A mathematical method that employs probability theory for inferring the properties of a population parameter from which the sample is taken is known as inferential statistics. Inferential statistics is a set of methods used to make generalizations, estimations, or predictions.

Use: Let’s say that we want to determine the statistical capability of a process. And, let’s say that 28 machines are producing a particular part. This process has 14 operators that run the parts. The operators use their own micrometers to measure key characteristics of the parts. There are three sources of raw materials that feed into the process. The process runs two shifts per day five days a week.

**Scenario one:** To determine process capability, the team measures the parts from Nicole’s machine number 16 on Tuesday’s first shift. The inference space is limited to one machine, with one person, with one measurement device, over a period of time of eight consecutive hours using just one of the three sources of raw materials. This is a very narrow inference space.

**Scenario two:** To determine process capability, the team measures a sampling of parts from each of the 28 machines produced by 14 operators using 14 measurement devices over two shifts over a period of one month. This is a broad inference space, and in this scenario, the team will have a much better insight into the true statistical capability of the process.

It is best to have as broad of an inference space as possible.