Internal Assessment · Biology · ESS · 8 min read
Which statistical test for your Biology or ESS IA? A decision guide with a worked example
Match your research question to the right test, check its assumptions, run it, and write up the result without claiming more than it shows.
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The right statistical test for a Biology or ESS IA depends on one question: are you comparing groups, looking for a relationship between two measured variables, or analysing counts in categories? Comparing two groups of measurements usually means a t-test (or Mann–Whitney U if the data aren't normal); three or more groups means ANOVA; a relationship means Pearson's or Spearman's correlation; counts in categories means chi-squared. Every test is run against a null hypothesis, usually at the 0.05 significance level.
Both subject guides expect this. The Biology guide lists the t-test and chi-squared test among the skills you should be able to apply, and the ESS guide names Pearson, Spearman's rank, the t-test, ANOVA and chi-squared as tests students should select and use.
Which test should I use? The decision table
| Your question | Data | Test | IA example | Degrees of freedom |
|---|---|---|---|---|
| Do two independent groups differ? | Continuous, roughly normal | Independent (unpaired) t-test | Stomatal density of sun leaves vs shade leaves from different plants | n1 + n2 − 2 |
| Do paired measurements differ? | Two values from the same individual or site | Paired t-test | Chlorophyll content of a sun leaf and a shade leaf from each of 12 trees | n − 1 (pairs) |
| Do three or more groups differ? | Continuous, roughly normal | One-way ANOVA, then a post-hoc test (e.g. Tukey) | Germination at four salt concentrations | Between groups k − 1; within N − k |
| Do two groups differ? | Skewed, ordinal or small samples | Mann–Whitney U (Wilcoxon signed-rank if paired) | Invertebrate counts in kick samples above and below an outflow | Uses n1 and n2 in the table |
| Are two categorical variables associated? | Counts in a contingency table | Chi-squared test of association | Presence/absence of two species in 60 quadrats | (rows − 1)(columns − 1) |
| Do counts fit an expected ratio? | Counts in categories | Chi-squared goodness of fit | Purple and yellow kernels on a maize cob vs a 3:1 ratio | categories − 1 |
| Are two measured variables linearly related? | Both continuous, roughly normal | Pearson's correlation (r) | Leaf area against leaf mass | n − 2 |
| Do two variables rise or fall together? | Ranked, skewed, or relationship not linear but consistently one direction | Spearman's rank (rs) | Distance from a path against percentage cover | Uses n in the table |
With four groups there are six possible pairs. Six t-tests at p = 0.05 give roughly a 26% chance of at least one "significant" result even if nothing is going on. ANOVA tests all groups at once; a post-hoc test then shows which pairs differ.
What assumptions do the tests make?
- Independence: each value comes from a separate sample. Ten leaves from one plant are not ten independent replicates of "sun plants"; they are one plant measured ten times. This mistake, called pseudoreplication, is a common hidden flaw in Biology and ESS IAs.
- Normality (t-test, ANOVA, Pearson): data roughly symmetrical and bell-shaped. With small samples you can't prove it, but a histogram or a quick look for strong skew or outliers is worth a sentence. Counts of organisms are often skewed, which is when Mann–Whitney or Spearman's is safer.
- Similar spread (standard t-test, ANOVA): if one group's SD is much larger, use Welch's t-test (type 3 in Excel's
T.TEST). - Chi-squared: use raw counts, never percentages or means, and every expected frequency should be at least 5. If not, combine categories or collect more.
- Correlation: plot the scatter graph first. Spearman's and Pearson's only detect relationships that keep going in one direction; a rise-then-fall (an optimum) can give r ≈ 0 even when the relationship is strong. The annotated science IA example shows how one student handled exactly this.
How do hypotheses, p-values and critical values work?
The null hypothesis (H0) says there is no difference or no relationship; the alternative (H1) says there is. Write them for your actual variables:
Loses marks"H0: there is no relationship. H1: there is a relationship."
Earns marks"H0: there is no correlation between distance from the footpath and percentage cover of greater plantain. H1: there is a correlation between distance from the footpath and percentage cover of greater plantain."
The p-value is the probability of getting a result at least as extreme as yours if H0 were true. If p < 0.05, a result like yours would be unusual under H0, so you reject H0. It is not the probability that H0 is true, and it says nothing about how big or important the effect is.
If you calculate by hand, you compare your test statistic with a critical value from a table, found using the significance level (0.05) and the degrees of freedom or sample size. For a t-test or chi-squared, a statistic larger than the critical value means p < 0.05. Two values to know: a two-tailed t-test with 18 degrees of freedom has a critical value of 2.101; chi-squared with 1 degree of freedom has 3.841.
Worked example: Spearman's rank correlation
The data below are illustrative, invented for this guide. A student places ten 0.25 m2 quadrats at 0.5 m intervals from a footpath and estimates the percentage cover of greater plantain (Plantago major), a trampling-tolerant species. Percentage cover estimates are not reliably normal, and the student expects cover to fall with distance but not necessarily in a straight line, so Spearman's rank is the right choice.
