“Lady Tasting Coff ee” by Maynard, Mulcahy & Kermick Page
by
Jacinth Maynard, Department of Mathematics, Lock Haven University of Pennsylvania
Mary Puterbaugh Mulcahy, Division of Biological and Health Sciences, University of Pittsburgh at Bradford
Daniel Kermick, Division of Biological and Health Sciences, University at Pittsburgh at Bradford
Part I – Co! ee Shop Wager
Characters
Model—an attractive young woman with impeccable taste, working as a successful model for an advertising fi rm.
Escort—a tall, dark and handsome young man, working as a marketing and survey researcher for the same
advertising fi rm.
Older Gentleman—an adjunct professor of biostatistics at a local college and a coff ee house regular; dressed in
slightly-aged tweed jacket.
Setting
# e red sports car makes a quick stop in front of the Philadelphia coff eehouse after an evening on the town. A
sleek model and her tall, dark, and handsome escort gracefully exit the car and approach the counter where
the escort purchases two cups of house coff ee. At the condiments table, the escort proceeds to pour milk into
the two coff ees, and the following dialogue results.
Dialogue
Lady Tasting Coffee:
A Case Study in Experimental Design
Model: Oh, no. I’ll need a fresh cup.
Escort: You like milk in your coff ee, right?
Model: Yes, I like milk in my coff ee, but only, and I say only, if it is added
to the cup fi rst.
Escort (laughing): Oh, come on, that’s ridiculous; you can’t possibly tell the diff erence.
Coff ee is coff ee whether you add the milk fi rst or second.
Model: Of course I can tell the diff erence; you’ve no right to laugh at me.
Older Gentleman: Pardon me for overhearing your conversation. Actually, the lady
may be able to tell the diff erence.
Escort: You’re kidding me, right?
Older Gentleman: Such claims have been made before. A woman made that claim at
an afternoon tea party in Cambridge in the s. She stated that
“Lady Tasting Coff ee” by Maynard, Mulcahy & Kermick Page
she could always tell whether milk was added before or after the tea was
poured in the cup. # e famous statistician Sir Ronald Fisher was at high
tea* that afternoon and immediately designed an experiment to test the
woman’s palate. Rumor has it that she shocked the guests because she
correctly told Sir Fisher whether milk had been added fi rst or second
after tasting multiple cups of tea. # e event became famous because Sir
Fisher used it to explain the basics of experimental design in one of the
fi rst textbooks ever published on the topic.
Escort: Well that’s a good story, but it also sounds suspiciously like a story
with no basis in reality, invented by an imaginative professor writing a
textbook. You certainly haven’t convinced me to buy the lady another
cup of coff ee.
Older Gentleman: From what I’ve read, it was a real event, and furthermore, humans have
very sensitive taste buds. I think she deserves a new cup.
Model: Now that the coff ee is cold, I certainly deserve a fresh cup.
Older Gentleman: Ma’am I fully agree. In fact, I think you deserve several cups of fresh
coff ee! Let’s set up our own experiment to determine whether this lady
can or can not discern whether milk was added to the cup before or after
the coff ee.
Model: How fun! Yes, let’s see who is right with our own tea test, I mean coff ee
test.
Older Gentleman: Clever pun, ma’am. You know the real student’s t-test was developed
in the early s by a taste tester of sorts at the Guinness Brewery in
Dublin, Ireland. Only he wasn’t tasting tea either. Sir, are you a gambling
man? How about a wager? If our experiment shows that she can tell
the diff erence, you will pay for the coff ee. If the experiment does not
demonstrate her discerning palate, I will pay for the fresh cups.
Escort: You’re on! But I want the rules hashed out before she starts sipping. I
mean, how many cups are we talking about? And what if she’s wrong for
just a few cups? I don’t want to pay for the coff ee just because she is a
good guesser.
Older Gentleman: Fisher would agree completely. Even the smallest experiment requires
forethought and planning. You must tell me, sir, just how sure do you
want to be that she isn’t guessing?
*Going all the way back to the s, many English people have enjoyed an afternoon tea. # e phrase “high
tea” refers to that traditional practice of people gathering in the late afternoon to drink tea, usually served with
some sort of meat, bread, crackers, or other food.
“Lady Tasting Coff ee” by Maynard, Mulcahy & Kermick Page
Questions
Imagine that you are going to design and perform the experiment described in the dialogue.
. What is the hypothesis that will be tested in this experiment?
