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Sampling Techniques

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Introduction I

A unit is the entity that is of interest to us. The population consists of all units of interest. The population size is the number of units in

the population. A frame is a list of all units in the population.

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Introduction II

Census is the process of investigating all the units in a population.

A sample is a subset of units selected from the population. Sampling is the process of taking a sample.

A parameter is a numerical summary derived from the population. A statistic is that derived from a sample.

The main purpose of sampling is to derive statistics and use them to approximate the parameters.

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Sampling problems

What is the appropriate sample size? This question will be answered in Chapter 4, Confidence interval analysis.

Which n units of the population should be selected? This question will be answered in this chapter.

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Sampling error and bias

Sampling error, introduced when sample mean is used to approximate population mean, is always there.- Sampling error due to luck is always there.- But sampling bias, the systematic error, can be

removed.- Other errors: non-response, false response, etc.,

will be there whether a sample or a census is used.

Simple random sample is used to remove bias.

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Simple random sample I

In a simple random sample, any n units will have equal chance to be selected before the selection.

- Example 1: 10 balls are in a bag. Only one ball will be selected, but each ball should have the same chance to be selected before the the selection. This is a simple random sample.

- Example 2: Lottery numbers. A group of six two digit numbers will be selected. Before the selection, each group of six two digit numbers should have the same chance to be selected.

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Small University I-- a counter example

A pollster comes to a small university with only 8 students, and decides to take a simple random sample of two students (sample size = 2)

The university has only 4 courses, in each course two students are enrolled. Each student can only take one course.

The pollster decides to randomly select two courses, then in each course randomly pick up one student. Eventually two students will be selected. Does this approach provide a simple random sample?

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Small University

John Tina Mary Janet David James Ben Joan

Course 1 2 3 4

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Simple random sample II

Step 1: Get the frame. Step 2: Determine the random digits needed. Step 3: Select n random numbers from the

random number table. Step 4: Select the corresponding units.

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Small University

1 John 2 David 3 Tina 4 James 5 Mary 6 Janet 7 Ben 8 Joan

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Remarks

For simple random sample, a frame is always needed. It may be difficult to obtain a frame.

We say “a simple random sample should ensure that any group of n units should have a equal chance to be selected”. The equal opportunity to be selected is before the selection, not after.

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Other random sampling techniques

Stratified sampling- First divide the whole population into several non-overlapping

sub-populations which are called strata.- A simple random sample will be taken from each stratum.

Cluster sampling- Divide the population into a number of sub-populations.- Only a random selection of sub-populations will be studied.

Systematic sampling

- One unit from the list is randomly selected.

- Every k-th (it can be the second, the 5-th, etc.) unit is then

systematically selected.