Analyzing Categorical Data Patterns

Pattern Recognition Through Frequency

a frequency analysis widget: By analyzing the frequency of the letters in the encrypted input message compared to the frequency of letters in a typical piece of English prose, you can start to narrow in on what some of the letter mappings might be. Did you know that ‘E’ is the most common letter used in the English language? Maybe the most common letter in your encrypted text maps to the letter ‘E’, but maybe not! You’ll have to do a bit of guess and check to see if that substitution makes sense. source

play with the cryptography/ frequency analysis widget here

Statistical analysis often begins with understanding how often things occur in our data. When working with categorical data, we use two complementary approaches: frequency analysis and contingency analysis.

Understanding the Two Approaches

Frequency analysis counts occurrences within a single variable. Think of it as taking inventory - how many times does each category appear in your dataset? For instance, counting the number of students who prefer different music genres gives you a frequency distribution. This distribution reveals patterns that might not be obvious in raw data, helping identify common categories or unusual patterns.

Contingency analysis explores relationships between multiple categorical variables. Instead of just counting one variable, we examine how different variables interact. For example, we might look at how music preferences vary across different age groups or geographic regions. This approach creates contingency tables (also called cross-tabulations) that show these relationships clearly.

Important

Remember: Frequency analysis examines one variable at a time, while contingency analysis reveals relationships between variables.