Natural Resource BiometricsAnalysis of VarianceAnalysis of variance, often called ANOVA is a technique that is used to test multiple samples or multiple levels of variables within a sample. It is very tempting to simply apply a t test multiple times to the data. In the case of multiple samples this is invalid. In analysis of variance we are simply partitioning the variance into categories that influence the variation in the sample design. Let us consider the following.
where C is the "correction term", N = sum of n_{i} , and k is the number of groups, and n_{i} = the number of observation in group i.
Using a Spreadsheet like EXCEL we can generate a standard ANOVA table as below. The summary section just lists the sample statistics of n, mean, and variance. The second table list the SS or Sums of Squares for between the groups (sample 1 or 2), within each group, and the total Sums of Squares. Next is the column for degrees of freedom df , the means Square MS, and the F test , which is the ration of the between group Sum of Squares and the within group Sums of Squares. The next column is the pvalue which is the probability that the F test is really less than the F crit value due to sampling error. The larger the pvalue the less sure you can be in the result. This table indicates that the two samples are significantly different and we are very sure of this result (p = 0.000446). Also See: Chapter 10  More on the Testing of Hypotheses pages 125149 in:
Chapter 10  Single factor Analysis of Variance pages 180191 in:

Natural Resources Biometrics by David R. Larsen is licensed under a Creative Commons AttributionShareAlike 4.0 International License . Author: Dr. David R. Larsen Created: July 19, 2000 Last Updated: September 13, 2014 