106 Chapter 5
5. t Distribution
The probability density function below is a popular topic in statistics.
When the probability density function for x looks like this, we say, “x follows a t distribu-
tion with n degrees of freedom.”
Here is a case with 5 degrees of freedom:
6. F distribution
The probability density function below is a popular topic in statistics.
When the probability density function for x looks like this, we say, “x follows an F distri-
bution with the first degree of freedom m and the second degree of freedom n.”
ƒ(x) =
− 1
df + 1
2
∫
∞
x
0
e
–x
dx
√df × �
× ∫
∞
x
0
e
–x
dx
×
(
1 +
x
2
df
)
−
df + 1
2
− 1
df
2
0−2−4−6 2 4 6
0.6
0.5
0.4
0.3
0.2
0.1
0
when x > 0:
when x ≤ 0: ƒ(x) = 0
first df
2
∫
∞
x
0
e
–x
dx
− 1
2
first df +
second df
( )
( )
× (first df)
second df
2
× (second df)
×
x
− 1
first df
2
(first df × x + second df)
∫
∞
x
0
e
–x
dx
( )
∫
∞
x
0
e
–x
dx
( )
− 1
second df
2
×
− 1
first df
2
2
first df +
second df
( )
ƒ(x) =
Let's Obtain the Probability 107
Here is a case in which the first degree of freedom is 10 and the second degree of
freedom is 5:
7. Distributions and Excel
Until the rise of personal computers (roughly speaking, around the beginning of the 1990s),
it was difficult for an individual to calculate the probability without tables of standard normal
distribution or chi-square distribution. However, these tables of distribution are not used
much anymore—you can use Excel functions to find the same values as the ones provided
by the tables. This enables individuals to calculate even more types of values than the ones
found in the tables of distribution. Table 5-1 summarizes Excel functions related to various
distributions. (Refer to the appendix on page 191 for more information on making calcula-
tions with Excel.)
Table 5-1: Excel functions related to various distributions
*
The probability density function for normal distribution is affected by the mean and standard deviation. Thus, it is impos-
sible to make a “table of normal distribution,” and no such thing exists in this world. However, by using Excel, you can
conveniently calculate the values and make a table relevant to the normal distribution.
0 2 4 6 8 10
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Distribution Functions Feature of the function
normal
*
normal
standard normal
standard normal
chi-square
chi-square
t
t
F
F
NORMDIST
NORMINV
NORMSDIST
NORMSINV
CHIDIST
CHIINV
TDIST
TINV
FDIST
FINV
Calculates the probability that corresponds to a point on the horizontal axis.
Calculates a point on the horizontal axis that corresponds to the probability.
Calculates the probability that corresponds to a point on the horizontal axis.
Calculates a point on the horizontal axis that corresponds to the probability.
Calculates the probability that corresponds to a point on the horizontal axis.
Calculates a point on the horizontal axis that corresponds to the probability.
Calculates the probability that corresponds to a point on the horizontal axis.
Calculates a point on the horizontal axis that corresponds to the probability.
Calculates the probability that corresponds to a point on the horizontal axis.
Calculates a point on the horizontal axis that corresponds to the probability.
Get The Manga Guide to Statistics now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
