Question

Distinguish clearly between sampling and non-sampling errors. In this context, describe why non-response errors arise. Explain the steps of Hansen-Hurwitz technique of sub-sampling of non-respondents for estimating the population mean. Obtain the variance of the suggested estimator

Answer 1

1) Sampling error is defined as the error that happens due to observing the Sample instead of taking the whole Population i.e. the Sample chosen is not a proper reflection of the whole population.

Non-Sampling error is defined as the error that happens during the data collection where the observed value differs from the true value. [ Example: During a survey, an enquirer goes to a house for a survey but didn't find anyone and asked the adjacent house to provide information and the information like monthly income, etc can never be observed correctly leading to non-sampling error. ]

2) Suppose a government official goes to a locality for a survey and he might ask questions that are too sensitive or some questions which an individual is reluctant to answer then the official chooses a number so as to complete the survey leading to a non-response error.

For a finite population U =( U1, U2 ....UN ) of size N and a random sample of size n is drawn without replacement. Let the characteristics under study, say, y takes value y_i on the unit U_i (i=1,2,...N). In a survey on the human population, it is often the case that n₁ unit responds on the first attempt while n₂ (=n-n₁ ) units do not provide any response. In the case of nonresponse of at initial stage Hansen and Hurwitz suggested a double sampling plan for estimating the population mean comprising the following steps :

(i) A simple random sample of size n is drawn and the questionnaire is mailed to the sample units;

(ii) A sub-sample of size r = (n₂/k), (k>1) from the n₂ non-responding units in the initial step attempt is contacted through personal interviews.

Now the suggested Hansen Herwitz estimator is where ,   ,

W₁=(N₁/N) and W₂=(N₂ /N).

The Variance of the estim