Understanding Data Structure in Statistics

Posted on Jan 8, 2025 in Mathematics

What is the Structure of Information?

Data consists of the unit of analysis, the variable, and the category. Data are the raw materials with which statistics work. Statistical processes transform data into useful information. Data extracted from reality should be the most appropriate data for the objectives of the work to be done.

Example: “Luis is 1.70 Meters Tall”

Identify the data, the unit of analysis, the variable, and the category in the following example: “Luis is 1.70 meters tall.”

In the statement “Luis is 1.70 meters tall,” ‘Luis’ is the unit of analysis, ‘height’ is the variable, and ‘1.70 meters’ is the assigned category.

Definitions of Unit of Analysis, Variable, and Category

• Unit of Analysis: The element about which a property is predicated. It can be a person, family, animal, chemical substance, or an object such as a denture or a table.
• Variable: The characteristic, property, or attribute that is predicted of the unit of analysis. For example, it may be the age of a person, the degree of cohesion for a family, the learning level reached by an animal, the specific weight of a chemical substance, the level of ‘health’ for a denture, and the size of a table.
• Category: One of the possible variations of a variable. For example, categories for the variable ‘sex’ are male and female; categories for the variable ‘occupation’ can be architect, doctor, etc.; and categories for the variable ‘age’ can be 10 years, 11 years, etc.

Definitions of Population Statistics, Value, and Measurement

• Population Statistics: The set of data about units of analysis (individuals, objects) in relation to the same property or attribute (variable).
• Value: When the variable is measured quantitatively, i.e., when expressed numerically, the category is often called a value. In these cases, the data includes a measurement unit, e.g., years, number of children, degrees of temperature, number of teeth, feet, etc. The value is, then, each of the possible variations of a quantitative variable.
• Measurement: Data are obtained through a process called measurement. From this point of view, measurement can be defined as the process by which we assign a category (or value) to a variable for a given unit of analysis.

Identifying Different Degrees of Accuracy in Measurement

The different degrees of accuracy or information content of a measurement are typically characterized as levels of measurement. Four levels of measurement are typically defined, and the data or measurement result obtained will be different for each:

• Nominal Level: Measuring simply means assigning an attribute to a unit of analysis (e.g., “Martin is an electrician”).
• Ordinal Level: Measuring means assigning an attribute to a unit of analysis whose categories can be ordered in an increasing or decreasing sequence (e.g., the category ‘complete secondary’ can be ordered in a series, as it is between ‘incomplete secondary’ and ‘incomplete university’).
• Quantitative Level: Measuring means assigning an attribute to a unit of analysis so that the assigned category allows us to know ‘how much’ higher or lower it is compared to another.

Examples of Unit of Analysis, Variable, Category, and Level of Measurement

Identify the unit of analysis, variable, category or value, and level of measurement in the following examples: