Page 176 - Statistics for Dummies

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Part III: Distributions and the Central Limit Theorem
there is no single “standard t-distribution” that you can use to transform the
numbers and find probabilities on a table. Because it wouldn’t be humanly
possible to create a table of probabilities and corresponding t-values for
every possible t-distribution, statisticians created one table showing certain
values of t-distributions for a selection of degrees of freedom and a selection
of probabilities. This table is called the t-table (it appears in the appendix). In
this section, you find out how to find probabilities, percentiles, and critical
values (for confidence intervals) using the t-table.
Finding probabilities with the t-table
Each row of the t-table (in the appendix) represents a different t-distribution,
classified by its degrees of freedom (df). The columns represent various
common greater-than probabilities, such as 0.40, 0.25, 0.10, and 0.05. The
numbers across a row indicate the values on the t-distribution (the t-values)
corresponding to the greater-than probabilities shown at the top of the
columns. Rows are arranged by degrees of freedom.
Another term for greater-than probability is right-tail probability, which indi-
cates that such probabilities represent areas on the right-most end (tail) of
the t-distribution.
For example, the second row of the t-table is for the t distribution (2 degrees
2
of freedom, pronounced tee sub-two). You see that the second number, 0.816,
is the value on the t distribution whose area to its right (its right-tail probabil-
2
ity) is 0.25 (see the heading for column 2). In other words, the probability that
t is greater than 0.816 equals 0.25. In probability notation, that means p(t >
2 2
0.816) = 0.25.
The next number in row two of the t-table is 1.886, which lies in the 0.10
column. This means the probablity of being greater than 1.886 on the t distri-
2
bution is 0.10. Because 1.886 falls to the right of 0.816, its right-tail probability
is lower.
Figuring percentiles for the t-distribution
You can also use the t-table (in the appendix) to find percentiles for a
t-distribution. A percentile is a number on a distribution whose less-than
probability is the given percentage; for example, the 95th percentile of the
t-distribution with n – 1 degrees of freedom is that value of t whose left-tail
n – 1
(less-than) probability is 0.95 (and whose right-tail probability is 0.05). (See
Chapter 5 for particulars on percentiles.)
Suppose you have a sample of size 10 and you want to find the 95th percentile
of its corresponding t-distribution. You have n – 1= 9 degrees of freedom, so

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