🧾 Big idea: The test gives you a number. Turning it into a sentence an examiner can award marks for is a separate skill — and it is the one most often lost. Choose the right test, phrase the decision in terms of the null hypothesis, and claim exactly as much as the data allows and no more.
Summary — What This Topic Covers
Choosing between the three tests from the shape of the data
What p < 0.05 actually means
Phrasing a conclusion around the null hypothesis
The four claims a statistical test can never support
Writing a full conclusion, with the evidence quoted
1. Choosing the Right Test
WHAT ARE YOU ASKING? TEST
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Do these two groups have different means? t-test
continuous data, roughly normal,
two groups, n ≈ 10+ each
Do these counts match what I predicted? chi-squared
raw frequencies in categories,
expected values from a hypothesis,
no expected value below 5
Do these two variables change together? Spearman's rank
pairs of measurements, at least 7
pairs, no normality assumed
The commonest error
Using a t-test on counts. If the data is "how many of each", it is chi-squared — no matter how tempting the two totals look like two means.
2. What p < 0.05 Means
The definition
p is the probability that a difference or correlation at least as large as the one observed would arise by chance if the null hypothesis were true.
p < 0.05 means that probability is less than 5 %, which biologists agree is low enough to call the result significant.
p < 0.05 significant less than 1 chance in 20 of arising by chance
p < 0.01 highly significant
p > 0.05 not significant the result could reasonably be chance
What p is not
p is not the probability that your hypothesis is correct, and it is not a measure of how big the effect is. It is only about how surprising the data would be if nothing were going on.
3. Phrasing the Decision
t-test and Spearman calculated ≥ critical → REJECT H₀
Chi-squared calculated ≥ critical → REJECT H₀
in every case: bigger than critical means significant
REJECT H₀ → "there is a significant difference / correlation"
ACCEPT H₀ → "no significant difference / correlation was found"
NOT "there is no difference"
Why the wording matters
Accepting H₀ means you failed to find evidence of a difference — which may be because there is none, or because your sample was too small. The two are indistinguishable from the test alone, so the conclusion must not claim more than that.
4. Four Claims a Test Cannot Support
"This proves…" — statistics deal in probability, never proof. Write "suggests", "indicates" or "provides evidence that"
"X causes Y" from a correlation — only a controlled experiment establishes cause
"There is no difference" from a non-significant result — you found no evidence of one, which is a different statement
"The effect is large / important" from significance alone — with a big enough n, a trivial difference becomes significant
What mark schemes look for
Hedged, precise language. "The results suggest a significant difference…" scores; "this proves that…" often loses the mark even when the statistics are right.
5. A Full Conclusion
"The mean shell height was 22.4 mm on the sheltered shore and 18.1 mm on
the exposed shore. A t-test gave t = 2.94 with 20 degrees of freedom,
which exceeds the critical value of 2.086 at p = 0.05, so the null
hypothesis is rejected.
There is therefore a significant difference between the mean shell
heights on the two shores, with less than a 5 % probability that a
difference this large arose by chance. This is consistent with the
hypothesis that wave action limits shell growth on exposed shores,
although other factors differing between the sites — such as food
availability or temperature — were not controlled and may contribute."
The figures being compared
The test statistic, df and critical value or p
The decision about H₀, in words
What it means biologically
A limitation — an uncontrolled variable, or the size of the sample
Easy marks
The limitation sentence is nearly always available and nearly always forgotten. One named uncontrolled variable is usually enough.
Practice Questions
Practice Question 1
A student compares the number of limpets found on north-facing and south-facing rocks and wants to know whether the distribution is even. State which test is appropriate and why.
Practice Question 2
Explain what is meant by p < 0.05 in the context of a t-test result.
Practice Question 3
A student writes: "The t-test proves that caffeine increases reaction speed." Rewrite this as an acceptable conclusion, assuming t exceeded the critical value.
Practice Question 4
A t-test on two samples of n = 5 gives a non-significant result, but the means differ by 30 %. Comment on what this shows.
What to Memorise
Two means → t-testCounts in categories → chi-squaredPaired variables → Spearmanp < 0.05 = significantp = chance of this result if H₀ is trueBigger than critical → reject H₀Never "proves"Never "no difference" from a non-significant resultSignificant ≠ importantAlways quote statistic, df and p
Concepts Checklist
Exam Tips
What mark schemes look for
Five elements: the figures, the statistic with df and p, the decision about H₀, the biological meaning, and a limitation. Marks are usually allocated to each.
The trap
"Proves" and "causes". Both appear in weak answers and both cost marks even when the statistics are correct.
Easy marks
Name one uncontrolled variable at the end of any fieldwork conclusion. It is nearly always available and nearly always missed.
Worth remembering
If a result is not significant but the means look different, the answer the examiner wants is that the sample was too small — increase n.