How do I design a valid experiment and use statistics to test whether results are significant?
Experimental design and statistics: variables, controls, validity and reliability; types of error and uncertainty; the chi-squared test; correlation and causation; and choosing an appropriate statistical test.
A focused answer to the experimental-design and statistics requirements of Eduqas A-Level Biology. Covers variables, controls, validity and reliability, types of error and uncertainty, the chi-squared test, correlation and causation, and choosing an appropriate statistical test.
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What this dot point is asking
Eduqas tests your ability to design a valid, reliable experiment and to analyse data, including choosing and using a statistical test such as the chi-squared test, and distinguishing correlation from causation. These skills are assessed across all three papers.
Variables, controls, validity and reliability
- The independent variable is the one you deliberately change; the dependent variable is the one you measure; control variables are kept constant.
- Validity means a fair test that measures what you intend, achieved by controlling the other variables.
- Reliability means consistent, repeatable results, achieved by repeating and taking a mean (and identifying anomalies).
- A control (for example with no treatment) provides a baseline so that the effect of the independent variable can be isolated.
Errors and uncertainty
The chi-squared test
The chi-squared test () tests whether observed frequencies in categories differ significantly from expected ones:
State the null hypothesis (no significant difference from the expected ratio), find the degrees of freedom (categories minus 1), and compare with the critical value at : below it, the difference is not significant (accept the null hypothesis); at or above it, the difference is significant (reject it).
Correlation, causation and choosing a test
A correlation is an association between two variables; it does not prove that one causes the other (a third factor may be responsible). To establish causation you need a controlled experiment and a plausible mechanism. Choose the statistical test to match the data:
- Chi-squared for comparing observed and expected frequencies (categories), for example genetic ratios.
- A correlation test (such as Spearman's rank) for an association between two continuous variables.
- A t-test for comparing the means of two samples.
Examples in context
Example 1. Why genetics uses chi-squared. Offspring fall into discrete phenotype categories with an expected ratio, so chi-squared (which compares observed and expected frequencies) is the right test, not a correlation or t-test.
Example 2. Smoking and lung disease. The historical debate showed that a strong correlation plus a plausible mechanism and controlled studies were needed before causation was accepted, a classic illustration of correlation versus causation.
Try this
Q1. Distinguish between a random and a systematic error. [2 marks]
- Cue. Random errors cause scatter and are reduced by repeating and averaging; systematic errors shift every reading the same way (for example an uncalibrated instrument) and are removed by calibration.
Q2. State what a null hypothesis is. [1 mark]
- Cue. A statement that there is no significant difference (or association), and that any difference seen is due to chance.
Q3. Which statistical test would you use to compare observed offspring numbers with an expected genetic ratio? [1 mark]
- Cue. The chi-squared test.
Exam-style practice questions
Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Eduqas 20194 marksExplain why a scientist would carry out a statistical test on their results rather than simply comparing the means, and explain what a null hypothesis is.Show worked answer →
Means can differ by chance alone, especially with variable biological data and small samples, so a difference between two means does not by itself show a real effect.
A statistical test calculates the probability that the difference (or association) occurred by chance, allowing an objective conclusion about significance.
A null hypothesis states that there is no significant difference (or no association) between the variables, and that any difference seen is due to chance.
The test result is compared with a critical value (usually at p equals 0.05) to decide whether to accept or reject the null hypothesis.
Markers reward the point that differences can arise by chance, a statistical test giving the probability of a chance result, and a correct definition of the null hypothesis.
Eduqas 20215 marksA student counted 90 offspring expecting a 3:1 ratio and observed 60 dominant and 30 recessive. Use the chi-squared test to decide whether the result fits the expected ratio. The critical value at p equals 0.05 and 1 degree of freedom is 3.84.Show worked answer →
Expected from 90 in a 3:1 ratio: 67.5 dominant and 22.5 recessive.
Chi-squared equals the sum of (O minus E) squared over E: (60 minus 67.5) squared over 67.5, plus (30 minus 22.5) squared over 22.5.
Equals 56.25 over 67.5, plus 56.25 over 22.5, equals 0.83 plus 2.5 equals 3.33.
Since 3.33 is less than the critical value 3.84, the difference is not significant; accept the null hypothesis that the result fits the 3:1 ratio (any difference is due to chance).
Markers reward the expected values 67.5 and 22.5, the chi-squared value of about 3.33, comparison with 3.84, and the conclusion that the result fits the ratio.
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Sources & how we know this
- Eduqas A Level Biology Specification (A400) — Eduqas (2015)