ANOVA (Analysis of Variance)

ANOVA (Analysis of Variance) is a powerful statistical tool for comparing means across more than three groups simultaneously. In biological research, ANOVA becomes essential when investigating the effects of different environmental conditions, treatment concentrations, or categorical variables on biological responses.​

The ANOVA test would be used to determine if there is a significant difference in the mean number of bird species in the seven locations.

The ANOVA is a single test to determine the significance of the difference between the means of three or more groups.

ANOVA consolidates all group comparisons into a single statistical test.  The test compares the variation between groups to the variation within groups. The math required of the ANOVA test is beyond the scope of IB Biology.  There are excellent on-line ANOVA calculators that will do the math and  draw a conclusion. 

The ANOVA tests the null and alternative hypothesis:

Null Hypothesis:
"There is not a significant difference between the groups; any observed differences may be due to random variation."

For example:  

• There is no significant difference between the number of birds at the different locations; the differences we see in the means of the groups may be due to chance and sampling error.

Alternative Hypothesis:
"There is a at least one group with a mean that is significantly different from the others."

​
For example:  

• There is a significant difference between the number of birds at the different locations; the difference we see in the means of the groups is mostly likely not due to chance or sampling error.

Performing an ANOVA 

ANOVA calculators produce a single p-value that indicates whether significant differences exist among the experimental groups. When the p-value falls below the predetermined significance level (typically 0.05), researchers reject the null hypothesis and conclude that at least one group mean differs significantly from the others. However, the ANOVA test does not identify which specific group(s) differ from one another, creating the need for additional statistical analysis. For instance, in an experiment comparing plant growth under five different light wavelengths, a significant ANOVA (p < 0.05) reveals that light wavelength affects plant growth, but does not specify whether red light differs from blue light, or which wavelengths produce similar growth responses. This limitation necessitates follow-up testing to identify specific group differences.

​Therefore, if the p-value of the ANOVA test is significant, it must be followed by a "post hoc" test to examine differences between each possible pair of groups. Tukey's Honestly Significant Difference (HSD) test serves as the most commonly used post-hoc analysis following significant ANOVA results. This test performs pairwise comparisons between all possible group combinations.  Each pairwise comparison in Tukey's test generates an individual p-value indicating whether two specific groups differ significantly. For example, when comparing enzyme activity across four different pH levels, Tukey's test would produce six pairwise comparisons:

• pH 4 vs pH 6
  
• pH 4 vs pH 8
  
• pH 4 vs pH 10
  
• pH 6 vs pH 8
  
• pH 6 vs pH 10
  
• and pH 8 vs pH 10.
  

Each comparison receives its own p-value, allowing researchers to identify which specific pH levels produce significantly different enzyme activities.

The Tukey's pairwise comparisons are displayed as letters on the column graph: If two groups share a letter, it means they are not significantly different from each other. See an example of a figure displaying ANOVA and Tukey's post hoc comparisons below:

This experiment examined the development of the immune system in house sparrows. Researchers took blood samples and measured the level of antibodies circulating in the blood. Birds were sampled at a range of ages from 3 days after hatching through adulthood. (Killpack, Oguchi, & Karasov, 2013).
​

The ANOVA test was significant, which told the researchers that at least one pair of age groups differed. A Tukey's test was run to learn which pair(s) significantly differed. Examine the letters above the bars in the figure. Which age groups significantly differed in antibody levels?

---