Lesson 1: Types of Data & Study Design

Welcome!

Let’s Pick A Section Marcher

Section Marcher Duties:

  • Take roll and report attendance
  • Designate a different inspector each day (find a system - rotate alphabetically?)
  • Everyone will do this multiple times

Inspections:

  • Polite check of uniforms - the idea is to help each other look right
  • No one is getting in trouble. We’re just helping each other avoid mistakes.
  • You can do the inspection before class starts

Introductions

Cadet Introductions

Draw the outline of your state on the board and put a star where your hometown is. Do not write the name of your state or hometown.

TipPlease Share
  • Name
  • Hometown
  • Company
  • Birthday
  • Academic Major
  • What you do in the Corps (Sport, Club, etc)
  • Favorite sports team
  • Possible Branch
  • What makes you unique?

CDT Dusty Turner: Center Point, Texas

  • Sprint Football
  • Sandhurst
  • OCF
  • F4
  • Dallas Cowboys, San Antonio Spurs, Texas Rangers

LTC Dusty Turner, PhD: Waco, Texas

NoteCareer Timeline
  • 2003-2007 BS, Operations Research: United States Military Academy (USMA)
  • 2007-2008 Engineer Basic Officer Course: Fort Leonard Wood, Missouri
  • 2008-2011 Platoon Leader / XO / AS3: Schofield Barracks, HI / Iraq
  • 2011-2012 Engineer Captain’s Career Course: Missouri S&T
  • 2012 MS, Engineering Management: Missouri S&T
  • 2012-2014 Company Commander: White Sands Missile Range, NM / Afghanistan
  • 2014-2016 MS, Integrated Systems Engineering: The Ohio State University
  • 2016-2019 Assistant Professor: United States Military Academy, West Point
  • 2019-2022 ORSA / Data Scientist: Center for Army Analysis, Ft. Belvoir
  • 2022-2025 PhD, Statistical Science: Baylor University (Waco, TX)
  • 2025-? Academy Professor: United States Military Academy, West Point

Jill: Saline, Michigan

NoteCareer Timeline
  • 2000-2004 BS, Economics: Michigan State University
  • 2004-2010 Project Manager: Epic Systems
  • 2011-2020 Consultant / Build Analyst (Epic Radiant & Cadence)
    • 2011-2013 Epic Radiant Build Consultant: Intellistar Consulting
    • 2014 Epic Radiant Build Analyst: Vonlay
    • 2016-2017 Epic Radiant Build Analyst: Huron
    • 2018-2020 Epic Cadence Build Analyst: Bluetree Network
  • 2020-Present Solutions & Application Architect / Principal Analyst: Mayo Clinic

Cal: Las Cruces, New Mexico

Reese: Columbus, Ohio

Expectations

What Are Your Expectations of MA206?

NoteMy Goals for the Course
  • Learn to Think Statistically
  • Develop Habits of Mind
  • Learn Army Systems
  • Responsible Use of AI

What Do You Expect of Me?

(Open discussion)

What We Can Expect from Each Other

NoteMy Commitments
  • Arrive prepared for each lesson
  • Encourage independent thinking
  • Maintain professionalism and respect at all times
  • Uphold the values of the Corps and our institution
  • Clear guidance and expectations for assignments
  • Be a professional mentor
  • Make Mistakes
NoteYour Responsibilities
  • Be responsible for your learning
  • Arrive prepared for each lesson
  • Engage actively in discussions and exercises
  • Maintain professionalism and respect at all times
  • Uphold the values of the Corps and our institution - you are junior members of this profession
  • Make mistakes

Class Rules

WarningClassroom Policies
Policy Details
Computers Course materials only
Food & Gum Not allowed in classroom
Drinks Spill-proof containers only
Bags & Gear Leave in the hallway
Staying Alert Stand up if you’re tired
Punctuality Arrive on time; don’t pack up early
Leadership Support the section marcher

Course Overview

The MA206 Story

Block I: Descriptive Statistics and Probability

Lessons 1-16, WPR I at Lesson 16.

Calendar weeks 1 through 7, Lessons 1 through 16

  • Descriptive Statistics - types of data, study design, measures of location and variability
  • Probability - set theory, basics, counting, conditional probability, independence
  • Random Variables - discrete (binomial, Poisson) and continuous (normal, exponential)

Block II: Statistical Inference

Lessons 17-28, WPR II at Lesson 28.

