Chapter 12. Analysis of Variance. Goals. List the characteristics of the F distribution Conduct a test of hypothesis to determine whether the variances of two populations are equal Discuss the general idea of analysis of variance Organize data into a ANOVA table
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Analysis of Variance
Do we want the parts to be identical or nearly identical? Yes!
We would test to see if the means are the same: Chapter 10 & 11
We would test to see if the variation is the same for the two machines: Chapter 12
What if two stocks have similar mean returns?
Would we like to test and see if one stock has more variation than the other?Why Do We Want To Compare To See If Two Population Have Equal Variances?
larger sample variance
as population 1
(allows us to
tables)Conduct A Test Of Hypothesis To Determine Whether The Variances Of Two Populations Are Equal
Significance level = .10
.10/2 = .05
Use .05 table in
Significance level = .05
Use .05 table in
If you have a df
that is not listed
in the border,
calculate your F
df = 11,
10 & 12
Let’s Look at
Colin, a stockbroker at Critical Securities, reported that the mean rate of return on a sample of 10 software stocks was 12.6 percent with a standard deviation of 3.9 percent.
The mean rate of return on a sample of 8 utility stocks was 10.9 percent with a standard deviation of 3.5 percent. At the .05 significance level, can Colin conclude that there is more variation in the software stocks?Example 1
Step 4:H0 is rejected if F>3.68 or if p < .05. The degrees of freedom are n1-1 or 9 in the numerator and n1-1 or 7 in the denominator.
Step 5: The value of F is computed as follows.
H0 is not rejected. There is insufficient evidence to show more variation in the software stocks.Example 1 continued
H0 : µ1 = µ2 = µ3 = µ4
H1 : The Mean scores are not all equal (at least one treatment mean is different)
α = .01
Now we move on to Step 5: Select the sample, perform calculations, and make a decision…
Are you ready for a lot of procedures?!!
The idea is: If we estimate variation in two ways and use one estimate in the numerator and the other estimate in the denominator: