Basic Statistics

Statistics is the science of learning from data. It involves collecting, analyzing, interpreting, and presenting information. Whether you are a psychology student analyzing survey results or a business owner tracking sales, understanding the basics of statistics is essential for making informed decisions.

This guide covers the core concepts you need to start your journey. If you need help designing a study or analyzing your first dataset, our statistical consulting team is here to help.

What is Statistics?

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data. It helps us answer questions like:

• “Is this new drug effective?”
• “Who is likely to win the next election?”
• “Does study time affect test scores?”

Population vs. Sample

This is the most critical distinction in statistics.

Population

The entire group you want to draw conclusions about (e.g., “All teenagers in the USA”). A numerical characteristic of a population is called a Parameter.

Sample

The specific group that you will collect data from (e.g., “500 teenagers from 5 different states”). A numerical characteristic of a sample is called a Statistic.

Types of Data (Variables)

Data comes in different forms, and the type of data dictates the type of analysis you can perform.

Qualitative (Categorical) Data

Describes qualities or characteristics.

• Nominal: Labels with no order (e.g., Blue, Red, Green).
• Ordinal: Labels with an order (e.g., Small, Medium, Large).

Quantitative (Numerical) Data

Describes quantities or amounts.

• Discrete: Whole numbers, counts (e.g., number of children).
• Continuous: Any value within a range, measurements (e.g., height, weight, time).

Levels of Measurement (NOIR)

Data is classified into four levels of measurement, often remembered by the acronym NOIR.

For visual examples of these levels, Khan Academy offers excellent tutorials.

The Two Branches of Statistics

Statistics is divided into two main areas:

1. Descriptive Statistics

Organizes and summarizes data using numbers and graphs. Learn more in our guide to descriptive statistics.

2. Inferential Statistics

Uses sample data to make estimates, decisions, predictions, or other generalizations about a larger set of data. Learn more in our guide to hypothesis testing.

For a comprehensive textbook approach, OpenStax provides free, peer-reviewed statistics resources.

Get Help with Your Research

Understanding basic statistics is the key to unlocking the power of data. Don’t let terminology hold you back. Our team of experts can help you design your study, collect your data, and analyze your results.