Determining the appropriate sampling method to use is often confusing for green belts and black belts. Statistical sampling is a highly useful quality tool as long as we follow the basic concepts and understand the various sampling methods. The first three methods we’ll look at fall under the category of probability sampling. They are:

- Random Sampling
- Stratified Sampling
- Systematic Sampling

The last sampling method falls under the category of non-probability sampling and is known as Block Sampling.

**Random Sampling**

This basic method involves drawing a sample from a targeted population in a manner so that each member of the sample has an equal probability of being chosen. In addition, every sample member is selected independently of every other member. There is no relationship between the subjects in each sample. This means that subjects in the first group cannot also be in the second group. No subject in either group can influence subjects in the other group. For example, to compare the heights of males and females, we could take a **random sample of 100 females and another random sample of 100 males**. The result would be two samples that are independent of each other.

The process for random sampling is as follows:

- Determine the sampling frame. The sampling frame is the list from which units are drawn for the sample. The ‘list’ may be an actual listing of units, as in a phone book from which phone numbers will be sampled, or some other description of the population, such as a map from which areas will be sampled.
- Assign each member of the population a number from 1 to N.
- Generate a sample size of n different random numbers between 1 and N.
- Select the members of the population associated with the n random numbers. This constitutes the sample.

Here is a graphical representation of random sampling.

**Stratified Sampling**

Stratified random sampling is a method of sampling that involves dividing a population into smaller groups–called strata. The groups or strata are organized based on the shared characteristics or attributes of the members in the group. For example, a stratified sample is one that ensures that subgroups (strata) of a given population are each adequately represented within the whole sample population of a research study. For example, one might divide a sample of adults into subgroups by age, like 18–29, 30–39, 40–49, 50–59, and 60 and above. The process of classifying the population into groups is called stratification.

The following is a graphical representation of stratified sampling.

**Systematic Sampling**

This sampling method, sometimes called interval sampling, involves sampling from an ordered population at a specified sampling interval, *i*. Systematic sampling is fast and efficient, but issues can arise if the sampling interval synchronizes with a natural periodicity in the ordered population. For example, if defects occur every *i* – 1, *i*, *i* + 1 interval. The chances of this occurring can be minimized by randomly starting within the first interval. I was involved in a process where this occurred. A team conducted a capability analysis on a process with a pneumatic pump. If the air pressure was high, no defects occurred, but when the pressure fell below a certain level, defects started to occur. Of course, their analysis showed the process was highly capable since they had conducted their study when the air pressure was high.

The graph below shows a representation of systematic sampling.

**Block Sampling**

Block sampling, sometimes called judgment block sampling, refers to the situation where an initial item is chosen from a population in sequential order and, consequently, the items in the balance of the defined block are automatically chosen. It falls into the category of non-probability sampling and is a sampling technique typically used in auditing. Sampling risk can be reduced by selecting a large number of blocks of samples. It is shown in the graph below.