Calendar weeks 7 through 12, Lessons 17 through 28

  • Sampling distributions and the Central Limit Theorem
  • Confidence intervals and hypothesis testing
  • One-sample \(t\), one-proportion \(z\), two-sample \(t\), paired data, two-proportion \(z\)

Block III: Regression and the Analysis of Variance

Lessons 29-40, Project and TEE.

Calendar weeks 12 through 18, Lessons 29 through 40 plus TEE week

  • Simple and multiple linear regression
  • Analysis of variance

Where the Points Are

Graded Event Points
WebAssign Homework 150
WPR I (Lesson 16) 175
WPR II (Lesson 28) 175
Project 200
    EDA (Lesson 14) 25
    IPR (Lesson 34) 25
    Products (Lesson 37) 50
    Brief (Lessons 38-39) 100
TEE 300
Total 1000

WebAssign

  • 150 points of the course.
  • Due before every lesson, at the start of class.
  • 5 attempts per sub-question.
  • AI is welcome here. Document it IAW the DAAW and own what you submit.

WPRs / TEE

Two Written Partial Reviews and the Term End Exam, 650 of 1000 points between them.

When Covers Points Time
WPR I Lesson 16 Lessons 1-13 175 55 min
WPR II Lesson 28 Lessons 18-26 175 55 min
TEE 15-18 Dec Lessons 1-39 300 3 hr 30 min
  • No AI.
  • You get the SRC, a cumulative reference card.
  • Cadet-led review the lesson prior (15, 27, 40).
  • The WPRs are not cumulative. The TEE is.

The Course Project

You will run a statistical investigation on real data from an actual Army unit, hosted inside Army Vantage. You pick one of five published unit-level datasets. Account instructions are on Canvas.

Event Lesson Points
Exploratory Data Analysis 14 (23-24 Sep) 25
In-Progress Review 34 (20-23 Nov) 25
Products 37 (3-4 Dec) 50
Brief 38-39 (7-10 Dec) 100
  • 200 points spread across the semester. Work it concurrently.
  • AI is welcome. Document it IAW the DAAW and own the result.

Course Support

TipResources
Resource Link
Canvas MA206 Canvas
Cengage WebAssign WebAssign (access instructions on Canvas)
Army Vantage Army Vantage
Syllabus Course Syllabus
Calendar Course Calendar
Textbook Devore, Probability and Statistics for Engineering and the Sciences, 9th Ed.
Supplemental Readings Posted on Canvas, labeled S1, S2, and so on in the Read column
Additional Instruction Email me to coordinate

Today’s Lesson

Objectives

  • Distinguish populations, samples, and processes; contrast descriptive and inferential statistics; and distinguish a statistic from a parameter. (SLO 3)
  • Classify data as categorical or numerical, and numerical data as discrete or continuous. (SLO 2)
  • Construct and interpret histograms, and describe distribution shape. (SLO 2)
  • Describe data-collection methods, including simple random sampling and observational versus experimental studies. (SLO 3)

Reading: Devore 1.1, 1.2 and Supplement S1

The Big Picture

Why do we collect data? Because we want to learn about something bigger than what we can directly observe.

Term Definition
Population The entire collection of objects or individuals we want to learn about
Sample The subset of the population we actually observe

Descriptive statistics summarizes the data you have. Inferential statistics uses that sample to make a claim about the population you cannot see. The whole course is built on that move.

Parameters vs Statistics

Population Sample
What we have Usually unknown Observable data
What we call it Parameter Statistic
Notation Greek letters (\(\mu\), \(\sigma\), \(p\)) Latin letters (\(\bar{x}\), \(s\), \(\hat{p}\))

A statistic is computed from the sample and is used to estimate a parameter.

Every time you see a number in this course, ask whether it is a parameter or a statistic. If it came from data, it is a statistic, and it will be a little bit wrong. Quantifying how wrong is Block II.

Types of Data

Type Definition Example
Categorical A label or category Branch, company, pass/fail
Numerical, discrete Values can be listed, usually counts Vehicles deadlined
Numerical, continuous Values form an interval Repair time, distance, weight

The type of variable determines how you summarize it, how you picture it, and which inference method you will use in Block II.

