Statistical Thinking

Applied Statistics

MTH-361D | Spring 2025 | University of Portland

January 15, 2025

Objectives

Introduce the concept of statistical thinking
Communicate the course learning outcomes
Activity: Reading and Writing Exercises

Data Science

The Data Science Life Cycle

Statistical Thinking: An Overview

What is statistical thinking?

A way of understanding the world through data.

Statistical Thinking in the Data Science Life Cycle

Example 1: Statistical Question

Question: What is the crime rate in Portland, OR?

This question requires:

Data collection from a representative sample of neighborhoods in Portland.
Statistical analysis to estimate the average crime rate.

Example 1: Preparation

Question: What is the crime rate in Portland, OR?

The analysis anticipates:

Variability. No two neighborhoods will produce exactly the same result.
Uncertainty. Because data varies, we’re often unsure about the “true” answer to the question.
Context. Numbers alone don’t tell the whole story. You need to consider the situation, the method of data collection, and any potential biases.

Example 1: Data Visualization

Portland crime rates in fiscal year 2020 to 2021.

Example 1: Confounders

Follow-up question: What types of crimes are usually reported?

Portland types of crimes in year 2020 to 2021.

Statistical Thinking: Steps

Statistical Thinking in the Data Science Life Cycle

Steps in Statistical Thinking:

Ask a question or identify a problem
Collect data, understand variability, identify patterns and relationships
Apply statistical analysis
Evaluate results and make a conclusion or predict an outcome

Course Learning Outcomes (1/2)

Data Fundamentals:
- Understanding Data: Comprehend data structures, collection methods, and limitations.
- Data Exploration: Perform exploratory data analysis, including data visualization and descriptive statistics.

Statistical Modeling:
- Regression Analysis: Apply and interpret linear regression models.
- Inferential Statistics: Conduct hypothesis testing, construct confidence intervals, and perform estimation.

The full course learning outcomes and objectives is in the Syllabus.

Course Learning Outcomes (2/2)

Probability Theory:
- Foundations: Understand random variables, probability distributions, and their applications in statistical analysis.
Data-Driven Conclusions:
- Critical Evaluation: Assess claims, draw meaningful conclusions from data, and make informed decisions.

R Programming:
- Implementation: Develop and execute R code for data analysis, modeling, and visualization.
Communication:
- Reporting: Produce clear and concise written reports summarizing findings and insights.

The full course learning outcomes and objectives is in the Syllabus.

Activity: Reading and Writing Exercises

Scenario: Researchers conducted a study to understand whether drinking coffee impacts productivity at work. They collected data on how much coffee people drink daily and how productive they feel during their workday. The study examined whether there is a consistent pattern between coffee consumption and productivity levels.

Discussion Questions:

What is the main focus of the study?
How might coffee consumption affect productivity, based on your intuition?
What could a strong relationship between coffee consumption and productivity suggest for coffee drinkers?
What other factors (confounders) might influence both coffee consumption and productivity? How could these affect the study’s conclusions?
If the study finds a meaningful connection, what practical advice could it offer to workers?