A squid’s giant axon is nearly a hundred times wider than one of yours, and yours still wins the race. Working out why leads straight into one of the most useful statistical ideas in the whole course.
📚 What you need to know
Two structural features affect the speed of transmission: myelination and axon diameter.
Myelinated neurones conduct much faster, because the impulse jumps between nodes of Ranvier — saltatory conduction.
A wider axon conducts faster, because it offers less resistance.
Squid giant axons are unmyelinated and up to 1 mm wide; human axons are typically 4–100 µm but usually myelinated.
Correlation is an association between variables. It does not prove causation.
The correlation coefficient (r) runs from −1 to +1. Zero means no linear correlation.
Pearson’s linear correlation needs data that is quantitative and normally distributed. Squaring r gives R2, the coefficient of determination.
Myelination and saltatory conduction
Schwann cells wrap around the axon in layers. Because their membranes are made of phospholipids, the resulting myelin sheath is largely lipid — and lipid has a high electrical resistance.
So the sheath acts as an electrical insulator. Impulses cannot pass through it at all. The only places the membrane is exposed are the small gaps between neighbouring Schwann cells: the nodes of Ranvier.
The consequence is neat. Depolarisation can only happen at the nodes, so the impulse effectively jumps from one node to the next rather than travelling through every millimetre of membrane. That jumping is called saltatory conduction, and it is dramatically faster.
It feels backwards that adding a coating speeds things up. The trick is that the impulse now has far fewer stretches of membrane to depolarise.
Axon diameter
The second factor is width. A wider axon conducts an impulse more quickly, because a wider tube of cytoplasm offers less resistance to the flow of ions.
This is the trick some invertebrates use instead of myelin. Squid have giant axons up to 1 mm across, which lets them fire their escape response fast. Human neurones are between about 4 and 100 µm — but most are myelinated.
Always check the x-axes before comparing two graphs like these. The left plot runs to 12 µm; the right runs to 800.
If a question shows you two axes with wildly different scales, that is the question. Comment on it. Reading both plots as though they shared an x-axis is the mistake the question is designed to catch.
Correlation and causation
Both of these are relationships between two variables, which puts us squarely in the territory of correlation — and that word needs handling carefully.
Correlation is an association or relationship between two variables.
Causation is when one variable actually influences the other.
A correlation does not necessarily imply causation. Two things can move together for all sorts of reasons.
The sign of r tells you the direction; how close it is to 1 tells you the strength. Both matter when describing a relationship.
Positive correlation: as A increases, B increases.
Negative correlation: as A increases, B decreases.
No correlation: r is 0, and knowing A tells you nothing about B.
Perfect correlation: every point lies exactly on a straight line, giving r = 1 or r = −1.
Pearson’s linear correlation
Eyeballing a scatter graph is a start, but you need a number. Pearson’s linear correlation is the statistical test that gives you one.
Conditions for using it: the data must be quantitative and must show a normal distribution. If those do not hold, Pearson’s test is not the right tool.
🧩 Testing for correlation
Plot a scatter graph of your data and look for a linear pattern.
State a null hypothesis — that there is no correlation between the two variables.
Calculate r using the formula. It is given to you in the exam; you are expected to be able to use it.
Interpret r. Close to +1 or −1 means a strong linear correlation, and the null hypothesis can be rejected.
Square it to get R2, and convert to a percentage if useful.
Multiply each pair together, then total those products
Σx2
Square each x value, then total them
Σy2
Square each y value, then total them
The coefficient of determination
Square r and you get R2, the coefficient of determination. It tells you how much of the variation in one variable can be accounted for by the other.
R2 close to 1 (or 100%): a strong association, and the dependent variable can be predicted accurately from the independent one.
R2 close to 0: no useful association, and no prediction is possible.
Worked examples
WORKED EXAMPLE
Axon diameter (µm) and conduction velocity (m s−1) were measured in five axons: (2, 12), (4, 25), (6, 35), (8, 50), (10, 58). Calculate Pearson’s r, then R2.
Step 1: work out the five totals, with n = 5Σx = 30, Σy = 180, Σxy = 1314Σx² = 220, Σy² = 7858Step 2: the top of the fraction(5 × 1314) − (30 × 180) = 6570 − 5400 = 1170Step 3: the bottom of the fraction(5 × 220) − 30² = 1100 − 900 = 200(5 × 7858) − 180² = 39290 − 32400 = 6890√(200 × 6890) = √1378000 = 1173.9Step 4: divide, then squarer = 1170 ÷ 1173.9 = 0.997R² = 0.997² = 0.993, or 99.3%r = 0.997 — a very strong positive correlationwork out all five totals in a table before you touch the formula
WORKED EXAMPLE
State what the value of r above means for the null hypothesis, and explain one limitation of the conclusion. [3]
Step 1: interpret r
r is very close to +1, so there is a strong positive linear correlation.
Step 2: the null hypothesis
It stated there was no correlation, so it can be rejected.
Step 3: the limitation
A correlation does not prove causation, and only five pairs were measured.
Reject the null hypothesis, but do not claim diameter causes the speed increase“strong correlation” and “proves cause” are not the same claim
WORKED EXAMPLE
A squid giant axon is 800 µm wide and conducts at 25 m s−1. A myelinated human axon is 12 µm wide and conducts at 90 m s−1. Calculate how many times wider the squid axon is, and explain why it is still slower. [3]
Step 1: compare the diameters800 ÷ 12 = 66.7 times widerStep 2: compare the speeds90 ÷ 25 = 3.6 times faster in the human axonStep 3: explain
The human axon is myelinated, so depolarisation happens only at the nodes of Ranvier.
67 times wider, yet 3.6 times slower, because saltatory conduction beats widthwidth does help — it is just a far weaker effect than myelination
💡 Exam tip
Name the process: saltatory conduction, and say the impulse jumps between nodes of Ranvier.
Explain the diameter effect with the word resistance. Wider means less resistance.
Set out Pearson’s calculation in a table of totals first. Most lost marks are arithmetic, not method.
Give r to three significant figures and remember it has no units.
Describe a correlation with both direction (positive or negative) and strength (how close to 1).
Never write that a correlation proves anything. Say it supports a relationship.
⚠ Common mix-up
Thinking myelin slows the impulse. Insulation speeds it up, because fewer stretches of membrane have to depolarise.
Saying the impulse physically jumps through the air. The depolarisation skips the insulated sections; nothing leaves the cell.
Treating correlation as causation. A strong r still does not prove that one variable causes the other.
Comparing two graphs without checking the axes. Different scales make very different data look similar.
Confusing r with R2. R2 is r squared, so it is never negative.
Using Pearson’s test on unsuitable data. It needs quantitative, normally distributed values.
Forgetting to square the sums correctly. Σx2 means square then total; (Σx)2 means total then square.
Up next: Synapses — what happens when the impulse reaches the end of the axon and finds a gap it cannot cross.
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