. Why is it important to off er the model more than just two cups (one with the milk added fi rst and one
with the milk added second)? Explain your answer.
. How many cups of coff ee should the model taste? Explain your answer.
. Describe exactly how the cups should be prepared. Does every cup need to be exactly the same in every
way except the order of the addition of milk and coff ee? Can you actually make every cup identical?
Explain your answer fully.
. In what order should the cups be presented? What method or decision rules might you use to decide
which cup is to be off ered fi rst, second, etc.?
. How do you recommend that the characters decide if the model is able to tell whether the milk was
added to the cup before or after the coff ee? (In other words, how many cups does she have to correctly
evaluate for you to conclude that she really can tell the diff erence?) Explain your choice.
. Without looking it up in a textbook or online, provide your own defi nition of “experimental design.”
“Lady Tasting Coff ee” by Maynard, Mulcahy & Kermick Page
Part II – Tasting Tea
Read Fisher’s essay entitled “Mathematics of a Lady Tasting Tea,” available online at
http://legacy.library.ucsf.edu/tid/fqie/pdf; then answer the questions below.
Questions
# e questions below ask you to compare your answers from Part I to the explanations found in Fisher’s essay.
. Referring to your answers to the questions in Part I, was the hypothesis you chose diff erent than the
null hypothesis given by Fisher in his essay? Explain your answer.
. What reason did you give for why it is important to off er the model more than just two cups (one
with the milk added fi rst and one with the milk added second)? Was your answer the same as Fisher’s
answer? Based on the essay, please describe Fisher’s answer to this question.
. How many cups did you say the model would taste? How many cups did Fisher say that the “tea
lady” in the story should taste? Please describe fully Fisher’s answer to this question, including any
mathematical considerations. Was your answer the same as Fisher’s answer? If not, how is it diff erent?
. Before reading Fisher’s essay, did you think that every cup needed to be exactly the same in every way
except the order of the addition of milk and coff ee? Does Fisher believe that every cup should be
prepared identically? Describe Fisher’s explanation for how to deal with uncontrollable variation among
cups.
. Before reading Fisher’s essay, what method did you recommend for choosing the order that the cups
should be presented? Was your answer diff erent than what Fisher recommends in his essay? Please
describe Fisher’s explanation for how to choose the cup order.
. In Part I, you answered the question of how one should decide if the model is able to tell whether the
milk was added to the cup before or after the coff ee. (In other words, how many cups does she have to
correctly evaluate for you to conclude that she really can tell the diff erence?) Compare your answer to
Fisher’s answer and then describe Fisher’s answer fully.
. Your instructor will provide you with a textbook defi nition of experimental design. Was your defi nition
complete? Your answers to all of the questions in Part I probably diff ered in small or large ways from
Fisher’s proposed design of a tea tasting experiment. Are there any diff erences that changed your
perception of statistics and experimental design? If yes, describe how Fisher’s essay enlightened you.
Even if you did not fi nd that Fisher’s essay changed your views, make a short summary list of the
important design concepts that you think are emphasized in Fisher’s essay.
. Following the guidance of your instructor, use Part III of the story or, alternatively, if your instructor
has provided materials, set up a mock event similar to the tea tasting experiment. Instead of tea, you
might consider seeing if your classmates can tell the diff erence between and milk, between two
brands of bottled water, between two brands of fl avored diet or regular soda, or some other simple taste
comparison. Adhere to the principles of Fisher’s paper, and draw conclusions based on your results,
using Fisher’s rules.
. Rumor has it that the real lady who had tea with Fisher on an afternoon in the s was able to
accurately tell whether the milk was added fi rst or second every single time she was off ered a new cup.
Can you conclude from her success that most people can tell the diff erence between milk-fi rst and teafi rst cups? Briefl y describe the design of an experiment that would test this broader question.
“Lady Tasting Coff ee” by Maynard, Mulcahy & Kermick Page
Part III – Tasting Co! ee
Setting
# e escort and the older gentleman prepared four cups of coff ee to which they added the milk fi rst and four
cups of coff ee in which they added the milk second. # e two men attempted to make sure that the cups were
identically prepared as much as possible in terms of the amount of coff ee, milk, etc. By writing the numbers
– on slips of paper and pulling the numbers out of the hat, the escort and older gentleman randomly decided
that cups #, , , and would be prepared with the milk added fi rst and cups #, , , and would be
prepared with the coff ee added fi rst. # e model has just fi nished sipping all cups (presented in order –), and
she has written down her decision.
