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UW-Madison STAT 411 - Lecture Notes on Non-Sampling Errors

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Ways to Convert Non-Responders Into RespondersReferences for Non-Sampling ErrorsStat 411 Lecture Notes on Non-Sampling ErrorsYour book has a short section on non-sampling errors. I will be going into much more detail about some of the topics, and skipping others – but regardless, I strongly suggest you read sections 3.3 – 3.6 in the book. Pay special attention to section 3.6, which gives a checklist for the planning stages, and will be particularly useful when writing your finalpaper.------------------------------------------------------------------------------------------------------------Non-sampling errors can be generally defined as any source of bias or error in the estimation of a population characteristic in which the uncertainty about the resulting estimate is NOT due to the fact that we’re sampling. You can think of them as errors for which increasing the sample size will not aid us in our estimation.There are two main types of non-sampling errors that we’ll talk about:Non-Response Errors – not all selected elements yield their information, which usually means that the population of interest is not the population from which the sample is drawnMeasurement Errors – measurements taken on selected elements are wrong, known with error, or not accurate enough-----------------------------------------------------------------------------------------------------------Let’s consider non-response first. This is a problem usually associated with surveys or interviews – any situation in which the human element is involved. People can and will refuse information for a wide variety of reasons – they could be busy, uninterested, suspicious of the surveyor’s intentions, afraid they won’t be anonymous, or simply uncooperative. The problem with non-response is that it changes our sampling frame – ifsome elements will not give us their information, then effectively we are sampling from the population of potential responders, not the population of interest. For example, let:N = total population size, and  = population meanN1 = total potential responders, and 1 = population mean of respondersN2 = total potential non-responders, and 2 = population mean of non-respondersSuppose we conduct an SRS from this population, with estimation via the usual sample mean (which is unbiased under SRS when all folks respond). Is the sample mean unbiased when there is non-response? No, because all of our data is drawn from the population of responders, and thus we are really estimating is 1, not . The bias in this case can be shown to be (N2 / N)*(X1bar – X2bar).You can think of this situation as a stratified sample where the population is broken into two strata, and we only have data from one stratum. Remember that the simple estimator used on data from a stratified sample is biased for  - the same thing applies here. Some of you might be wondering – can’t we think of this as a two-stage sample where wechoose m=1 of the M=2 strata, then take an SRS within that group? Not quite. And the reason is because we are not randomly choosing the group that we take in the first stage –we are forced to take the group of responders. IF there was equal chance of getting eithergroup, THEN we could use a two-stage estimator.Notice that if 1 = 2, in other words, if the populations of responders and non-responders are the same, then 1 = , and we’re out of the woods – we can do everythingin the same manner as we have all along. Evaluating whether or not the responders and non-responders are the same involves making an assumption, and that assumption is more or less reasonable depending on each specific situation.So what if we can’t reasonably assume that the groups of responders and non-responders are similar, or if we prefer not to let our analysis ride on a subjective assessment? There are some alternatives.The most obvious (but practically speaking, usually the hardest and/or most expensive) method of reducing non-response bias is to convert non-responders into responders. Recall the equation for non-response bias: (N2 / N)*(X1bar – X2bar). One way to reduce the absolute value of this quantity is to reduce N2/N, i.e., reduce the proportion of non-responders in the population. The ways to do this are numerous. Here is a medium-sized list, with short discussions of pros and cons. Some are specific, some are general, some are practical and some are psychological. They appear in no particular order.Ways to Convert Non-Responders Into Responders1. If you are conducting a telephone or face-to-face interview, make sure you call/visit at times when the person to be interviewed is likely to be home. For the average working Joe, this means sometime in the evening after 6pm. But don’t call too late either, or you may incur non-response because of a sleepy and annoyed individual. Sometime between 6 and 8 is best.2. If you intend to send a mail survey, confirm that the people you wish to survey still live at the address you have on file - registries of this sort become obsolete quickly (20% of American families move each year). If a particular individual does not respond, you may want to send a representative to the address to find outif they are there, or perhaps to find out to where they have moved. If you want to sample whoever is currently living in the address you’ve selected, label the envelope, for example, “Mr. and Mrs. Smith or current resident.”3. For mailed surveys in particular, studies have shown that using attractive, high quality, official-looking envelopes and letterhead can improve response significantly. Include a carefully typed cover letter explaining your intentions, and guaranteeing their confidentiality. Get a big-wig from your company or organization to sign it (personally, if possible). Always send materials through first-class mail, and include a return envelope with first-class postage.4. Keep surveys and interviews as short as possible. As a general rule, the more questions you ask, the less likely you are to get accurate (or any) information.5. Use the guilt angle whenever possible (but do it implicitly, don’t beg). What I mean by this is simply to increase the amount and quality of personal contact withyour population. Psychologically speaking, for most people it’s easy to throw away a mailed survey, considerably harder to hang-up on an interviewer, and harder yet to walk away. Therefore,


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