How a Cup of Tea Laid the Foundations for Modern Statistical Analysis

In the early 1920s, a trio of scientists sat down for a interruption astatine Rothamsted cultivation probe presumption successful Hertfordshire, UK. One of them, a statistician by the sanction of Ronald Fisher, poured a cupful of tea, past offered it to his workfellow Muriel Bristol, an algae specializer who would aboriginal person the works C. muriella named aft her. Bristol refused, arsenic she liked to enactment the beverage successful earlier the tea. Fisher was skeptical. Surely it didn’t matter? Yes, she said, it did. A cupful with beverage poured archetypal tasted better.

“Let’s trial her,” chipped successful the 3rd scientist, who besides happened to beryllium Bristol’s fiancé. That raised the question of however to measure her tasting abilities. They would request to marque definite she was fixed some types of tea, truthful she could marque a just comparison. They settled connected pouring respective cups, immoderate tea-then-milk and others milk-then-tea, past getting her to effort them 1 astatine a time. But determination were inactive a mates of problems. Bristol mightiness effort to expect the series they’d chosen, which meant cups needed to get successful a genuinely random order. And adjacent if the ordering was random, she mightiness get a fewer close by chance. So determination would request to beryllium capable cups to guarantee this was sufficiently unlikely.

Fisher realized that if they gave her six cups—three with beverage archetypal and 3 with beverage second—there were 20 antithetic ways they could beryllium randomly ordered. Therefore, if she simply guessed, 1 successful 20 times she’d get each six correct. What astir utilizing 8 cups instead? In this situation, Fisher calculated determination were 70 imaginable combinations, meaning determination was a 1 successful 70—or 1.4 percent—probability she’d get the series close by sheer luck. This was the experimentation they decided to tally with Bristol. They poured 8 cups, 4 of each type, and got her to trial them successful a random order. She named the 4 she preferred, and the 4 she disliked, past they compared her conclusions with the existent pattern. She’d got each 8 correct.

The crushed for Bristol’s occurrence was yet down to chemistry. In 2008, the Royal Society of Chemistry reported that tea-then-milk volition springiness the beverage a much burnt flavour. “If beverage is poured into blistery tea, idiosyncratic drops abstracted from the bulk of the beverage and travel into interaction with the precocious temperatures of the beverage for capable clip for important denaturation to occur,” they noted. “This is overmuch little apt to hap if blistery h2o is added to the milk.”

Fisher aboriginal described the tea-tasting experimentation successful a 1935 publication titled simply The Design of Experiments. Among different things, the publication summarized the important techniques they’d pioneered successful that Rothamsted beverage room. One was the value of randomization; it wouldn’t person been a rigorous trial of Bristol’s quality if the ordering of the cups was someway predictable. Another was however to get astatine a technological conclusion. Fisher’s basal statistical look was simple: commencement with an archetypal theory—he called it the “null hypothesis”—then trial it against data. In the Rothamsted beverage room, Fisher’s null proposal had been that Bristol couldn’t archer the quality betwixt tea-then-milk and milk-then-tea. Her occurrence successful the resulting experimentation showed Fisher had bully crushed to discard his null hypothesis.

But what if she’d lone got 7 retired of 8 correct? Or six, oregon five? Would that mean the null proposal was close and she couldn’t archer the quality astatine all? According to Fisher, the reply was no. “It should beryllium noted that the null proposal is ne'er proved oregon established, but is perchance disproved, successful the people of experimentation,” helium aboriginal wrote. “Every experimentation whitethorn beryllium said to beryllium lone successful bid to springiness the facts a accidental of disproving the null hypothesis.” If Bristol had got 1 oregon 2 wrong, it didn’t needfully mean she had zero quality to separate beverage order. It conscionable meant the experimentation hadn’t provided beardown capable grounds to cull Fisher’s archetypal presumption that it made nary difference.

If Fisher wanted experiments to situation null hypotheses, helium needed to determine wherever to acceptable the line. Statistical findings person traditionally been deemed “significant” if the probability of obtaining a effect that utmost by accidental (i.e. the p-value) is little than 5 percent. But wherefore did a p-value of 5 percent go specified a fashionable threshold?