DOUBLE SAMPLING FOR NONRESPONSE

 

DOUBLE SAMPLING FOR NON-RESPONSE

 Smithu Sony(2048136)

30/Nov/2020

INTRODUCTION:

What is a Non –sampling error?

A non sampling error is a statistical term that refers to an error that results during data collection,causing the data to differ from the true values.i.e the differences between estimates and population quantities that do not arise solely from the fact that only a sample,insead of the whole population is observed.

What is a Non –Response?

Non response means failure to obtain a measurement on one or more study variables for one or more elements k selected for the survey.The self selection of respodents may produce bias.i.e only people with certain opinions will respond to some questions.

PROCEDURE

Double sampling can be used to adjust for non response in the form of call backs.Non response is an important problem to consider in any survey.We can consider the two groups-response and non-response in two strata.

The two steps of double sampling for non-response:

1.   Step1:                                                                                                                                                 

n’ initial simple random samples are selected from a population of N units.These units are classified into two strata-response and non-response.

n1’ of these response is stratum1

n2’ of these do not response is stratum2

 

2.   Step2:


Call back n2 samples by simple random sampling from the n2’ non-respondents.Thus,we are in a double sampling setting where n1=n1’ ,n2 is the number of call backs.

 

APPLICATION 

Double sampling can be used to adjust for non-response in the form of call backs. Non-response is an important problem to consider in any survey.It is widely used for forest and forest ecosystems

To find the estimate the mean and also the variance of the estimate.

The estimate for the mean is:

The estimated variance of this estimate is:

For example:Time spent studying

In a college with 1000 students, a questionnaire is mailed to a simple random sample of 106 students asking them about the amount of time they spend per week studying. Out of these students, 46 respond. From the 60 non-respondents, a simple random sample of 20 is selected and intensive efforts are made by telephone and personal visit to obtain responses.

These are the data obtained.Here Questionnaire is "the student responding to questionnaire"" and Telephone and Vist is "the students contacted and responded to telephone and visit".Sample mean of Questionnaire is 20.5 hours and Telephone and Visit is 10.9 hours.Also SD of sample in Questionnaire is 6.2 hours and Telephone and Visit is 5.1 hours.

    
 CONCLUSION:
     
 Sample mean of the student responding to questionnaireis 20.5 hours and the students contacted and responded to telephone and visit is 10.9  hours.Also SD of sample in the student responding to questionnaire is 6.2 hours and the students contacted and responded to telephone and visit is 5.1 hours are given.we obtained the estimated mean is 15.06604 and the estimated variance is 0.7309267.

 

  Selecting the Number of Call Backs

  • c0: the initial cost of sampling each respondent (the set-up cost for each respondent)
  • c1: the cost of a standard response (cost of producing the response)
  • c2: the cost of a call back response

 

  Total cost =(n′×c0σ22)+(n1′×c1)+(n2×c2)

 

 We want to determine the value k(k > 1) where: n2=n2′/k.

  As ,its variance can be derived and one can find the value of k and n'        that minimize the expected cost of sampling for a desired fixed value of,            which we denote as V0 .

  When N is large, the optimal value of k and n' are:

 where σ2 is the variance of the entire population and σ22is the variance of the non-response        group. 

 Example:Weekly living expenditures

In a college of 1000 students, we want to find out students' average weekly living expenditure.  The response rate is anticipated to be about 60%. It is thought that the response group has  a higher variance than the non-response group. The overall variance σ2  120 and the variance of the non-response group σ22~80,c0=0,c1=1,c2=4

     CONCLUSION:
 From 1000 students,the response rate is anticipated to be about 60%. Therefore,w1=0.6 and w2=0.4.It   is thought that the response group has a higher variance than the non-response group.The overall variance σ2  is 120 and the variance of the non-response group σ22~80,c0=0,c1=1,c2=4 are given.We obtained the optimum value for k is 2.708013 ,n_dash is 34  and The value of n2 is 5.038762

   Disadvantages of Non-Response 

  • It invalidates the results of an investigation or research.
  • It may result in higher variances for the estimates since the sample size the researcher ends up with is lesser than what was expected.
  • It may lead to inconclusive research.

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