With the aid of examples briefly explain the difference between fixed effect and random effects models in experimental design.

remolatg 2021-02-16 Answered
With the aid of examples briefly explain the difference between fixed effect and random effects models in experimental design.
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d2saint0
Answered 2021-02-17 Author has 89 answers
Step 1
Introduction:
Experimental study:
In a designed experimental study, researchers allocate individuals to a certain group under study and change the values of an explanatory variable intentionally, after which, the values of the response variable for each group is recorded.
Step 2
Explanation:
Fixed effect:
The fixed effect in an experimental design is defined as the data that has been gathered from all the levels of the factor that are of interest. Fixed effects will be constant across the individuals.
Example:
Suppose that 3 different dosages of drug are given to three different groups of subjects. The objective of the investigator is to compare the effect of reactions of three different dosages of a drug. In the given scenario "Dosage" is the factor and 3 different dosages of drug are 3 different levels of the experiment. Here, interaction of any 2 dosages is not included in the experiment. That is, the investigator is studying only fixed effect. Main interest is effect of each dosage.
Random effect:
The random effect in an experimental design is defined as the factor that have many possible levels, interest is in all possible levels, but only a random sample of levels is included in the data. The random effect is constant across individuals.
Example:
Suppose that patients are classified into 2 surgical procedures randomly and there are five separate surgical teams. To prevent potential conflict between care and surgical team, each team is qualified in both procedures, and each team performs equal numbers in each in the two types of operations. As the investigator wants to compare the procedures, the goal is to generalize to other surgical teams. The surgical team is a random factor, not a fixed factor.
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New questions

The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual racetracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is bolted to the car using existing holes in the car's frame. Model DRW is a heavier roll bar that must be welded to the car's frame. Model DRB requires 20 pounds of a special high alloy steel, 40 minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires 25 pounds of the special high alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Deegan's steel supplier indicated that at most 40,000 pounds of the high-alloy steel will be available next quarter. In addition, Deegan estimates that 2000 hours of manufacturing time and 1600 hours of assembly time will be available next quarter. The pro?t contributions are $200 per unit for model DRB and $280 per unit for model DRW. The linear programming model for this problem is as follows:
Max 200DRB + 280DRW
s.t.
20DRB + 25DRW 40,000 Steel Available
40DRB + 100DRW ? 120,000 Manufacturing minutes
60DRB + 40DRW ? 96,000 Assembly minutes
DRB, DRW ? 0
Optimal Objective Value = 424000.00000
Variable Value blackuced Cost
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
DRB 1000.00000 0.00000
DRW 800.00000 0.00000
Constraint Slack/ Surplus Dual Value
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1 0.00000 8.80000
2 0.00000 0.60000
3 4000.00000 0.00000
Objective Allowable Allowable
Variable Coef?cient Increase Decrease
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
DRB 200.00000 24.00000 88.00000
DRW 280.00000 220.00000 30.00000
RHS Allowable Allowable
Constraint Value Increase Decrease
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1 40000.00000 909.09091 10000.00000
2 120000.00000 40000.00000 5714.28571
3 96000.00000 Infnite 4000.00000
a. What are the optimal solution and the total profit contribution?
b. Another supplier offeblack to provide Deegan Industries with an additional 500 pounds of the steel alloy at $2 per pound. Should Deegan purchase the additional pounds of the steel alloy? Explain.
c. Deegan is considering using overtime to increase the available assembly time. What would you advise Deegan to do regarding this option? Explain.
d. Because of increased competition, Deegan is considering blackucing the price of model DRB such that the new contribution to profit is $175 per unit. How would this change in price affect the optimal solution? Explain.
e. If the available manufacturing time is increased by 500 hours, will the dual value for the manufacturing time constraint change? Explain.