We are interested in testing the effect of 5 different chicken feeds on egg production. We wish to test egg production in a number of different breeds of chicken (we’re not interested in the particular breeds, so we take a random sample of 4 breeds) to enhance the generalizability of our study. Some breeds of hens are indeed known to produce more eggs per week than other breeds. Accordingly, we emply a randomized block design (with the breeds as blocks) to minimmize this effect and estimate our treatment effects more precisely.

Egg production data:

Breed (blocks)

a b c d Mean

Feed I 5.00 3.25 3.00 4.00 3.81

Type II 7.00 2.00 4.00 2.50 3.87

III 4.00 2.50 3.25 4.40 3.56

IV 6.50 6.00 6.50 4.75 5.94

V 4.50 3.25 3.50 2.00 3.41

Mean 5.40 3.30 4.05 3.55

Test [alpha = .05] to determine whether the five feed types tested differ in average egg production per week.

Some numbers to aid in the analysis: SS(Feeds) = 17.7 SS(Breeds) = 12.4 SS(Residual) = 12.7

Source of Variation SS df MS F P-value

Feeds (treatments) 17.7 4 4.42 4.18 .01<P<.025

Breeds (blocks) 12.4 3 4.14

Residual (interaction + error) 12.7 12 1.06