Variable type Summarize with Picture with Block II method
Categorical Proportion \(\hat{p}\) Bar chart \(z\) procedures for proportions
Numerical Mean \(\bar{x}\), SD \(s\) Histogram, boxplot \(t\) procedures for means

A variable coded with numbers is not automatically numerical. Company coded 1-9, or a 1-5 satisfaction rating, is still categorical. Ask whether the arithmetic means anything: is the average of Company 2 and Company 4 really Company 3?

Histograms

A histogram splits the number line into bins of equal width, counts how many observations land in each bin, and draws a bar of that height. It answers three questions at a glance: where is the data centered, how spread out is it, and what shape does it have?

Repair times for 60 jobs. Notice what the long right tail does: it drags the mean above the median. The mean follows the tail; the median does not.

To read a histogram, report center, spread, and shape, then say whether anything is unusual. Outliers and gaps are findings, not nuisances. In the Army they are often the whole point: the one vehicle that took 40 hours to fix is the one your commander wants to hear about.

Describing Shape

Shape is named for the direction the tail runs.

Shape Tail Center
Right-skewed (positively skewed) Runs right mean > median
Symmetric Halves mirror each other mean \(\approx\) median
Left-skewed (negatively skewed) Runs left mean < median

Collecting Data

How you got the data limits what you are allowed to say about it.

A simple random sample (SRS) of size \(n\) is chosen so that every possible sample of size \(n\) has the same chance of being selected. This is what makes inference from the sample to the population legitimate.

There are two kinds of study.

Study What you do What limits it
Observational Observe and record; you do not assign the conditions Groups may differ in ways you did not measure
Experiment Assign subjects to conditions, ideally at random Random assignment balances what you did not think to measure

That distinction sets up a rule that survives the whole course.

Random sampling buys you the right to generalize from the sample to the population. Random assignment buys you the right to claim the treatment caused the difference. They are different tools, and you need both to say this caused that and it holds for everyone. An observational study, no matter how large, does not establish causation.

Board Problem: A Motor Pool Study

The battalion maintenance officer wants to know whether a new diagnostic procedure shortens repair times. There are 240 vehicles in the battalion. She selects 30 at random, records the repair time in hours for each, and finds a mean of 12.4 hours.

  1. What is the population? What is the sample?
  2. Is 12.4 a parameter or a statistic? What notation would you use?
  3. Classify “repair time in hours” and “vehicle type” by data type.
  4. Is this an observational study or an experiment?
  5. She finds that vehicles run through the new procedure averaged 3 hours less. Can she conclude the procedure caused the reduction? What would she have had to do differently?

  1. Population: the repair times of all 240 vehicles in the battalion. Sample: the 30 vehicles she selected.

  2. A statistic, written \(\bar{x} = 12.4\). The corresponding population parameter \(\mu\) is unknown, which is exactly why she took a sample.

  3. Repair time: numerical and continuous (any value in an interval). Vehicle type: categorical, even if the motor pool codes it as a number.

  4. As described, observational. She recorded what happened; she did not assign vehicles to procedures.

  5. No. Vehicles that got the new procedure may differ systematically, maybe newer vehicles, maybe a more experienced crew, maybe the easy jobs. To claim causation she needs to randomly assign vehicles to the old or new procedure. Random selection alone gets her generalization; random assignment is what gets her cause.

Before You Leave

Today

  • Population vs sample
  • Descriptive vs inferential statistics
  • Parameter vs statistic: Greek is unknown truth, Latin is what your data gave you
  • Categorical vs numerical, and discrete vs continuous
  • Histograms: center, spread, shape, and what the tail does to the mean
  • Skew is named for the tail
  • Random sampling gets you generalization; random assignment gets you causation

Any questions?

Next Lesson

Lesson 2: Measures of Location & Variability

  • Sample mean, median, and trimmed mean, and their sensitivity to outliers
  • Sample variance, standard deviation, range, and fourth spread (IQR)
  • Boxplots, comparative boxplots, and identifying outliers

Reading: Devore 1.3, 1.4 and Supplement S2

Upcoming Graded Events

  • WebAssign 1.1, 1.2 - Due at the start of Lesson 2
  • EDA (Project) - Lesson 14
  • WPR I - Lesson 16 (covers Lessons 1-13)