this week's discussion board, I found a peer reviewed article published
by Journal of Statistics Education. The article, written byNicholas P. Maxwell, University of Washington, uses a flipping coin exercise to introduce p-value.
The p-value can be introduced with a coin flipping exercise. One
person, A, flips a coin ten times and has the other, B, call each flip. B
records his thoughts after each flip. A reports that the caller calls
every flip correctly. In this exercise B intuitively rejects a null
hypothesis because the p-value is too small. B is reassured to learn
from this concrete example that they intuitively followed the logic of
statistical inference before they studied statistics.
The meaning of the p-value is essential for understanding
statistical inference. Nonetheless, many people have trouble keeping
track of what a p-value is. It is common to confuse the p-value with the
probability that the null hypothesis is right, or with the probability
that the alternative, experimental hypothesis is wrong (Phillips 1971, p. 80; Freedman et al. 1991, p. 435).
Popham and Sirotnik (1992) provide a compelling example of an intuition that follows the logic of statistical inference. They write:
Joe and June are betting for cups of coffee on the basis of a tossed
coin, with the loser buying. Joe does all the coin flipping, and June
decides to call tails every time, figuring to win approximately half of
the cups of coffee. If the coin turns up heads ten times in a row, June
... might begin to suspect that there is something suspicious about the
coin -- or the person flipping it! (Popham and Sirotnik 1992, p. 48)
can follow this story, even without a background in statistics or
probability. This example can be brought into the classroom, and
students can be placed in June's position. They can see for themselves
that, like June, they would reject an idea when something happens that
would have been very unlikely had the idea been true.
Maxwell uses a classroom version of Popham and Sirotnik's (1992)
example. To introduce statistical inference, he flips a coin ten times
and has a student call each flip. After each flip, he reports how the
caller did and then ask the class to record their thoughts about what is
happening. While the students record their thoughts, he records on the
blackboard whether the caller was correct, leaving space to add the
students' thoughts later. The trick for teaching statistical inference
is that he lies: He reports that the caller calls every flip correctly.
Initially, this is a fairly bland exercise, but as the caller
succeeds in calling correctly three flips, four flips, and then five
flips, the class gets extremely agitated very quickly. Some students get
so excited that he must ask them to be quiet to allow others to write
down their thoughts as the exercise progresses. During the exercise, he
tries to act surprised, but it is not necessary to do a great acting
job. The exercise depends on the students figuring out that something
funny is going on, so if his expression betrays the ruse, no harm is
done. After the last flip, he asks the students what they thought and
when they thought it, and he writes their thoughts about each flip on
So, what can we conclude about what was happening? The students report
that they concluded that he was lying or that he had prearranged some
sort of magic trick with the caller. "Why did you make that conclusion?"
They report that they made this conclusion because there is too small a
chance that the caller could call ten coin flips in a row correctly.
When pressed, they report that, assuming it is a fair coin, and assuming
that he's not lying, and assuming that the caller is not telepathic,
then it is extremely unlikely that the caller would call ten flips
correctly. He asks, "Seeing that there are several aspects to your
initial conception of what was happening, what is the best way to
summarize your conclusions?" Most agree (with some prompting) that all
they can conclude from the experiment itself is that at least one aspect
of their initial conception is likely to have been false; to reach a
final conclusion, they have to consider what they know about each of the
assumptions to decide which to discard.
He points out that they started with a particular idea of what was
going on: the idea was that it was a fair coin, that the caller was not
clairvoyant, and that he was reporting the caller's successes honestly.
He explains that an initial conception of what is going on is called the
"null hypothesis," that the probability of the results occurring, if
the null hypothesis is true, is called the "p-value," and that the
cut-off used to decide whether to reject the null hypothesis is called
Professor Maxwell uses this exercise just before introducing
significance testing and then refers back to it throughout the course
whenever students seem to have lost track of what the p-value is.
Because the exercise is very memorable, it takes only brief reminders to
bring students back to a clear understanding of the p-value.
i would like someone to read this paper and write a one page paper based on their own insight and experience regarding this topic