Analysis of Variance

Please read the lecture and respond to the discussion questions APA format with
reference
Analysis of Variance (ANOVA)
Introduction
When hypothesis testing is performed in clinical research, the data embedded into each
sample corresponds to a specific sample. If there are one or two treatments, then use t-
tests to analyze the effectiveness of the treatments. If there are more than two
treatments, then the use of analysis of variance (ANOVA) is applied to determine the
effectiveness of treatments.
Analysis of Variance
The tests discussed so far are appropriate when making only one comparison, whether it
is a comparison of two populations, a sample taken from a population, or a comparison of
two samples to each other. However, most studies or experiments are designed to
compare more than two samples, populations, or treatments. Comparing more than two
samples requires the use of variance instead of means. For example, in the case
treatments, the goal is to discover how much of an effect treatments have on the
variance of the samples.
Homogeneity of variance is an important part of this discussion. When two independent
samples are compared, it is assumed that the variances of the two are similar. Each of
the samples mentioned above will have its own variance. The variance inherent within
each group gives an estimate of the population variance. If there is no treatment applied,
the variance for all groups together should be similar to the variation within each group.
Suppose a treatment is applied to one group. Each individual should be affected by that
treatment in a similar way−not exact but similar. This is analogous to adding or
subtracting a constant value to each individual in the group−the distribution of the whole
group will shift in the same direction, thereby maintaining homogeneity of variance. This
will make the variance between groups substantially different from the variance within
groups.
One-Way ANOVA
One-way ANOVA is used to compare three or more population means when there is one
factor of interest.
The requirements for one-way ANOVA are as follows.
1.The populations have distributions that are approximately normal.
2.The populations have the same variance.
3.The samples are simple random samples of quantitative data.

4.The samples are independent of each other.
5.The different samples are from populations that are categorized in only one way.
One-way ANOVA is a hypothesis test (Triola, 2010). There are still seven steps. An
example a one-way ANOVA is shown in the Visual Learner: Statistics .
Posthoc Tests
Analysis of variance is used to determine treatment differences among multiple
treatments. A limitation of this procedure is that although it will indicate whether there is a
treatment difference, it will not tell which treatment is different. Procedures called post
hoc tests are used to pinpoint treatment differences. These procedures use various
assumptions and methods for reducing the potential for error and bias. They are
essentially methods for comparing two treatments at a time, and are not used unless an
ANOVA has already shown that there is a significant effect. The ANOVA shows that
there is an effect due to a particular treatment, and the posthoc test is used to determine
which treatment is different.
Conclusion
Analysis of variance is a useful tool for investigating multiple treatments. Multiple levels of
a single factor can be assessed to get a clearer picture of how a certain variable
responds to that factor. More complex experiments, such as monitoring experimental
units over time in a repeated measures experiment, are useful in seeing how things
change, or even adapt, over time. Other complex experiments, such as those assessing
two or more factors yield information on the effects and possible interactions of each
factor. These complex experiments provide information that could not be obtained with
simpler analysis, such as t-tests.
References
Triola, M. (2010). Elementary statistics (11th ed.). Boston, MA: Addison Wesley.
Discussion 1
How would you explain the analysis of variance, assuming that your audience has not
had a statistics class before?
Discussion 2
What is an interaction? Describe an example and identify the variables within your
population (work, social, academic, etc.) for which you might expect interactions?

Answer Preview…………..

How would you explain the analysis of variance, assuming that your audience has not had a statistics class before? For one to understand analysis of variance (ANOVA), they need to understand variance first. Variance is a measure of how much data in a population is spread out. For instance, in a population where all data has a value of 10, the variance is zero, and thus the data is centrally placed. The variance of zero is often not possible with natural populations. The higher the variance, the more spread the data is. The variance of data is measured from the mean that is obtained from the data. On the other hand, ANOVA compares the variances of different population samples to come up with the correlation between the samples. When comparing different groups (typically three or more), ANOVA is used to examine the variation of data within the groups with the variation between groups (Triola, 2010). When population samples are taken from a population group, the expectation is that the means of these samples differ mainly because they are samples and not entire populations. This…………..

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