Probability vs Statistics

Probability

A measure on how likely an event occurs
Computing probabilities have rules
Logical reasoning
One answer

Statistics

Methods on answering how likely it is that a claim is true
It’s an Art
Data-driven approach to write conclusions
Multiple ways to solve problems

Motivating Example 1

Vaccine Efficacy vs Vaccine Effectiveness

Image: Vaccine Efficacy Rates. [1]

Efficacy means that for a vaccinated person in a clinical trial, they will be X% less likely to contract the disease. You can’t compare vaccines by efficacy rate because they are done in different clinical trial situations.

Quick References:

[1] “Why comparing Covid-19 vaccine efficacy numbers can be misleading?” by Umair Irfan, Vox

[2] “The Statistical Secrets of COVID-19 Vaccines” by Adam Rogers, Wired

What is “efficacy”? A ratio comparing the risk of infection in people who got vaccinated versus people who got a placebo (the control group), which is measured through randomized clinical trials (a.k.a experimental study).
How is “effectiveness” measured? Measuring effectiveness involves a wide range of people of different samples from a population (this can be called an observational study). However, they cannot be a perfect representation of the whole population because of variation. Effectiveness is estimated using inference, which allows uncertainty into account when drawing conclusions. [2]

Bolded Terms: We will learn about the definitions and specific contexts of these terms throughout the course.

Motivating Example 2

Semantic/Sentiment Analysis and Question-Answering

Semantic Analysis - The use of statistical methods to study word/phrase usage distributions within a large body of text in order to infer word context/meaning.
Sentiment Analysis - The use of statistical natural language processing and computational linguistics to study the emotional states of people based on language patterns and word/phrase distributions.
Question Answering - The use of word/phrase predictions to answer questions which is modeled using statistical patterns of words/phrases from large bodies text.

Quick References:

[1] UnQover Website: unqover.apps.allenai.org

Uncovering Stereotypical Biases Through a Question-Answering Model [1]

Open Question:

Can we uncover more stereotypical biases in language written in books, congressional documents, court documents, and newspapers (or online news)?

Statistics is Widely Applicable

Mathematics

Physics

Chemistry

Biology

Sociology

Linguistics

Humanities

Statistics is an interdisciplinary field which is concerned with developing and studying methods for collecting, analyzing, and interpreting data.

Tentative Topics Schedule

Week	Dates	Topic
1	8/30 – 9/3	Class Introductions, R, and Sources of Data
2	9/7 – 9/10	Natures of Data & Data Visualizations
3	9/13 – 9/17	Linear Regression
4	9/20 – 9/24	Probability & Logistic Regression
5	9/27 – 10/1	Hypothesis Testing & Confidence Intervals Part 1
6	10/4 – 10/8	Hypothesis Testing & Confidence Intervals Part 2
7	10/11 – 10/15	Review & Midterm
8	10/18 – 10/22	Fall Break!
9	10/25 – 10/29	Statistical Models & Decision Errors
10	11/1 – 11/5	Inference for Proportions
11	11/8 – 11/12	Inference for Two-Way Tables
12	11/15 – 11/19	Inference for Means
13	11/22 – 11/24	Inference for Linear Regression
14	11/29 – 12/3	Inference for Logistic Regression
15	12/6 – 12/8	Review & Project Period
16	12/13 – 12/16	Final Exams

Resources

Textbook
OpenIntro: Introduction to Modern Statistics (2021)
by Mine Çetinkaya-Rundel and Johanna Hardin, First Edition.

Course Website
reed-statistics.github.io/math141-fall2021

Slack Workspace
math141-quijano.slack.com
Please use your Reed email address to sign-up.
join.slack.com/t/math141-quijano/signup.

Email
aquijano@reed.edu
Please put the “MATH 141” keyword in your subject line.

R Studio Server
rstudio.reed.edu

Office Hours

Alex John Quijano
Tuesday and Thursday at 3:00 PM - 4:00 PM
Wednesday and Friday at 1:00 PM - 2:00 PM
(or by appointment)
Library 394

Lab Assistants
Maxwell - MW 4:30 PM - 6:00 PM (ETC 205b)
Gillian - MTu 7:30 PM - 9:00 PM (Zoom: reed-edu.zoom.us/j/94604917095)
Robin - Thu 4:30 PM - 6:00 PM (ETC 205b)

Assignments

Reading
The textbook reading assignments are listed in the course website under the topics schedule.

Homework
Weekly, posted every Monday, and due in one week. Most of the questions will be from lectures and textbook.

Lab
Bi weekly, posted every other Tuesday, and due in two weeks. The lab assignments are R programming and report writing which involves applying statistical methods on data.

Project
The final report is a group research project that demonstrates a comprehensive understanding of basic data analysis, statistical modeling, and inference. The project rubric details will be announced this upcoming Friday.

Submissions through Gradescope
Homework, lab, project assignments, and exams are submitted through gradescope.com. Please sign-up as a student with your Reed email using this Gradecope entry code: 2R8X6V.

Today’s Activity

Let’s set ourselves into groups of 4 people each.
Introduce yourselves to your group - name, pronouns, major, favorite fictional superheroes (Spiderman, Doctor Strange, Scarlet Witch, Black Panther, Naruto, Saitama etc.)
Write your individual answers of these four questions and discuss it with your group (these questions will be part of your first homework assignment).
- To what extent is your experience in probability and statistics?
- What do you hope to learn in this class?
- What are you excited about in this class?
- What are your anxieties and concerns about the class?

1 - Class Introductions MATH 141: Introduction to Probability and Statistics Fall 2021