IB · Internal Assessment · Data analysis

Which test?

A guide for IB students, whatever your investigation. Answer a few plain-language questions about your research question and data to find the right statistical test. Each test comes with a worked example, the hypotheses, Excel steps, a reporting template and the mistakes examiners look for. Then paste your data into the calculators for report-ready results, and draw the matching graph.

For every IB IA
Built from IB guidance

Find your test

Start from your research question, not from a test someone told you to use. Each question has an explanation and examples underneath.

Before you run any test

Your sample size decides which spread statistic and which test you can use. These thresholds come from the IB Biology TSM.

Sample size rules

Replicates per group	Spread to report	Tests possible
fewer than 5	Range (max − min)	None reliable; describe only
5 – 9	Standard deviation	ANOVA, Mann–Whitney, Wilcoxon, correlations
10 – 29	Standard deviation	Adds t-tests (TSM: "n < 10 is usually too small")
30 or more	SD or standard error	All of the above

TSM scale: n > 30 is a large sample, 15–30 small, 5–14 very small. With little data, the mean and range can still earn top marks if that processing fits the RQ.

Which error bars?

Bar	Use when	Why
Range	n < 5, or always as a simple option	Accepted at any sample size
±1 SD	n ≥ 5. The default for most IAs	Shows the real spread of your repeats
±1 SE	n ≥ 30 only	Moderators mark down SE used with small samples

Always say which one in the caption. Unlabelled error bars lose marks.

Three questions to answer first

1. What exactly is the DV?
Is it a measurement, a count or a rate? Calculate rates for each trial first, then average them. Averaging the raw readings first was marked down by IB moderators.

2. Are the replicates independent?
Five tubes filled from one shared solution are really closer to one replicate than five. If so, say it in the evaluation.

3. Outliers?
Never delete one by default. Identify it (1.5 × IQR, data booklet), justify any exclusion with an observation, and show the results with and without it.

Calculators

Paste your raw data straight from Excel or Google Sheets. Each calculator gives you a methods sentence with hypotheses, a results table and a conclusion sentence, ready to paste into Word or Google Docs. Check the numbers with your own software as well, and name it in your method.

Graph maker

Draw the graph that matches your test, with error bars, Tukey letters, p-values or the trend line equation already on it. The caption is written for you. Download the graph as an image and paste it into your report.

Critical values (p = 0.05, two-tailed)

For each test, the "significant if" column tells you which way to compare your value with the critical value. Check these against your textbook or software output before relying on them.

Pearson's r

significant if |r| ≥ value df = n − 2

df	r	df	r
3	0.878	12	0.532
4	0.811	14	0.497
5	0.754	16	0.468
6	0.707	18	0.444
7	0.666	20	0.423
8	0.632	25	0.381
9	0.602	30	0.349
10	0.576	40	0.304

Spearman's rₛ

significant if |rₛ| ≥ value uses n

n	rₛ	n	rₛ
5	1.000	12	0.587
6	0.886	14	0.538
7	0.786	16	0.503
8	0.738	18	0.472
9	0.700	20	0.450
10	0.648	30	0.362

χ² (IB data booklet)

significant if χ² ≥ value

df	p = 0.05	p = 0.01
1	3.84	6.63
2	5.99	9.21
3	7.81	11.34
4	9.49	13.28
5	11.07	15.09
6	12.59	16.81
7	14.07	18.48
8	15.51	20.09

Mann–Whitney U

significant if U ≤ value equal group sizes

n per group	U
5	2
6	5
7	8
8	13
9	17
10	23
15	64
20	127

Wilcoxon T

significant if T ≤ value non-zero pairs

n pairs	T
6	0
7	2
8	3
9	5
10	8
12	13
15	25
20	52

Tukey q

HSD = q × √(MS within ÷ n) k = number of groups

df	k=2	3	4	5	6	7

Reporting checklist

A test only earns credit if the examiner can follow it. Tick off every item.

In Data analysis

Name the test and give a one-sentence reason it fits this RQ and data type.
State H₀ and H₁ with the test, not in the introduction (TSM).
Say what data went in: raw replicates or means, and n.
Name the software and function (e.g. "Excel T.TEST, type 3") or the named online calculator.
Report the statistic, df (or n) and p in a small table.
ANOVA: include the post-hoc result (Tukey letters or pairs).
Correlation: give r with its sign, its p-value, and R² for the trend line.
Graph caption names the error-bar type and the n.

In the Conclusion

Compare p with 0.05 in words: "p = 0.003 < 0.05, so H₀ is rejected".
Say what the result means biologically, not just statistically.
Use "supports", never "proves".
Explain what R² means ("the line accounts for 96% of the variation"), don't just state the number.
Note the sample size and its effect on confidence.
A non-significant result is still a result: report it honestly.
Correlation ≠ causation: name at least one alternative explanation.

