An analysis of variance, or ANOVA, is a statistical test measuring the difference between two or more groups. The essential objective of the test is to determine if the difference between two groups is greater than the differences among subjects within a group. In academic literature, it's important to report the results of ANOVA tests accurately and with all the required information so readers can accurately interpret the results.
Researchers often divide subjects into groups so they can isolate important variables, according to Washington State University. For example, if a scientist wanted to find out if monkeys grow faster eating bananas or grapes, she would divide the monkeys into two groups -- grape-eaters and banana-eaters -- and then weigh the monkeys in each group over time. If the scientist found that grape-eaters were, on average, 5 pounds heavier, she would be tempted to conclude that grapes help monkeys grow more than bananas do. The problem with this approach is that some monkeys may naturally grow faster than others no matter what they eat. The scientist could use an ANOVA test to solve this problem because the test would measure whether the difference between the banana- and grape-eaters was too big to be coincidental.
Researchers use ANOVAs to test predictions about the subject of their research. Each prediction actually includes two hypotheses: a null hypothesis predicting no difference between groups and an alternative hypothesis predicting significant differences. In the example above, the scientist's alternative hypothesis would be something like "monkeys grow faster when they eat grapes than when they eat bananas." The null hypothesis would state that "there is no difference in the growth rates of monkeys that eat bananas and monkeys that eat grapes." If the ANOVA test shows a significant difference between the two groups, the scientist would reject the null hypothesis and accept evidence for the alternative hypothesis. If the ANOVA found no significant difference, the researcher would reject the alternative hypothesis and accept the null hypothesis.
Key Components for Reporting ANOVAs
To ensure published papers include all of the important mathematical information, researchers have established a system of rules for reporting the results of ANOVAs. Summary statements for ANOVAs should include three basic components: an explanation of what the ANOVA tested, an F-ratio with degrees of freedom, and a p-value. Degrees of freedom refers to the number of groups in the study and the number of individuals in each group. The F-ratio is the actual value of the ANOVA test, while the p-value is a measure of the probability that the F-ratio occurred by chance. The closer the p-value is to zero, the less likely it is that differences between groups occurred at random.
Example of an ANOVA Summary Statement
In the hypothetical study discussed above, suppose the scientist had two groups of 25 monkeys. If so, the scientist's summary statement would look something like this: "Measures of the weight of banana-eating and grape-eating monkeys showed statistically significant differences between the two groups as demonstrated by a one-way ANOVA, F(2, 25) = 4.425, p<.05." This statement reports the F-ratio with degrees of freedom, shows that the probability of random coincidence is less than 5 percent, and explains which hypothesis the test supports.
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