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

remolatg
2021-02-16
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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.

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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c) What is the 95% confidence interval for the proportion of smokers in the population?(to 4 decimals)?

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