These notes are thoughts offered by instructors in various graduate courses that I attended, from my own experiences in the application of statistics, and other resources. These are not meant to be seen as 'definitive', but rather are intended to offer -- for non-statisticians -- some insight into what the field of statistics offers that other fields (such as engineering) may not.
What is the field of "statistics"? What does it do for us that the fields of Engineering and Science (physics, chemistry, etc.) do not?
What do statisticians offer that other professions do not?
From an article by Stefan Steiner and R. Jock MacKay in "Quality Engineering", 26:44-60, 2014
"The purpose of statistics is to learn, in either an exploratory or confirmatory sense."
Some might commonly suppose that statistical methods are meant to give an estimate of the measure of some thing. Maybe an average, or perhaps a maximum value.
This is true. However, another of the functions of the field of statistics is to give us an idea of the uncertainty of the estimate.
For example, if we wanted to know something about a product, we might measure its average value (arithmetic mean) by weighing a number of samples. Almost anyone can calculate an average value using one of the many available software packages.
But unless the population is very small it is usually not feasible to measure every member of product within the population. Therefore, we are uncertain just how well this sample average represents what we are really interested in: the population.
It is this uncertainty that the statistician is interested in.
See also: Confidence Misunderstood
From Mathematical Statistics with Applications (Wackerly):
"The objective of statistics is to make an inference about a population based on information contained in a sample from that population and to provide an associated measure of goodness for the inference."
Another thought shared by a former professor is that statisticians are exceptionally good at partitioning variance; they use tools to find the possible sources of variation, and -- by explaining the variation -- they extract signal from noise.
Other links within this site:
Confidence interval for GR&R components
(see the notes about calculating confidence intervals around GR&R components ... practical examples are available)
(see also the book "Design and Analysis of Gauge R&R Studies: Making Decisions with Confidence Intervals")
Confidence interval for Process Capability
Confidence Interval for sample variance