Q. 205  Let us consider a situation where drawing/testing large number of samples is disadvantageous and the Lean Six Sigma analyst has decided to use limited samples. What are the precautions that the analyst should take so as to limit biased and unbiased sampling errors ? Explain with suitable examples. 

 

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Benchmark Six Sigma Expert View by Venugopal R

Any sampling method that is used to evolve conclusions for a population is bound to have errors. However, it is not practical to assess entire populations in many situations and one has to rely on sampling methods. Hence it is important to understand about the errors that could arise while using a sample and we take decisions based on the knowledge about sampling errors.

 

Biased & Unbiased sampling errors

Biased sampling errors occur when a sample is drawn from a large base, and there is a likelihood that certain types of members are not included in the population, or disproportionately included. For instance, in a bank, in order to understand reasons for delayed payments for of loan installments, we take a sample of defaulters who are employed with various companies. This could be a biased sampling since we are getting the causes only from ‘salaried’ people. Defaulters who are not salaried (say businessmen) may have different causes.

 

Biased errors can happen when the measuring instrument used for measuring the sample has a bias. For example, if samples are weighed using  a weighting machine with bias, we get biased errors.

 

Despite taking necessary precautions to minimize bias, sampling can still have errors due to chance variation and they are unbiased sampling errors. As we know for variable data, by the principle of central limit theorem, the variance of samples will be equal to variance of the population divided by n. In general, if we keep increasing the sample size, the sample characteristics will tend towards the population characteristics and hence lower the errors.

 

Sampling Techniques

There are various methods within sampling that may be chosen for a given situation to limit the errors due to sampling bias. Given below are a few of them.

 

Use discretion while using ‘Non-Probability samples’, which do not make use of a ‘frame’. Such samples are likely to be subjected to unknown bias and are advisable to be used only for rough estimates.

 

For Probability samples, decide the best ‘frame’ for sampling, such that the units within the frame best represent the population.

 

Simple random sampling

The random sampling method has a frame with every item numbered from 1 to N, where N is the population size. Random numbers are used to select n samples. Statistically, random samples do not have bias on mean value. The sampling error can be evaluated and kept within limits by controlling the sample size.

 

Stratified sampling

If we can divide the population into portions based on some common characteristic within each portion, then a ‘Stratified sample’ can be used. Here the frame is divided into portions or strata and simple random sampling applied for each stratum. The results may be combined finally. Stratified sampling will help to reduce the sample size and hence the costs, compared to simple random sampling without compromising the bias. For example, if we need to pick samples of products produced at different sites, assuming that within each site the samples exhibit homogeneity of characteristics, we may use the stratified sampling technique.

 

Systematic sampling

Another method is the ‘systematic sampling’. Here the population inside the frame is divided into number of groups depending upon the sample size and a sample is picked at equal intervals. Such method could be useful while taking samples from a running production or for a customer feedback in a supermarket and other such situations. However, if there is some sequential pattern involved in the characteristic, this method will induce bias.

 

Factors to determine sample size

One more useful information - While doing comparative tests like tests of hypothesis, a lower sample will play safe will tend to keep the H0 as true. In some of the statistical softwares, you can provide inputs on the delta that you consider important, apart from the confidence level and power of the test to determine the minimum sample size.

Sampling Errors are of two types (as already mentioned in the question) - Biased and Unbiased.

 

Biased Sampling Error - is one which results in a bias in the sample. The effect of this bias is that the result of the sample will not reflect the true nature of the population. There are three sources of such bias

1. Survey Bias: where the survey questionnaire or the process of collecting data is biased

2. Researcher Bias: bias introduced by the researcher of the study

3. Respondent Bias: bias in the responses if the respondent chooses not to give the correct answer

 

Unbiased Sampling Error - is one which is the resultant of chance. The sample will never reflect the population simply because the observations will vary from each other. 

 

Selecting a large sample size is one way in which both these biases could be avoided. However, since our analyst has decided to choose a smaller sample size, he should take care of the following things

 

1. Sampling method: choose the one which gives a random representative sample

2. If there is a questionnaire involved, then ensure that there are no leading questions or questions for which the respondents might have a tendency to not give the right response. Make the survey anonymous so that respondents could give correct responses

3. Determine which is more important - alpha or beta error? Since sample size is fixed, he could then determine either the significance level or Power of the Test that he is going to get and whether it is ok or not

Winner for this question is Natwar Lal. Please go through expert view by Venugopal as well.