Chapter 1: Stats Starts Here

What Is Statistics?

Statistics is both a discipline and a set of tools for reasoning with data. It helps us understand the world by collecting, analyzing, and interpreting data. The term statistics can also refer to specific calculations made from data, such as the mean or median.

• Statistics (discipline): The science of learning from data.

• Statistics (plural): Calculated values from data (e.g., mean, median).

• Data: Values with a context; numbers, names, or labels that are meaningful only when their context is known.

Key Point: Data are useless without their context.

What Is Statistics Really About?

Statistics is fundamentally about variation. It seeks to understand how and why data values differ, whether due to random chance or underlying causes.

• Variation is expected in opinions, measurements, and experimental results.

• Statistics helps determine when differences are meaningful or simply due to random variation.

The "W's" of Data

To provide context for data, statisticians use the "W's":

• Who: The individuals or cases for which data are collected.

• What: The variables measured (and their units).

• When: The time data were collected.

• Where: The location of data collection.

• Why: The purpose of the data collection.

• How: The method of data collection.

Note: The answers to "who" and "what" are essential for understanding data.

Describing Data: Tables and Context

Data Tables

Data tables organize information by showing the context of the data. Columns typically represent variables (the What), and rows represent individual cases (the Who).

Key Point: Data tables clarify the relationship between variables and cases, making analysis possible.

Who: The Cases in Data

The Who refers to the individual cases for which data are collected. Depending on the context, these may be called:

• Respondents: Individuals answering a survey.

• Subjects/Participants: People in experiments.

• Experimental Units: Animals, plants, or objects in experiments.

• Records: Rows in a database.

The Who is a subset of the Population of Interest—all cases we want to learn about.

What: Variables and Their Types

Variables are characteristics recorded about each individual. They should be clearly named and defined.

• Categorical Variables: Name categories and answer questions about how cases fall into those categories.

  • Nominal: Categories with no inherent order (e.g., gender, race).

  • Ordinal: Categories with a specific order (e.g., satisfaction rating).

• Quantitative Variables: Measured variables (with units) that answer questions about quantity.

  • Discrete: Take on counting numbers (e.g., number of siblings).

  • Continuous: Can take any value in a range (e.g., height, weight).

• Identifier Variables: Categorical variables with exactly one individual in each category (e.g., Social Security Number). Used for identification, not analysis.

Collecting Data: Methods and Context

How the Data Are Collected

The method of data collection is crucial for valid statistical analysis. Poorly collected data (e.g., voluntary surveys) can lead to misleading conclusions.

• Sound statistical design is essential for meaningful results.

• Always identify the W's (and How) when collecting or analyzing data.

Three Steps to Doing Statistics Right

1. Think: Know your goal and why you are collecting data.

2. Show: Calculate statistics and create graphical displays.

3. Tell: Explain your results in context so others can understand your conclusions.

Describing Categorical Data: Frequency Tables

Counts Count

Frequency tables are used to summarize categorical variables by showing the count of cases in each category.

Key Point: Frequency tables help us see the distribution of categorical variables.

Counts for Quantitative Data

When focusing on quantities, counts are used differently. For example, tracking the number of teenage customers each month helps forecast sales.

Examples and Applications

Identifying Variables and Context

Consider the following examples to practice identifying the W's and types of variables:

• "How many AP tests will you take?" — Quantitative, discrete; Who: students; What: number of AP Exams.

• "How far did the catapult throw the soup can?" — Quantitative, continuous.

Example: Ecological Study

Students collect data on streams, recording variables such as stream name, substrate, acidity (pH), temperature (°C), and BCI (biological diversity measure).

• Who: Streams in upstate New York

• What: Stream name, substrate, acidity, temperature, BCI

• When: Each year

• Where: Upstate New York

• Why: To learn about stream ecology

• How: Collecting water and ground samples

Example: Monitoring the Future Project

Surveys are used to study changes in beliefs, attitudes, and behaviors of 8th, 10th, and 12th graders in the U.S. Variables include alcohol, illegal drug, and cigarette use.

• Who: 8th, 10th, and 12th grade students

• What: Alcohol, illegal drug, and cigarette use

• When: Spring 2004

• Where: United States

• Why: To study changes in youth behavior

• How: Survey

Tips for Success and Common Pitfalls

• Always decide if data is categorical or quantitative before analysis.

• Be careful: Not all numbers are quantitative (e.g., jersey numbers, zip codes).

• Be skeptical and do not take data for granted—always consider context.