ANOVA stands for analysis of variance. The two-way with replication ANOVA test examines data from repeated trials during which both "factors" and "levels" are varied. For example, an ANOVA experiment might look at the growth rates of three different varieties of wheat (the factors) using three different fertilisers (the levels). Excel's ANOVA function calculates statistical "F" values which show whether changing different factors or levels resulted in a significant change in the trial results. Just as importantly, it tells you if there are interactions between factors and levels.

- Skill level:
- Moderate

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### Things you need

- Excel ANOVA output

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## Instructions

- 1
Examine the table of data that Excel used for the ANOVA test. It shows the data that resulted from repeated trials switching between the two factors and also between two or more levels of those factors. Each row represents trials at a particular factor, and each column will represent trials at a particular level of factor, with every possible combination represented. In the case of the wheat example, there would be nine different trials -- wheat 1/fertiliser 1, wheat 1/fertiliser 2, and so on -- with at least two repeats of each trial.

- 2
Examine the worksheet containing the Excel ANOVA output and locate the table labelled "ANOVA."

- 3
Find the rows labelled "Sample," "Columns" and "Interaction" in the leftmost column of the ANOVA table. Follow these rows to the right until you reach the column with the heading "F." In this column, you will find the calculated F values associated with your original trials. There will be one F value each for Sample, Columns and Interactions. F is a test statistic that Excel calculates based on how much variation there is within groups of data, such as all the trials using the same factor, compared to between groups.

- 4
Continue following the same rows to the right until you reach the column with the heading "F crit." In this column, you will find the critical F values for Sample, Column and Interactions. This is a standard value that Excel looks up in an internal database. It is a pass/fail threshold based on various statistical factors, including the number of trials.

- 5
Compare the F value for the Sample row to the critical F value for that same row. If the F value is greater than the critical F, this means that changing between factors in your trials had a statistically significant effect on the outcome of those trials. In the case of the wheat example, it would mean that the type of wheat used affected the observed growth rate. If the F value was below the critical F, the factor had an effect no greater than expected random variation and was not significant.

- 6
Compare the F value for the Columns row to the critical F value for that row. This time, if the F value for this row exceeds the critical F, it means that varying the levels of the factors had a significant effect. In the example, this would mean that the particular fertiliser used made a difference to the growth rate of the wheat that could be distinguished from random chance variation.

- 7
Compare the F value for the Interactions row to that row's critical F value. If the F value for this row exceeds the critical F, it tells you that there were significant interactions between your factors and your levels. This means that the amount of variation you get when changing from one factor to another will depend on what level you are at. For instance, wheat 2 may have the highest growth rate, but only when using fertiliser 3.

#### Tips and warnings

- Remember that, like many statistical analyses, this test has a chance of being wrong. The percentage chance of making a mistake in your conclusions is represented by the alpha value that was input into Excel when you initially chose parameters for the ANOVA test.