Dialogue
Older Gentleman: Are we all in agreement that we will use Fisher’s rules for deciding
the conclusion for the experiment?
Escort: Yes, we are. Please tell us which cups you think had the milk added fi rst.
Model
(smiling broadly): It is so obvious that cups #, , , and had the milk fi rst.
Older Gentleman: Are you sure? Is this your fi nal answer?
Model: Yes, those are the cups that had the milk added fi rst.
Escort: Ha! Based on Fisher’s rules, you can’t really tell the diff erence! # e
milk was added fi rst to cups #, , , and . Hot dog, mister! YOU
will have to pay for the cups!
Model: But I got of the correct! # at’s pretty good! Who is this Fisher guy
to say I can’t do it?
Older Gentleman: I have to agree ma’am that you may be able to tell the diff erence,
but we did decide beforehand that we would use Fisher’s rules, and
his rules are quite strict. We can only conclude that you can tell the
diff erence if there was less than a chance that your success could
be explained by good guessing.
Model: But I didn’t guess! I really can tell; it seems unfair that you accuse me
of guessing just because I made one mistake!
Escort: We aren’t really accusing you of guessing; the rule is the common
cutoff that is used in many statistical analyses.
Model: Fisher’s rules are too strict. Give me another two cups and, if I get it
right this time, my success rate will be better than the guess rate.
I’ll show you that I really am able to tell the diff erence!
Escort: Hold on! It would be cheating to change the plan now. No more cups.
Please, let’s quit while I’m ahead!
“Lady Tasting Coff ee” by Maynard, Mulcahy & Kermick Page
Case copyright © by the National Center for Case Study Teaching in Science. Originally published August , at
http://www.sciencecases.org/lady_tasting_tea/case.asp.
Please see our usage guidelines, which outline our policy concerning permissible reproduction of this case study.
Questions
. Did the characters correctly follow Fisher’s rules when they concluded that the results do not allow us
to conclude that the woman can tell the diff erence between the two types of cups?
. Do you think the lady really can tell the diff erence between the milk-fi rst versus the milk-second cups?
. Which of the following sentences do you think most accurately and clearly states the conclusion of the
experiment? Propose your own statement if you fi nd fl aws in all of the statements below.
a. # e model cannot tell the diff erence between the milk-fi rst and the milk-second cups.
b. # ere is a or greater chance that the woman guessed her answers.
c. At the level, the model cannot signifi cantly tell the diff erence between the milk-fi rst and the
milk-second cups.
. Would it be acceptable to add two more cups now? Why or why not? What is the value of deciding the
experimental design before you begin an experiment and not changing it in the middle of the experiment?
. Do you think Fisher’s rules are too strict? Why or why not?
a. Would you feel the same way about his rules if we were testing whether a monitor at a nuclear
power plant can really recognize elevated levels of radiation?
b. Would you feel the same way if we were testing whether a new children’s vitamin caused increased
risk of kidney dysfunction?
c. In order to answer these questions better, read the more detailed descriptions of these two
hypothetical experiments given below. For each design, state the null hypothesis. # ere are two
types of mistakes that statisticians can make at the conclusion of a signifi cance test: they can
incorrectly reject a true null hypothesis (Type I error) or they can incorrectly fail to reject a
false null hypothesis (Type II error). # e rule ensures that a Type I error is never made at a
greater rate than , and the likelihood of making a Type I error is often inversely related to the
likelihood of making a Type II error. Type II error rates are usually not controlled in scientifi c
experiments, and can be considerably higher than . For the following two experiments,
what would be the human ethical consequence of making Type I and Type II mistakes in
your conclusion at the end of the experiment? Would you recommend the rule for these
experiments? Why or why not?
i. Nuclear Monitor Experimental Design: # e monitor is exposed to eight environments (four
high and four low radiation levels) and the experimenter records whether the monitor warning
light comes on or not.
ii. Vitamin Experimental Design: Eight children are given a placebo and eight children are given
the new vitamin. Urine from the children is collected and the pH in the urine is monitored and
compared between the two groups. Both high and low pH are indications of kidney dysfunction.
. Return again to the coff ee-tasting experiment. Does the outcome described prove that the model
cannot tell the diff erence between the two types of cups of coff ee?
2-lady_tasting_tea-scientific_method
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