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Suppose a friend says they can taste the difference between two brands of cola. How would you test that fairly? Ronald Fisher asked almost exactly this question about a cup of tea, and his answer became the basis of how scientists design experiments, from crop trials to medical studies. This post covers who he was, his tea-tasting example worked through with combinations, and why random order matters.
Who was Ronald Fisher?
Fisher was born in London on 17 February 1890 and died in Adelaide, Australia, on 29 July 1962, according to his MacTutor biography. He studied mathematics at Cambridge, graduating in 1912. Poor eyesight kept him out of the army in 1914, and he taught mathematics and physics in schools until 1919.
That year he was offered two jobs at once and chose to become statistician at the Rothamsted Agricultural Experiment Station rather than work for Karl Pearson. At Rothamsted he introduced randomisation and the analysis of variance into the design of experiments. His book Statistical Methods for Research Workers (1925) ran to many editions, and he published The Design of Experiments in 1935. He later held professorships in London and Cambridge, and received the Royal Society's Copley Medal in 1955. His honorary degrees included ones from the University of Calcutta (1938) and the Indian Statistical Institute (1962).
There is a darker side. MacTutor records that Fisher was an active supporter of eugenics from his student years and proposed social policies based on it. His statistical methods remain in use; his social views are a reminder that skill in one field is not authority in another.
What was the lady tasting tea?
Chapter II of The Design of Experiments begins with a lady who "declares that by tasting a cup of tea made with milk she can discriminate whether the milk or the tea infusion was first added to the cup". Fisher's test: mix eight cups, four each way, and present them in random order. She is told the plan and must divide the cups into two groups of four.
How likely is a perfect score by luck? A worked example
This uses only the combinations from Class 11, listed in Unit 4 of the JEE (Main) 2026 syllabus.
She must pick which 4 of the 8 cups had milk first. The number of ways is 8C4 = (8 × 7 × 6 × 5)/(4 × 3 × 2 × 1) = 1680/24 = 70.
Only one of those 70 choices is fully correct. Someone with no ability gets all eight right with probability 1/70, about 0.014.
What if she gets 3 of each kind right and 1 wrong? She has chosen 3 of the 4 correct cups and 1 of the 4 wrong ones: 4C3 × 4C1 = 4 × 4 = 16 ways. So the chance of doing at least that well by guessing is (16 + 1)/70 = 17/70, about 0.24. That is not convincing evidence.
Fisher also shows why 6 cups are too few. With 3 of each kind there are only 6C3 = 20 ways, so a guesser gets everything right 5 times in 100. He notes that experimenters usually take 5 per cent, or 1 in 20, as a standard for significance. If you want to ignore results that luck produces that often, 6 cups are useless.
Why does random order matter?
Fisher points out that the cups can never be identical. They may differ in thickness, in the amount of milk, in the strength of the tea or in temperature. In his words, "the uncontrolled causes which may influence the result are always strictly innumerable". If, say, all the milk-first cups also had sugar, she could sort by sweetness and the 1 in 70 calculation would be meaningless.
Making everything equal is impossible. Randomising the order is his solution: whatever differences remain are then spread by chance, not by anyone's choice, so the probability calculation stays valid. The same idea is why fertiliser trials assign treatments to plots at random, and why medical trials assign patients to groups at random.
Common mistakes when designing a test
Too few trials. As the 6-cup case shows, a small experiment may be unable to give convincing evidence even if the claim is true.
Letting someone choose the order. Human choices follow patterns, which can line up with the thing being tested.
Changing one factor at a time. MacTutor notes that Fisher's designs, which vary several factors together and separate their effects with statistics, were more efficient than the older one-at-a-time approach.
Deciding what counts as success afterwards. Fix your criterion before collecting data.
You can try a fair-test design at home with our kitchen science experiments, and see an earlier example of careful counting in our post on Mendel's pea experiments. If permutations and combinations still feel shaky, the Fermi Concept Library covers every concept in mathematics, each with its own lesson.
What can a student take from Fisher's way of working?
Turn a vague claim into a test. "I can taste it" became eight cups, four of each, in random order, with a rule for what counts as success.
Count before you conclude. The 1 in 70 figure is what makes a perfect score meaningful. A result means little until you know how often luck alone would produce it.
Accept that you cannot control everything. Use randomness to protect your conclusions.
Design an eight-cup taste test for a claim someone in your family makes, and work out the 1 in 70 before you start.
