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A randomized complete block design study was performed to investigate the effects of irrigation method (with 5 levels) on the harvest of orange trees in a particular grove. The grove was divided into eight blocks to account for local variation in the grove, and irrigation methods were assigned to trees within each block at random. Each method appeared in every block. At harvest, the fruit from the trees was weighed.

Considering the blocking factor to be a random effect, carry out an ANOVA with a mixed model. Use the results from the appropriate F-test to decide whether the irrigation method effect is significant.

SAS Institute Inc.

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The Methods data set contains data about five irrigation methods that were used on an orange grove, and the weight of the fruit at harvest.

These are the variables in the data set:

This data is sample data from SAS Institute Inc.

The Type III test for the effect of irrigation method yields an F statistic of 3.27 with a corresponding p-value of 0.0254. So at a level of α = 0.05, you can conclude that the effect of irrigation method on the harvest of orange trees at this grove is significant.

Six animals from two species (fox and coyote) were tracked, and the diameter of the area that each animal wandered was recorded. Each animal was measured four times, once per season. The animals were selected randomly form a large population, and the variability from animal to animal is from some unknown distribution. Use a random effects-mixed model, specifying subject(species) as the random effect, to test how wandering radius differs between species. (Recall that the radius is simply half of the diameter.) Base your conclusion on a significance level of α = 0.05.

Lee Creighton (modified by Paris Faison)
SAS Institute Inc.

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The Animals data set contains recordings of the diameter of the area wandered by six animals from two species. The individual animals were identified as subjects within each species. Each animal was measured four times, once per season.

These are the variables in the data set:

Sall, J., Creighton, L., & Lehman, A. (2006). JMP Start Statistics, Third Edition. Cary, NC: SAS Institute Inc.

The MIXED procedure in SAS gives the following result:The F test for the mixed model gives an F statistic of 11.89 and a p-value of 0.0261 for the species effect. This outcome is significant at the α = 0.05 level, and thus we can conclude that there is a difference in wandering radius between foxes and coyotes.