Question

Why do we apply random sampling and assignment in statistical experiments? (Explain the effect of randomization on both the variability and bias).

Answer 1

Randomisation refers to the process of assigning the treatment among the experiental units where every treatment has a equal chance of being assigned to any experimental unit. Now, we apply random sampling and assignment in statistical experiments because of the following reasons:

1). Obseravation collected will be independently distributed.

2). This method removes all bias and the other sources of extraneous variation which is uncontrollable.

3). It helps in ensuring validity of test and helps in having objective comparison among treatment.

Effect of randomisation on variability is that it elimates the nuisance factors that is factors that may influence the experimental response but in which we are not directly interested. For this we use the local control to improve the precision with which comparison among the factors of interest are made. In this we divide the experimental units into different groups that are homogeneous within and heterogeneous in between on the basis of nuisance factors.The variantion among these groups is eliminated from the error and thereby efficiency is increased.

Effect of randomisation on bias is that it removes the selection bias that is experimentor, or subject do not have any prior knowledge of there selection. Like they don't know whether they are going to assign into treatment group or in a control group. This process increase the fairness of data selection and experiment.