Database Reference
In-Depth Information
SIDEBAR: HOW ANOVA IS WORKING UNDER THE HOOD—cont'd
(2
.
25−3
.
39) =−1
.
14
(4
.
38−3
.
39) =0
.
99
(4
.
50−3
.
39) =1
.
11
(3
.
04−3
.
39) =−0
.
35
(2
.
74−3
.
39) =−0
.
65
These differences add to −0.04, a value near zero, and if we took a weighted average, based on
the slightly different sample sizes of the columns, we would get exactly zero (except for any round-
ing error). But, obviously, the ive column means don't have zero difference! So, adding up the
differences (with or without using a weighted average) is not a useful way to measure how different
the column means are from one another.
Thus, we need to get a bit more inventive in getting a measure of how different the column means
are (n.b.: it involves squaring the differences, so that they accumulate, rather than cancel out). After
that, we still need to ind the right way to “put it all together”—incorporate the differences among the
individual data values and the samples sizes used. Oy! Forget it! You don't want any more detail. The
only other thing we will mention is that the appropriate test is not a t-test, but what we can mathemati-
cally prove is called an “F-test.” The F-distribution is a probability curve that does not look like a
normal curve—indeed, it's not even symmetric—but it is based on the individual data points following
a normal curve, and can be deined in terms of a function of a normal curve.
We repeat that, since the “
p
-value says it all,” some of the even sketchy details we gave you in
the last couple of paragraphs are not crucial for you to “master.” Of course, this is true as long as
you believe what we tell you and show you. Trust us!! It is!!
6.4
THE ANALYSES
6.4.1
EXCEL
First, import your data into Excel. Then go to the “data” column on the main menu
of Excel and click on “Data Analysis”—which you have activated as discussed in
Chapter 1. Then highlight “Anova: Single Factor” (see arrow in
Figure 6.1
).
Now, we click on the highlighted command (or the “OK”) and consider the dialog
box that comes up. Fill in the location of each “variable”—i.e., tell Excel where the
data values are located. See
Figure 6.2
.
Note that we requested that the output be put on a new worksheet (i.e., page!!)
that we arbitrarily named “abbyj.” See vertical arrow in
Figure 6.2
.
SIDEBAR: KEEP
'
EM TOGETHER IN EXCEL
It can be seen in
Figure 6.2
that we have indicated that the input data values are from A1 to E28 (n.b.: We
need to use “E28” even though column E has only 23 values, to assure that the 28 values in column A are
included—Excel will realize that other columns have fewer data points. See dashed arrow in
Figure 6.2
.
Keep in mind that in Excel, when conducting an ANOVA, all columns of data need to be contiguous
(immediately next to each other). When you type “a1:e28” (you can use either small letters or capital let-
ters), Excel knows that you have data in the block denoted by columns A through E, and whatever rows
are illed in. Had there been labels atop each column (such as “age-group 1,” “age-group 2,” etc., so that
the data started in row 2 and ended in row 29—column A ending in row 29), we would have indicated
“a1:e29,” and checked off “Labels in First Row”—see horizontal (solid) arrow in
Figure 6.2
.
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