A two-factor factorial experiment is conducted to compare litter sizes of Yorksh

Question

A two-factor factorial experiment is conducted to compare litter sizes of Yorkshire and Landrace sows derived either from a line unselected for litter size or from a line that has gone through 15 years of selection for increased litter size. Two sows of each breed are randomly selected from each line. Their litter sizes are as follows:

Yorkshire Landrace   

Unselected line 8 9

   9    10

Selected line 11    11

   10    9

The partially completed ANOVA table is as follows:

Source df SS    MS    F

Total                              7.875

Line                               3.125            3.125    3.57

Breed

Line x Breed

Error                              3.500            0.875

Find the calculated F value for breed.

Frame score in beef cattle is based on height at the hips and is used as a measure of skeletal size. Frame scores range from 1 to 10 with a higher number indicating a taller animal. Independent random samples of frame scores were selected from the Angus and Simmental breeds of beef cattle with the following results:

In the Analysis of Variance table, the calculated F value used to test if the breed means are equal is:

3.57143

Explanation / Answer

1) from above data here is ANOVA table:

calculated F value for breed =0.14286

2)

below is ANOVA table:

calculated F value used to test F=4.09

Source of Variation df SS MS F total 7 7.875 line 1 3.125 3.125 3.571 breed 1 0.125 0.125 0.143 line *breed 1 1.125 1.125 1.286 error 4 3.5 0.875

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