Statistics and Measurements

Author

DOFPro group

Why Statistics and Measurements

All chemical and thermal processes have one or more outputs, whether it be a chemical product such as benzene or electrical power. The goal of almost all process engineers is to maximize the output for a given cost or minimize the cost for a given output. Engineering is a quantitative discipline, and we have to quantitatively report our inputs and outputs. Since all processes experience random fluctuations from the process itself or from the measurement process, the engineer needs to be able to account for the noise. Statistical methods are the most common ways to report both the inputs and outputs, and the variations or noise in the inputs or outputs. There are seventeen videos discussing common statistical methods used in Chemical and Thermal Processing and other fields of engineering, divided up into basic statistics, linear regression, error propagation, nonlinear regression, and error propagation in integrals and derivatives

Basic Statistics

The most commonly used basic statistics are the arithmetic mean, the standard deviation, and the confidence interval. These three are covered in the videos and web pages listed in the table below. The column labeled JTF contains links to the Just The Facts videos, intended mainly for review. The TFS videos are The Full Story videos, with more explanation and discussion. The Info Page contains additional information and definitions for the videos.

How Deviant and Mean Are Your Data? Intro and Basics Part 1, Just the Facts
Mean (\(\mu,\ \bar{x}\)) and Standard Deviation (\(\sigma,\ S\))
Video, Info Page, Visuals

How Deviant and Mean Are Your Data? Intro and Basics Part 1, The Full Story
Mean (\(\mu,\ \bar{x}\)) and Standard Deviation (\(\sigma,\ S\))
Video, Info Page, Visuals

How Deviant and Mean Are Your Data? Part 2
Standard Error (\(S_{\bar{x}}\)) and Confidence Interval (\(2\lambda\))
Video, Info Page, Visuals

Basics Statistics by Hand
\(\bar{x}\), \(S\), \(S_{\bar{x}}\), \(\lambda\) by hand
Video, Info Page, Visuals

Basic Statistics on a Spreadsheet
\(\bar{x}\), \(S\), \(S_{\bar{x}}\), \(\lambda\) with a spreadsheet
Video, Info Page, Visuals

This is NOT a DOFPro video.
Basic Stats in MATLAB
\(\bar{x}\), \(S\), \(S_{\bar{x}}\), \(\lambda\) with MATLAB
Video, Info Page, Visuals

Basic Statistics in R
\(\bar{x}\), \(S\), \(S_{\bar{x}}\), \(\lambda\) in R
Video, Info Page, Visuals

Linear Regression

A very common means of presenting and analyzing sets of data pairs is linear regression or fitting a linear function to the data. We only present methods for least-squares linear regression. The method is covered in the videos listed in the table below. The column labeled JTF contains links to the Just The Facts videos, intended mainly for review. The TFS videos are The Full Story videos, with more explanation and discussion. The Info Page contains additional information and definitions for the videos.

This is NOT a DOFPro video.
Linear Regression
Derivation of the equations for linear regression
Video, Info Page, Visuals

This is NOT a DOFPro video.
Linear Regression Spreadsheet
Performing linear regression with a spreadsheet
Video, Info Page, Visuals

This is NOT a DOFPro video.
Linear Regression MATLAB
Performing linear regression with MATLAB
Video, Info Page, Visuals

Linear Regression in R
Linear Regression in R
Video, Info Page, Visuals

Error Propagation

Experimental data taken by engineers are usually further processed as part of design or analysis procedures. The question often arises as to how the uncertainty in the measured data affect the uncertainty in the final calculation. There are both analytical and numerical methods for evaluating how the undertainty or error propagates. These methods are explored in the videos listed in the table below. The column labeled JTF contains links to the Just The Facts videos, intended mainly for review. The TFS videos are The Full Story videos, with more explanation and discussion. The Info Page contains additional information and definitions for the videos.

This is NOT a DOFPro video.
Error Propagation
Propagating errors or uncertainties through equations and calculations
Video, Info Page, Visuals

This is NOT a DOFPro video.
Integrals and Derivatives Part 1
Propagating errors or uncertainties through numerical integrals and derivatives
Video, Info Page, Visuals

This is NOT a DOFPro video.
Integrals and Derivatives Part 2
More propagating errors or uncertainties through numerical integrals and derivatives
Video, Info Page, Visuals

Nonlinear Regression

When the model for fitting data contains parameters that are non-linearly related to the fitting function, the model parameters may be determined through nonlinear regression. The method is covered in the videos listed in the table below. The column labeled JTF contains links to the Just The Facts videos, intended mainly for review. The TFS videos are The Full Story videos, with more explanation and discussion. The Info Page contains additional information and definitions for the videos.

This is NOT a DOFPro video.
Nonlinear Regression
Derivation/explanation of nonlinear regression
Video, Info Page, Visuals