Step 1: rank each variable separately (smallest = 1). With tied values, give each the mean of the ranks they share; there are no ties here.
| Distance / m | Rank | Cover / % | Rank | d | d2 |
|---|---|---|---|---|---|
| 0.5 | 1 | 34 | 9 | −8 | 64 |
| 1.0 | 2 | 41 | 10 | −8 | 64 |
| 1.5 | 3 | 28 | 7 | −4 | 16 |
| 2.0 | 4 | 25 | 6 | −2 | 4 |
| 2.5 | 5 | 30 | 8 | −3 | 9 |
| 3.0 | 6 | 18 | 5 | 1 | 1 |
| 3.5 | 7 | 12 | 3 | 4 | 16 |
| 4.0 | 8 | 15 | 4 | 4 | 16 |
| 4.5 | 9 | 8 | 2 | 7 | 49 |
| 5.0 | 10 | 6 | 1 | 9 | 81 |
| Σd2 | 320 | ||||
Step 2: calculate rs.
rs = 1 − (6Σd2) ÷ (n(n2 − 1)) = 1 − (6 × 320) ÷ (10 × 99) = 1 − 1920 ÷ 990 = 1 − 1.939 = −0.94
Step 3: compare with the critical value. For n = 10 at p = 0.05 (two-tailed), the critical value is 0.648. The size of our value, 0.94, is larger, so the correlation is significant at the 0.05 level (it would also pass at 0.01). Software gives p < 0.001.
Step 4: decide. Reject H0: there is a significant negative correlation between distance from the path and plantain cover in this sample.
What to write in the IA
Spearman's rank correlation showed a strong, significant negative correlation between distance from the footpath and percentage cover of P. major (rs = −0.94, n = 10, p < 0.05; critical value 0.648), so H0 is rejected. This is consistent with P. major tolerating trampling better than competing species near the path. However, the test shows an association, not a cause: soil compaction, light and nutrient input from walkers all change with distance and were not measured separately. All ten quadrats lay on one transect, so the result describes this stretch of path only.
Notice the structure: test, statistic, sample size, significance, decision, then what it means biologically and what it can't show. The ecology field IA guide covers how to sample so that last limitation goes away (several transects, randomly placed).
The same idea for a t-test
For two groups, the write-up has the same shape: "Mean stomatal density was higher in sun leaves (mean ± SD) than in shade leaves (mean ± SD); an independent t-test showed the difference was significant (t = …, df = 18, p = …)." In Excel, =T.TEST(range1, range2, 2, 2) returns the two-tailed p-value directly (the last argument is 1 for paired, 2 for equal variance, 3 for unequal variance). CHISQ.TEST returns a chi-squared p-value from observed and expected ranges, and CORREL gives Pearson's r; for Spearman's, rank both columns with RANK.AVG and apply CORREL to the ranks.
What do students get wrong when interpreting results?
- "This proves my hypothesis." A test can support a hypothesis or fail to; it never proves one. Write "supports".
- Correlation as causation. In fieldwork especially, many variables change together. Name the confounding variables you didn't control.
- "p > 0.05, so there is no effect." It means you found no significant evidence of one with this sample. A small sample can miss a real effect.
- Significant means large. With big samples, tiny differences become significant. Report the means (with their uncertainties or SDs) or rs as well as p.
- Testing the wrong thing. A t-test on the IV values, or a correlation on data from two categorical groups, shows the test was picked from a list rather than from the question.
- Removing "outliers" to reach significance. Decide on and justify any exclusion before you run the test, and report it.
Show the result visually too: a scatter graph for a correlation, means with error bars for a comparison. The IA graphs guide covers what the error bars should show and why overlap isn't a test.
Questions students ask
Do I have to do a statistical test in my Biology IA?
The criteria don't name a required test. They ask for processing that is relevant to your research question and carried out appropriately and accurately. If your question asks whether conditions differ or whether two variables are related, a test is usually the most direct evidence you can give. Check with your teacher.
How many repeats do I need for a t-test?
There's no fixed rule, but with three per group a t-test can only detect very large differences. Five or more per group is a sensible minimum for a school IA, and more is better if your method allows it.
What if my p-value is just above 0.05?
Report it honestly: the difference is not significant at the 0.05 level. Don't switch tests or remove data until it drops below. Discuss what a larger sample might show, and note the size of the difference you did see.
Should I use a one-tailed or two-tailed test?
Use two-tailed unless you predicted the direction before collecting data, for a scientific reason you state in your hypothesis. Decide before you see the results, not after.
Can I use software instead of calculating by hand?
Yes. Excel, Google Sheets, a GDC or a reputable online calculator is fine. Report the test, the test statistic, n or degrees of freedom, and the p-value or critical value, so a reader can check your work.
Try one: Biology
A student records whether two moss species, A and B, are present or absent in each of 60 randomly placed quadrats on a woodland floor. The research question asks whether the two species tend to occur together.
Which statistical test is most appropriate?
- An independent t-test comparing the mean number of quadrats containing A and containing B
- Spearman's rank correlation between the presence of A and the presence of B
- A chi-squared test of association on a 2 × 2 contingency table, with 1 degree of freedom
- A chi-squared goodness-of-fit test with 3 degrees of freedom
Show the answer and why
Answer: C
Presence/absence data are counts in categories (A present or absent × B present or absent), so the test is chi-squared for association. A 2 × 2 table has (2 − 1)(2 − 1) = 1 degree of freedom. Options A and B both need a measured value for each quadrat, and presence/absence gives categories, not measurements. D is tempting because there are four cells, but goodness of fit compares counts with a theoretical ratio, and 4 − 1 = 3 is not the degrees of freedom for an association test.