Example investigations

Find the investigation most like yours. Each one explains which test fits and why, and the button walks you through the questions.

Enzymes and temperature

How does temperature (20–60 °C) affect the rate of starch breakdown by amylase?

Data: 5 temperatures × 5 repeats, measured as a rate. Shape: rises, then falls (an optimum).

Test: ANOVA + Tukey, to show the peak is higher than its neighbours. A single correlation would cancel out.

Osmosis in potato

How does sucrose concentration (0–1.0 mol dm⁻³) affect the % change in mass of potato cylinders?

Data: 6 concentrations × 5 repeats = 30 points. Shape: a steady straight-line fall.

Test: Pearson's r with a significance test. Bonus: read off where the line crosses 0 % to estimate the potato's solute concentration.

Sun and shade leaves

Is there a difference in stomatal density between sun and shade leaves of Hedera helix?

Data: 2 separate groups, 12 leaves each, counted per mm².

Test: unpaired t-test (Welch). With fewer than 10 leaves per group, use Mann–Whitney instead.

Exercise and heart rate

Does a 2-minute step test change the pulse rate of 16–17-year-old students?

Data: the same 12 students measured before and after, so the data are paired.

Test: paired t-test. Needs consent, and a PAR-Q questionnaire under the IB guidelines.

Comparing brands or species

Which of four brands of antacid neutralises the most acid?

Data: 4 categories (brands have no natural order) × 5 repeats, measured as a volume of acid.

Test: one-way ANOVA + Tukey. Six separate t-tests would raise the false-positive risk to about 26 %.

Fieldwork: trampling

Is the number of plantain plants related to distance from a footpath?

Data: quadrats every 1 m for 10 m. Neither variable was controlled, and the counts level off away from the path.

Test: Spearman's rank correlation. Remember: correlation, not causation.

Genetics: a monohybrid cross

Do the kernels on an F2 maize cob fit the expected 3:1 purple to yellow ratio?

Data: counts in 2 categories, compared with a ratio from Mendelian theory.

Test: chi-squared goodness of fit, df = 1.

Ecology: are two things linked?

Is the shell colour of dog whelks associated with exposed and sheltered shores?

Data: each whelk counted once, in a 2 × 2 table (colour × shore).

Test: chi-squared test of association, df = 1. Use counts, not percentages.

Key words

The words you'll meet when choosing and reporting a test, in plain English.

Independent variable (IV)The thing you change or choose.temperature, salt concentration, distance from path

Dependent variable (DV)The thing you measure.rate of reaction, mass change, number of plants

ReplicateA repeat of the same condition. More replicates make your mean more trustworthy.5 potato cylinders in 0.4 mol dm⁻³ sucrose

nThe number of values: per group, or in total for a correlation.n = 5 per concentration; n = 30 points

MeanThe average: add up and divide by n. Use =AVERAGE().(4.1 + 3.6 + 4.4) ÷ 3 = 4.0

RangeLargest minus smallest value. The simplest measure of spread.4.4 − 3.6 = 0.8

Standard deviation (SD)The typical distance of values from the mean. Use when n ≥ 5. =STDEV.S().mean 182 ± 21 stomata mm⁻²

Standard error (SE)How precisely the mean is known. Only for large samples (n ≥ 30); most IAs should use SD.SE = SD ÷ √n

Measurement vs countA measurement sits on a scale; a count puts each individual into a category.mass 2.45 g vs 14 of 20 seeds germinated

Paired vs independentPaired: the same individuals measured twice. Independent: different individuals in each group.pulse before and after vs sun leaves and shade leaves

Symmetric vs skewedSymmetric: most values in the middle, tailing off evenly. Skewed: bunched to one side with a long tail.heights (symmetric) vs invertebrate counts (skewed)

Null hypothesis (H₀)The "nothing is going on" statement that the test tries to reject.there is no correlation between light and O₂ bubbles

p-valueThe chance of getting results like yours if H₀ were true. Below 0.05, reject H₀.p = 0.003 → significant

SignificantUnlikely to be due to chance (p < 0.05). It doesn't mean large or important.a small but significant difference

Critical valueThe threshold your test statistic must pass (or fall below, for U and T) to be significant.χ² critical = 3.84 at df = 1

Degrees of freedom (df)A number from your sample size that tells you which row of the critical-value table to use.Pearson: df = n − 2

Correlation (r)How closely two variables follow a straight line, from −1 to +1. The sign gives the direction.r = −0.91: strong, negative

R² (coefficient of determination)How much of the variation the trend line explains, from 0 to 1. Always positive.R² = 0.83: 83 % explained

OutlierA value far from the others. Check with Q3 + 1.5 × IQR (data booklet); never delete one without a reason.one cylinder gained mass when the rest lost it

Correlation ≠ causationTwo things changing together doesn't prove one causes the other.ice-cream sales and sunburn both rise in summer