Topic 8: Transformations of the data [S&T Ch



Topic 8: Transformations of the data [S&T Ch. 9.16]

8. 1. The assumptions of ANOVA

8. 1. 1. Additive effects

The treatment ((i), block ((j), and error terms (ij are added

"The treatment effects remain constant over blocks (or replications) and the block effects remain constant over treatments.”

Tukey's test for RCBD with one observation per cell (Topic 6.4.1)

Uses 1 df from the error to test if the multiplicative effects are significantly larger than the rest of the error.

Violation of this assumption results in larger MSE, smaller F values, and a less sensitive test that increases the probability of Type II errors

8. 1. 2. Independence of errors

This says that the values of the (ij are statistically independent. Failure of this assumption is often caused by a failure to properly randomize the plots:

• The self-similarity of experimental units adjacent in space or time is called positive autocorrelation. Regular alternation of positive and negative errors is a manifestation of negative autocorrelation.

• Independence of errors in a sequence of continuous variates may be tested using a test based on the differences between adjacent values (Biometry p394 –395).

• However, the process of randomly allocating the treatments to the experimental units ensures that the (ij will be independent.

8. 1. 3. Normally distributed errors

Violation of normality means that the (ij are not normally distributed.

This is the least influential assumption on the F test.

Normality can be checked using

• A plot of the residuals produced using the OUTPUT statement

• Shapiro-Wilk (ST&Dp.567) using PROC UNIVARIATE normal

• Reject if W very different from 1, and P ................
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