Introduction to Statistics: Data, Variables, and Context

Chapter 1: Statistics Starts Here

What is Statistics?

Statistics is the scientific discipline concerned with the design of studies, collection of data, summarization and analysis of data, interpretation of results, and drawing of conclusions. It enables us to make informed decisions or inferences about specific phenomena based on limited information.

• Definition: Statistics involves the entire process from planning how to collect data to making conclusions based on the data.

• Purpose: To draw conclusions about populations or processes using data from samples.

• Key Point: Conclusions are often made with incomplete or limited data, emphasizing the importance of proper study design and analysis.

Data and Its Context

Understanding Data

Data are collections of observations, such as numbers or categories, that require context to be meaningful. Without context, data cannot be properly interpreted or used for analysis.

• Example: Consider the following data:

  • Numbers: 35, 42, 21, 59, 47, 55, 55, 38, 50, 41, 51, 44, 31, 42, 30, 32, 40

  • Yes/No responses: Yes, No, No, No, Yes, No, No, Yes, No, No, No, No, Yes, No, Yes, Yes, Yes

• These numbers and responses are meaningless without knowing what they represent (e.g., exam scores, number of snowy days, survey answers).

• Key Point: Always specify what the data represent to provide necessary context for analysis.

Example: Medical Data Table

Consider data extracted from medical records of 50 patients with low back pain. Each row represents a patient, and each column represents a variable of interest.

Subject	Age	Sex	In employment?	Duration of pain	Severity of pain
1	35	F	No	3 weeks	mild
2	42	F	Yes	13 weeks	severe
3	21	M	Yes	4 weeks	moderate
4	59	F	No	72 weeks	moderate
...	...	...	...	...	...
50	40	M	Yes	30 weeks	severe

Types of Variables

Definition of a Variable

A variable is a characteristic or attribute that can take on different values among subjects in a study. Examples include age, sex, employment status, duration of pain, and severity of pain.

• Qualitative (Categorical) Variables: Variables that describe qualities or categories. If the categories have a natural order, they are called ordinal variables.

• Quantitative Variables: Variables measured on a numerical scale. Units should always be specified (e.g., years, weeks).

Examples of Variable Types

Variable	Type (qualitative or quantitative?)	Ordinal?	Unit
Age	quantitative	N/A	years
Sex	categorical	not ordinal	N/A
In employment?	categorical	not ordinal	N/A
Duration of pain	quantitative	N/A	weeks
Severity of pain	categorical	ordinal	N/A

• Note: Sometimes numbers are used to represent categories for convenience (e.g., 1 = Yes, 0 = No for employment status; 1 = mild, 2 = moderate, 3 = severe for severity of pain). These should not be misinterpreted as quantitative variables.

Understanding the Data: The 'Five Ws and How'

To fully understand any dataset, it is essential to consider the following aspects:

• Who: The subjects or units being studied.

• What: The variables of interest being measured or observed.

• Where: The location or setting where the data are collected.

• When: The time point or period during which the data are collected.

• Why: The purpose or motivation for collecting the data.

• How: The method or process used to collect the data.

Example Application: In the medical data example, the 'Who' are the 50 patients with low back pain, the 'What' are variables like age, sex, employment status, etc., and the 'Why' might be to study factors associated with pain severity or duration.

Additional info: Understanding the context of data collection is crucial for proper analysis and interpretation in statistics. This foundational knowledge sets the stage for more advanced topics such as sampling, experimental design, and statistical inference.