INTRODUCTION TO ANOVA

Analysis of variance is a technique which partitions the total variation in an experiment into components or sources. It also allows one to assess whether differences between treatments are real or due to random variation.

Where possible it is advisable to use a proper statistical package to perform analyses of variance (ANOVA) since in Excel there are a number of limitations with the ANOVA tool. In Excel only simple designs can be handled and missing values are not dealt with correctly (Excel views these as text values). However, Excel does have useful features such as residual plots and Normal probability plots.

Read in the grass data which has been taken from a laboratory grass drying experiment. Shape describes the shape of the drying curves obtained from each of the 24 samples. The second variable, drytime represents the time taken for each grass sample to reach a certain moisture content. The first six observations are based on samples from a grass cutting machine, and the subsequent eighteen are in batches of six from each of the three machines which condition the grass to accelerate the drying process.

For the grass, there are two sources of variation:

The variation between the means of the individual treatments (the machines) and the overall mean
The variation within each treatment about that treatment mean

Illustrate this by producing a plot showing the drying times for each treatment. Use a scatter plot and enter drytime as the Y-Values of four series - one for each treatment. Put six ones as the x values of treatment 1, six twos for treatment 2 etc and you should get the plot on the right.

In one-way analysis of variance, the variation within each treatment is a measure of the random variation in the experiment. If there are no differences between the treatments, then the variation amongst the means will also be a measure of the random variation. Genuine differences between the treatments will cause the variation amoung means to be much larger than the random variation. An F-test is used to test whether the ratio between these two variances is likely to have arisen by chance.

INTRODUCTION TO ANOVA

Basic statistics in Excel 23.2.99 Page: 20 of 25