MEGR 3171 — Week 2: Statistical Analysis & Error Characterization

Overview

Week 2 at a Glance

Week 2 moves from the vocabulary of measurement performance into the mathematical tools for characterizing error. You will learn to separate bias (systematic) error from precision (random) error, compute descriptive statistics from repeated measurements, apply the normal distribution to estimate probabilities, and construct confidence intervals that tell you how much you can trust your data.

These statistical methods are used every week for the remainder of the course — in uncertainty analysis, calibration, sensor characterization, and experimental reporting.

Systematic vs. random errorDescriptive statisticsNormal distributionConfidence intervalst-distributionHypothesis testing

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Why it matters in practice. A result without a confidence interval is an incomplete result. Industry and regulatory standards require you to report not just a value but a range within which the true value lies with a stated probability. This week teaches you how.

Objectives

What You Will Be Able to Do

Course objectives (CO) define program-level skills. Module objectives (MO) define specific weekly targets that build toward them.

Course Objectives (CO)

CO1: Apply statistical methods to characterize experimental measurement data.

CO2: Compute confidence intervals and perform hypothesis tests.

Module Objectives (MO) — Week 2

Distinguish systematic (bias) error from random (precision) error and identify sources of each in a measurement system.
CO1

Compute mean, standard deviation, and standard error of the mean from a set of repeated measurements.
CO1

Apply the normal distribution to estimate the probability of a measurement falling within a given range.
CO1

Construct confidence intervals using the t-distribution for small sample sizes.
CO1

Perform a t-test to determine whether two measurement populations are statistically distinguishable.
CO2

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Review these objectives before you start each assignment. They map directly to what is assessed on the quiz, homework, and exams.

Suggested Learning Path

How to Work Through This Week

Follow this sequence. Each step prepares you for the next. Do not attempt graded work before completing the instructional material it depends on.

1

Read Alciatore Ch. 2

Focus on Sections 2.1-2.5 for the core statistical material. The worked examples in Section 2.4 (confidence intervals) are especially important — work through them with pencil and paper.

2

Review: Normal distribution and the 68-95-99.7 rule

If statistics is rusty, spend 15 minutes reviewing the empirical rule before lecture. A solid mental model of the normal distribution makes everything else in this module easier.

3

Attend Lecture

Lecture 1 covers descriptive statistics and error characterization. Lecture 2 covers confidence intervals and the t-distribution. The in-class problem session applies both to real sensor data.

4

Complete Module 1 Homework — due this week

Module 1 Homework is due at the end of Week 2. Use this week's lecture content to complete any remaining problems from Week 1, especially any calibration or data presentation problems.

Instructional Material

Required Readings, Videos, and Resources

Complete all required items before moving to graded activities. The Aligns to column maps each resource to the module objectives it directly supports.

Resource	What You Will Gain	Aligns to	Est. Time
Read Alciatore Ch. 2 — Statistical Considerations for Measurements (5th Ed.)	Systematic vs. random error taxonomy, population vs. sample statistics, normal distribution, t-distribution, and confidence interval construction.	MO1-MO5	60-75 min
Watch Micro-lecture: Confidence Intervals in 5 Minutes	A condensed visual walkthrough of the confidence interval formula and how the t-factor changes with sample size and confidence level.	MO4	5 min
Explore NIST/SEMATECH e-Handbook of Statistical Methods (online)	The gold standard reference for engineering statistics. Chapter 1 aligns directly with this week's content and is freely available online.	MO1-MO5	Optional

Graded Learning Activities

Assignments and Due Dates

All graded work is submitted through Canvas. Complete the listed prerequisites before attempting each assignment.

Assignment	Prerequisites	What Is Assessed	Aligns to	Points
Module 1 Homework: Measurements Fundamentals End of Week 2	Complete Ch. 1 and Ch. 2 readings. Week 2 lecture content directly supports the statistics and calibration problems.	Measurement chain analysis, static performance metric calculation, calibration procedure, and uncertainty reporting.	MO1-MO5	50 pts

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Academic integrity. The Module 1 Homework statistics problems require you to use your own measured data from the Arduino lab setup. Fabricating data or copying another student's numerical values is academic dishonesty and will be treated accordingly.