# statistic discussion 4

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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 wayâˆ’not exact but similar. This is analogous to adding or subtracting a constant value to each individual in the groupâˆ’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?

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