Statistics and Measurements

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.

Title	JTF Link	TFS Link	Info Page	Subject
How Deviant and Mean Are Your Data? Intro and Basics Part 1	Link	No	Page	Mean and Standard Deviation
How Deviant and Mean Are Your Data? Part 2	Link	No	Page	Standard Error and Confidence Interval
Basics Statistics by Hand	Link	N/A	Page	\(\bar{x}\), \(S\), \(S_{\bar{x}}\), \(\lambda\) by hand
Basics Statistics with a Spreadsheet	No	N/A	Page	\(\bar{x}\), \(S\), \(S_{\bar{x}}\), \(\lambda\) with a spreadsheet
Basics Statistics in Python	No	N/A	Page	\(\bar{x}\), \(S\), \(S_{\bar{x}}\), \(\lambda\) in Python
Basics Statistics in R	No	N/A	Page	\(\bar{x}\), \(S\), \(S_{\bar{x}}\), \(\lambda\) in R

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.

Title	JTF Link	TFS Link	Info Page	Subject
TBD	No	No	No	Linear Regression
Linear Regression with a Spreadsheet	No	N/A	No	Slope, Intercept, and Functional Bounds with a spreadsheet
Linear Regression in Python	No	N/A	No	Slope, Intercept, and Functional Bounds in Python
Linear Regression in R	No	N/A	No	Slope, Intercept, and Functional Bounds in R

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.

Title	JTF Link	TFS Link	Info Page	Subject
TBD	No	No	No	Error Propagation in Algebraic and Transcendental Functions
TBD	No	No	No	Error Propagation when integrating and Differentiating Time Series, Part 1
TBD	No	No	No	Error Propagation when integrating and Differentiating Time Series, Part 2

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.

Title	JTF Link	TFS Link	Info Page	Subject
TBD	No	No	No	Noninear Regression, Parameter Fitting, and functional and observational bounds
Noninear Regression with a Spreadsheet	No	N/A	No	Parameter, and Functional Bounds with a spreadsheet
Linear Regression in Python	No	N/A	No	Slope, Intercept, and Functional Bounds in Python
Linear Regression in R	No	N/A	No	Slope, Intercept, and Functional Bounds in R