Question

1. A poultry company undertook an experiment to determine the effect of certain treatments on chicken growth. A sample of 24 young chicks were given one of three possible treatments to aid their growth. In order of cost from least to most costly, the three treatments were as follows: a cheap food; an expensive food; the expensive food plus an injection of a growth serum. After a fixed period of time, the application of the treatments was halted and the chickens were weighed. The response was their increase in weight (in pounds) over the time period of the experiment. Because of space considerations, the experiment had to be carried out in four different laboratories. These laboratories were randomly selected and labeled as “North”, “South”, “East” and “West”. Each laboratory employed a different technician to carry out the experiment. Six chickens were assigned to each laboratory, and the three treatments were randomly assigned to the chickens within each laboratory (two chickens having each treatment within each laboratory). In your mini-report, explain why it makes sense to design and analyze this as a block design. Using the sample data, formally test whether it turned out to be sensible to use blocks, providing numerical justification (test statistic and P-value) for your conclusion. Also formally assess the main research question of interest: whether the three treatments yield significantly
different mean growth, again providing numerical justification (test statistic and P-value) for your conclusion. If you find a difference across the treatments, investigate exactly which treatments differ significantly from each other. Provide recommendations to the poultry company about their best practices based on your findings.

SAS code:

/* Problem 1 */

DATA one;
INPUT lab $ treatment :$12. growth;
cards;
East Cheap 4.62
East Cheap 4.93
East Expens 6.25
East Expens 5.97
East Expens_Serum 6.41
East Expens_Serum 6.54
West Cheap 5.36
West Cheap 5.49
West Expens 6.53
West Expens 6.62
West Expens_Serum 6.81
West Expens_Serum 6.63
North Cheap 4.65
North Cheap 5.32
North Expens 5.96
North Expens 6.12
North Expens_Serum 6.33
North Expens_Serum 6.44
South Cheap 5.76
South Cheap 6.32
South Expens 6.47
South Expens 6.68
South Expens_Serum 6.71
South Expens_Serum 6.78
;
run;

Answer 1

Output:

Where alpha(level of significance) = 0.05.

From Anova table:

The lab F-statistics = 14.31 and P-value = 0.0003, it is means in lab have significant difference.

The treatment F-statistics = 79.54 and P-value = <0.0001, it is mean in treatment have significant difference.

But In Interaction lab*treatment F = 2.22 and P-value = 0.1131, it is mean there is no significant difference.

Multiple Comparison for Lab:

Which means covered by bar it means there is no significant difference.

Now see who are significant:

There is a significant difference between South and North, South and East.

There is a siginificant difference between West and North, West and East.

Multiple Comparison for Treatment:

Which means covered by bar it means there is no significant difference.

Now see who are significant:

There is a significant difference between Expens_Serum and Cheap.

There is a siginificant difference between Expens and Cheap.