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Variables, controls, and what an experiment can actually show

An investigation is a machine for ruling things out. The levels you choose, the quantities you refuse to let move, the tube with nothing interesting in it — each one closes off a way the result could have been produced by something other than the thing you were testing.

Before this Measuring with a ruler, balance, thermometer and timer · Reading a line graph

What you should be able to do

• Name the independent, dependent and controlled variables in an investigation you have not seen before, and justify the levels chosen.
• Distinguish a control variable from a control experiment, and say which of the two a question is asking about.
• Explain what a negative control rules out and what a positive control rules out, and why those are different jobs.
• Identify a confounding variable and explain why repeating the measurement does not deal with it.
• Set out the evidence that would raise a correlation to a causal claim.
• Use validity, accuracy, precision, repeatability and reproducibility to mean five different things.

Three kinds of variable, and only one of them moves

Every investigation has one quantity you change on purpose, one you measure to see what happened, and a list you go to some trouble to keep still. Those three are the first mark on almost every practical question, and the wording matters: examiners want each variable named with the unit it is measured in.

Independent variable

The quantity you change on purpose, and the only one that should differ between your treatments. It goes on the horizontal axis.

Dependent variable

The quantity you measure, whose value depends on the independent variable. It goes on the vertical axis.

Control variable

A quantity held the same across every treatment, so that it cannot be the reason the dependent variable changed.

Control experiment

An extra run of the method, differing in one deliberate way, done to rule out an explanation the main runs cannot rule out on their own.

Choosing the levels of the independent variable is a real decision and it is examined. Five levels is the usual minimum for anything you intend to draw a curve through, because four points can be joined by a straight line that a fifth would have refused. Space them across a range wide enough to contain whatever is interesting: an enzyme investigation that runs from 30 °C to 40 °C will produce a rising line and will miss the optimum entirely.

Whether the independent variable is categoric or continuous decides how the results are drawn. Species of plant and brand of antiseptic are categories, and categories get a bar chart with gaps between the bars. Temperature, concentration and time are continuous, and get a line or scatter graph. A bar chart of a continuous variable throws away the shape of the relationship, which is usually what the question was about.

Controlled variables are the ones that go wrong quietly. You cannot list every quantity in the universe, so list the ones that plausibly affect your dependent variable, and say how each was held rather than that it was. 'Temperature was controlled' scores nothing; 'each tube was held in a water bath at 35 °C for five minutes before the reaction was started' scores, because it describes something somebody could repeat.

A control variable is not a control experiment

Once the controlled variables are pinned, there is still a question the main runs cannot answer: would the result have appeared anyway? That is what a control experiment is for, and there are two of them doing opposite jobs.

A negative control is the run in which the factor you are testing has been removed or destroyed, with everything else left exactly as it was. Boiled enzyme, distilled water in place of the extract, an agar disc soaked in nothing but the solvent. If the effect shows up in the negative control, the effect was never yours: the apparatus, the solvent or the handling produced it. A negative control guards against a false positive.

A positive control uses something already known to produce the effect: a disc of an antibiotic the organism is sensitive to, a glucose solution in a set of Benedict's tests. If it shows nothing, the method failed and the flat readings from your real samples mean nothing at all. A positive control guards against a false negative.

That is why one cannot stand in for the other. Test six plant extracts for antibacterial activity, get no zones anywhere, and a blank solvent disc showing nothing is exactly what you wanted — but a lawn that never grew, discs that never dried and a cold incubator would all produce the same picture. Only a disc of a known antibiotic tells the two apart.

Confounding: when one change is really two

A confounding variable is one that changes along with your independent variable and could produce the same effect on its own. It is the most serious fault an investigation can have, because it does not show up as scatter, an anomaly or a disappointing result. It shows up as a clean, convincing graph of the wrong thing.

The pondweed and the lamp is the standard case. Move the lamp closer and the light intensity rises — and so does the temperature of the water, because a filament lamp is mostly a heater. Oxygen production rises. You cannot tell from the readings whether it rose because of the light or because of the warmth, and no number of repeats will separate them, because every repeat changes both things together in exactly the same way. The fix is in the design: put a heat shield of water between the lamp and the beaker, or use an LED source, and then measure the temperature to show it stayed put.

It is also what makes some biological questions genuinely hard. Ask whether people who eat oily fish have fewer heart attacks and you are also asking about people who can afford oily fish, who cook at home, who were told by a doctor to change their diet. Ruling those out means measuring them and comparing people who match on them, which is why an epidemiological paper spends most of its length on adjustment and a paragraph on the result.

Confounding variable

A variable that changes with the independent variable and could itself explain the change in the dependent variable, so the two effects cannot be separated by the data collected.

Randomisation

Assigning subjects or sample positions by chance rather than by choice, so that variables nobody thought of are spread evenly between the groups.

Randomisation is the general answer to the confounders nobody thought of. Assign which leaf disc goes into which concentration by drawing lots rather than by picking, and the discs that happen to be thicker, older or nearer the midrib are spread across every treatment instead of piling into one.

