would distort the mean; use the mode for common categories or repeated discrete values. Report the raw context and sample size.

Income-like values 2, 2, 3, 3 and 20 have mean 6 but median 3, so the median better represents a typical observation.

No summary statistic tells you the spread or the mechanism producing the data.

A scatter diagram pairs two measured variables. Direction, strength and form of the pattern describe association; they do not by themselves identify a causal mechanism.

Plot the independent variable consistently, inspect outliers and restricted ranges, and use a correlation measure only with the assumptions and data type it requires.

Light intensity and photosynthetic rate may rise together before a plateau; the pattern suggests a relationship, while temperature or CO₂ could also influence both.

No correlation does not prove no biological relationship, and correlation never rules out confounding variables.

An order of magnitude is a factor of ten. Rewrite values in standard form and compare the powers of ten before worrying about small coefficient differences.

For a quick estimate, round the coefficient to a convenient value, state the scale and then return to the exact calculation if the distinction matters.

A bacterium near 2 × 10⁻⁶ m and a cell near 2 × 10⁻⁵ m differ by one order of magnitude, even though both coefficients are 2.

A factor of two is not an order-of-magnitude difference; do not confuse percentage change with powers of ten.

A statistical test compares data with a null expectation. Choose it from the variable type, paired or unpaired design, distribution and question—not from the result you hope to obtain.

State the null hypothesis, identify the test assumptions and report the test statistic or probability with a conclusion about the null. Keep biological importance separate from statistical significance.

A before-and-after treatment on the same organisms is paired; independent groups need a different comparison. A correlation question is not answered by a two-group test.

A significant result does not prove causation or guarantee a large effect.

Range gives the distance from the smallest to largest value; standard deviation summarises typical spread around the mean. Both describe variability, not the cause of it.

Use the same units as the measurements, inspect outliers and report a spread alongside the centre. Do not compare spreads without considering scale and sample size.

Two groups can have the same mean growth rate but different standard deviations; the second group is less consistent even though its average matches.

A small standard deviation does not prove the measurements are accurate; they may be consistently biased.

Uncertainty describes the plausible range around a measurement because of instrument resolution, variation or method limits. It should travel with the value through interpretation.

Record resolution and repeat variation, use consistent units and avoid reporting more precision than the method supports. Compare differences with their uncertainty rather than only their central values.

A 10.0 ± 0.5 cm reading and a 10.3 ± 0.5 cm reading overlap strongly; the data do not justify a confident difference.

Uncertainty is not the same as an error or mistake, and repeating a biased method does not remove systematic uncertainty.