Analysis of Variance
1) What is ANOVA?
It is a method of testing the equality of three or more population means
by analyzing sample variances.
2) Setting up the Null/Alternative hypothesis:
Test the claim that different populations have the same means.
H 0 : μ1 = μ2 = μ3 = ..... = μk
H1 : at least one mean is different.
3) Distribution curve & Critical value:
1) Use the F Distribution.
2) Tests are always right-tailed.
3) K = number of samples, n = sample size.
4) Critical value is found in the F distribution table with
Numerator degrees of freedom = k – 1,
Denominator degrees of freedom = k(n – 1)
4) Setting-up TI-83 or TI-83 Plus to perform ANOVA Test:
1) Enter the data into L1, L2, L3, and so on.
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4) Using TI-83 or TI-83 Plus to perform ANOVA Test:
1) Select STAT, TESTS, ANOVA( , ENTER to select
2) Now enter L1, L2, L3, and so on to get ANOVA(L1, L2, L3),
now press ENTER to perform the test.
5) Decisions:
Traditional Method:
When the computed Test Statistic falls
in
then we
Non-Critical Region,
Fail to Reject
Critical Region,
Reject
H 0 (Equality of means)
H 0 (Equality of means).
P-Value Method:
P − Value
>α,
≤α,
then we
When the
Fail to Reject
Reject
H 0 (Equality of means).
H 0 (Equality of means)
5) Observations:
1) Small value of F test statistic and a large P-value implies equality
of population means
2) Large value of F test statistic and a small P-value implies at least
one population mean is different.
7) Conclusions:
Translate your decision into a simple, non-technical terms, present a direct
conclusion in reference to the original claim stated in the problem.
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