Correlation and causation, argued rather than asserted

'Correlation does not imply causation' is true and not much use on its own, because half of biology consists of causal claims built out of correlations. Smoking causes lung cancer. Nobody has ever run the experiment that would settle it — assigning people at random to smoke twenty a day for thirty years is not something anyone will do — and the claim is as secure as anything in medicine. The useful question is what has to be added to a correlation before it will carry a causal claim.

Correlation

A relationship in which two variables tend to change together. It may be positive, negative or absent, and it makes no claim about which variable moved first.

Causation

A relationship in which changing one variable changes the other. It cannot be read off a scatter graph.

Three things produce correlations with no causal link between the variables plotted. A common cause may sit behind both, as the summer sits behind ice cream sales and drowning deaths. The arrow may run the other way — reverse causation — as when a nutrient is low in people with a disease because the disease stopped them absorbing it. And with enough variables plotted against enough others, some pairs correlate by coincidence, which is why a relationship found by trawling data has to be tested on a fresh set.

What raises a correlation towards a causal claim is a stack of separate arguments, none of them decisive alone:

An A-level answer does not need all six. It needs you to stop writing 'correlation is not causation' as though it were a conclusion, and start naming which of the three alternatives you are worried about and what would settle it.

Five words that are not synonyms

Validity, accuracy, precision, repeatability and reproducibility get used interchangeably in ordinary speech and are worth separate marks in an exam. They also fail in different ways, so knowing which one you have lost tells you what to change.

Valid

A measurement is valid if it measures what it claims to measure; an investigation is valid if its design allows its conclusion to follow. A confounding variable destroys validity however careful the measuring was.

Accurate

Close to the true value.

Precise

Repeat readings close to one another. Precision says nothing at all about being right.

Repeatable

The same person, using the same method and the same apparatus, gets the same results again.

Reproducible

Somebody else, or the same person using different apparatus or a different method, gets the same results.

Resolution

The smallest change an instrument can register — 0.01 g on a three-decimal-place balance, 1 mm on a metre rule.

The two kinds of error map onto two of those words. A random error scatters readings above and below the true value — judging a meniscus, starting a stopclock late, tissue that was not quite identical. It damages precision, and a mean of several repeats reduces its effect because the scatter partly cancels. A systematic error shifts every reading the same way: a balance that was not zeroed, a thermometer reading 2 °C high, a bubble in a burette tip. It damages accuracy, and repeating the measurement a hundred times gives a hundred readings wrong by the same amount. That is the bottom left target, and it is why precision is no evidence of accuracy.

Reliability is the word to be careful with. Boards use it loosely to mean that repeats agree, and a mark scheme will accept it, but repeatable and reproducible are sharper and cost nothing. An anomaly is a reading that does not fit the pattern the others make: identify it, say so, and leave it out of the mean only with a reason — the bubble in the tube, the sample that was dropped. Discarding a point because it spoils the line is not data handling, and an unexplained exclusion loses the mark.

What the experiment can actually show

The last step of a good write-up is the one most often skipped: saying what the result does not cover. A conclusion that reaches further than the data is wrong even when the data are perfect.

Your result holds over the range you tested and for the material you used. If your temperatures ran from 20 °C to 50 °C you know nothing about 60 °C, and reading a value off an extended line — extrapolation — is guesswork with a ruler, while reading between two measured points is interpolation and is fine. Catalase from potato is not catalase from liver, and cultured cells are not tissue, so name the organism and the tissue.

It describes what happened, not why. An investigation showing that rate falls above 45 °C shows that rate falls above 45 °C; denaturation is an explanation brought to it from elsewhere, and the honest sentence says 'this is consistent with the enzyme denaturing' rather than 'this shows the enzyme denatured'.

And it holds for the sample you took. Five leaf discs from one leaf tell you about that leaf. Extending the claim to the plant or the species needs a sample drawn to represent them, which is a decision made before any measuring starts and cannot be repaired afterwards.

In the exam

• Name the variables with their units. 'Temperature in degrees Celsius' and 'volume of oxygen in cm³' score; 'temperature' and 'the gas' do not.
• When a question asks how a variable was controlled, describe the method — a water bath at a stated temperature, a buffer at a stated pH, tissue cut with the same cork borer. The mark is for the technique, not the intention.
• Read 'control' carefully. Control variable wants a quantity held constant; control experiment wants a run of the method with something deliberately removed or deliberately known to work.
• 'Suggest why this conclusion may not be valid' almost always points at a confounding variable or at a sample too narrow to support the claim. Say which, and name it.
• Never answer an evaluation question with 'repeat it more times'. Repeats improve precision and do nothing for a systematic error or a confounder.
• Precision and accuracy carry separate marks. Describing readings that agree closely earns the precision mark and leaves the accuracy one still to be earned.

Questions

Written to the command words the boards use. Try them on paper before opening a scheme: the marks go to points made, not to length.

Handling data: units, scales, rates and uncertainty →