Page 190 - Intermediate Statistics for Dummies

15_045206 ch09.qxd 2/1/07 10:12 AM Page 169
Chapter 9: Going One-Way with Analysis of Variance
the heart of the ANOVA procedure. This test is the actual hypothesis test of
Ho: µ 1 = µ 2 = . . . = µ k versus Ha: At least two of µ 1 , µ 2 , . . . µ k are different.
You have to carry out three major steps in order to complete the F-test (don’t
get these steps confused with the main ANOVA steps; consider the F-test a
few steps within a step):
1. Break down the variance of y into sums of squares.
2. Find the mean sums of squares.
3. Put the mean sums of squares together to form the F-statistic.
I describe each step of the F-test in detail and apply it to the example of com-
paring watermelon seed spitting distances (see Table 9-1) in the following
sections.
Because data analysts rely heavily on computer software to conduct each
step of the F-test, you can do the same. All computer software packages orga- 169
nize and summarize the important information from the F-test into a table
format for you. This table of results for ANOVA is called (what else?) the
ANOVA table. Because the ANOVA table is a critical part of the entire ANOVA
process, I start the following sections out by describing how to run ANOVA in
Minitab to get the ANOVA table, and I continue to reference this section as I
describe each step of the ANOVA process.
Running ANOVA in Minitab
Using Minitab to run ANOVA, you first have to enter the data from the k sam-
ples. You can enter the data one in of two ways:
Stacked data means that you enter all the data into two columns.
Column one includes the number indicating what sample the data value
is from (1 to k), and the responses (y) are in column two. To analyze this
data, go to Stat>ANOVA>One-Way Stacked. Highlight the response (y)
variable and click Select. Highlight the factor (population) variable and
click Select. Click OK.
Unstacked is the other method of entering data: a separate column for
the data in each sample. To analyze the data entered this way, go to
Stat>ANOVA>One-Way Unstacked. Highlight the names of the columns
where your data are located. Click OK.
I typically use the unstacked version just because I think it helps visualize the
data. However, the choice is up to you, and the results come out the same no
matter which one you choose.