Chpater 11 Notes
ANOVA
One-way analysis of variance: used when comparing three or more means.
Purpose is to make inferences, based on the sample data, on the population
means. The purpose is to gain insight into the population means, not the sampek
means. Essentially ANOVA is a hypothesis testing with the null hypothesis been:
all the population means are equal.
Ho: 1 = 2 = 3
The alternative hypothesis will be not all population means are equal. Note, this
does not mean that all population means are not equal. There are many possible
cases.
Distinction between 1-way ANOVA and other kinds of ANOVA
One-way ANOVA (or 1-factor) deals with only one independent variable, one
dependent variable, focuses on means and independent samples.
Independent variable is the characteristic (that is important to the researcher)
that distinguishes one group from another. For example, favorite TV show,
number of siblings etc. Sometimes, the independent variable is also referred to
as between-subject variable when researchers want to clarify that comparisons
are made with data from independent samples.
Even if there is only one independent variable, it does not mean it is
automatically one-way ANOVA. If there is more than one dependent variable,
then it is not a one-way ANOVA.
Presentation of Results
One-way ANOVA is a F-test. Typically only results are shown: e.g.
F(3, 801) = 7.93 (p = .00001)
3 is the “between groups” number. Add one to get the number of groups in the
sample.
801 is the “Within groups” number.
Add 3 and 801 together, and add 1 to this sum to get the total number of sample
size.
If a one-way ANOVA F-test result is significant, it means the null hypothesis is
rejected, meaning not all population means are equal.
Multiple one-way ANOVAs
Sometimes researchers will conduct multiple one-way ANOVAs (instead of 2-way,
3-way ANOVAs) and present the results on the same table. This case, each oneway ANOVA will have its own null hypothesis.
To compensate for inflated Type I Error, the Bonferroni Adjustment technique is
used. Each one-way ANOVA level of significance is obtained by dividing the
desired overall study significance by the number of tests.
Assumptions of one-way ANOVA
Same assumptions as for other tests covered previously:
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Independence
Randomness
Normality
Equal variance
Tests can be conducted prior to one-way ANOVA to see if assumptions are met
(give extra credit to researchers who did).
If assumptions are not met, several options:
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Identify and eliminate outliers
Transform sample data
Use other tests (don’t use one-way ANOVA)
Statistical vs Practical Significance
To avoid with a result that is statistically significant but not practically significant,
researchers can do several things:
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Conduct power analysis before data is collected to see how large sample
size should be (for a given power, level of significance)
Estimate strength of association
Compute effect size
If null hypothesis is rejected, the result of not all population means are equal may
not be useful to researcher. They may want to probe further. This case, they can
use post hoc analysis or comparison analysis. (Covered in Chapter 12)