Essential Statistics

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Chapter 16: One-Way Analysis of Variance

Section Review

Next we will discuss how to validate the one-way ANOVA assumptions.

16-7 The One-Way ANOVA Model and Validating the Model

Assumptions

We will motivate the ideas in this section by considering an example.

Suppose a farmer would like to test the effectiveness of five different

fertilizers (1, 2, 3, 4, and 5) on his corn crop and the farmer has 100 acres of

land to grow his crop. Assume these 100 acres are of the same soil content.

Suppose the farmer divides the land into 1 acre plots with 10 rows (and 10

“columns”) and plants the same number of corn plants per acre. In addition,

suppose the cost per unit for the fertilizers are the same and equal amounts

of the different fertilizers are

randomly

administered to 20 acres each. The

farmer has no control of the weather but we will assume no adverse weather

affected the growing season.

Figure 16-20

shows a possible randomization

scheme to administer the fertilizers per acre. The figure displays 10 rows

and 10 columns (



100 acres) in which the number 1 represents fertilizer 1;

the number 2 represents fertilizer 2 etc. One can generate random numbers

to help with the random assignment of the fertilizers to the different acres.