In randomization that is random process in which all the treatments are assigned to the experimental units. The experimental unit is one of the smallest divisions of the main experimental unit. The main aim of randomization is that they have to remove bias and also other source of variation that is not controllable. There are some advantages of randomization that include it forms the bias of any valid statistical test. The randomization also able to remove bias those are not controllable.

In replication there is repetition of the basic experiment that has been performed. The replication is performed when many experiments has been performed. This type of variations can be removed easily with the help of using number of experimental units. Through this method the errors can easily be found. This is one of the most basis advantages of using replication method.

Local control

This method is used when all the sources like replication and randomization are unable to remove variation so this local control method is used. This method is used for removing all the variations that are unable to remove with the help of other two methods. The main aim of this local control method is that will increase efficiency of the experimental unit through decreasing the experimental error. The work control and local control are two different methods the work control is used when there is no treatment of the experimental design has been found.

b. Write down at least three specific differences between observational study and experimental study. Briefly explain the differences with specific examples.

In experimental studies, there are some experiments that has been performed by the researcher on the basis of observation. In observation the researcher don’t need to perform any experiment.

In the experiment studies the researchers are only involved in observing things through different studies. Whereas in the observational studies the researchers are only involved in observing different objects in nature

In experimental studies the human intervention is present but whereas in the observational studies the human intervention is not present.

Example of experimental studies is Hawthorne studies

Example of observational studies is related with determining the relationship between smoking and lung cancer.

c. What is the difference between nested design and split plot design?

The main difference between the nested design and split plot design, in nested design the level of one factor is similar to the next one but they are not identical for another factor, whereas in the split plot designs the randomized blocks are used. This design is used when we are unable to randomize the order of the runs so for this we design randomized blocks.

In nested designs the criteria of identical levels is not identical whereas in split plot design the criteria of identical levels is identical

In nested design the criteria of sources of variation are many and whereas in the split plot the criteria of sources of variation is minimum.

2. For a fixed-effect Randomized Complete Block Design (RCBD), answer the following questions

a. Show that

1. A 2³ experiment was performed to improve the yield of a chemical process. Two
replicates of a completely randomized experiment were run. The results are shown in the following table.

b. Suppose there is only one replication of the experiment. Provide a plan on how you will compute F ratio to test the main factor effects.

F ratio is the mean value of the two numbers

a. What are the degrees of freedom for interaction effect AB.

According to the experiment design the degree of freedom for interaction is less than 0.05.

1. In an experimental study, yields of electric equipment were recorded on different oven temperatures and at different times. For this the researchers set a temperature first and randomly taken out equipment from the oven at different times. The whole process is replicated three times. Now answer the following questions.

a. What kind of design is it?

In the experimental study this design is nested design.

b. The experiment could be performed randomly assigning temperature and a time on equipment. Give a reasoning why the researchers opted a temperature of the oven first and then selected equipments at different times.

The researchers put the temperature of the oven first because he wanted a experimental design, he can easily performed through the use of nested design that’s why he have arrange this technique.

a. Write down mathematical equation for the model to analyze the data. Include all the assumptions and descriptions of the notations used. What impact does this decision have on the analysis?