Datasheet

14
Part I: Statistics and Excel: A Marriage Made in Heaven
the total number of events that can happen. In each of the three examples,
the event we were interested in (head, 3, or club) only happens one way.
Things can get a bit more complicated. When you toss a die, what’s the prob-
ability you roll a 3 or a 4? Now you’re talking about two ways the event you’re
interested in can occur, so that’s (1 + 1)/6 =
2
/6 =
1
/3. What about the probabil-
ity of rolling an even number? That has to be 2, 4, or 6, and the probability is
(1 + 1 + 1)/6 =
3
/6 =
1
/2.
On to another kind of probability question. Suppose you roll a die and toss a
coin at the same time. What’s the probability you roll a 3 and the coin comes
up heads? Consider all the possible events that could occur when you roll a
die and toss a coin at the same time. Your outcome could be a head and 1-6,
or a tail and 1-6. That’s a total of 12 possibilities. The head-and-3 combination
can only happen one way. So the answer is
1
/12.
In general the formula for the probability that a particular event occurs is
I began this section by saying that statisticians express their confidence
about their decisions in terms of probability, which is really why I brought
up this topic in the first place. This line of thinking leads us to conditional
probability — the probability that an event occurs given that some other
event occurs. For example, suppose I roll a die, take a look at it (so that you
can’t see it), and I tell you that I’ve rolled an even number. What’s the prob-
ability that I’ve rolled a 2? Ordinarily, the probability of a 2 is
1
/6, but I’ve
narrowed the field. I’ve eliminated the three odd numbers (1, 3, and 5) as pos-
sibilities. In this case, only the three even numbers (2, 4, and 6) are possible,
so now the probability of rolling a 2 is
1
/3.
Exactly how does conditional probability plays into statistical analysis?
Read on.
Inferential Statistics: Testing Hypotheses
In advance of doing a study, a statistician draws up a tentative explanation —
a hypothesis — as to why the data might come out a certain way. After the
study is complete and the sample data are all tabulated, he or she faces the
essential decision a statistician has to make — whether or not to reject the
hypothesis.
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