Lecture 1 - Introduction to Statistics (WJC)

Lecture 1: Introduction to Statistics for the Behavioural Sciences

Overview of the Lecture

• Presented by David Butler

• Key areas of focus include definitions, types, and applications of statistics in behavioural sciences.

Objectives

• Definition of Statistics: Understanding the discipline that handles data collection, organization, analysis, and interpretation.

• Data & Variables: Learn the differences between various types of data and the variables that represent them.

• Types of Variables: Explore qualitative vs. quantitative variables.

• Measurement Levels: Different levels at which variables can be measured and their implications.

• Population vs. Sample: Understand the concepts of population and sample in research.

• Types of Statistics: Differentiate between descriptive and inferential statistics.

• Sampling Techniques: Introduction to different methods used to collect samples for analysis.

Statistics: Definition and Purpose

• Statistics: The study of collecting, organizing, analyzing, and interpreting numerical data.

• Emphasizes how to systematically handle data to draw meaningful conclusions.

Individuals and Variables

Individuals

• Definition: Individuals refer to the entities (people or objects) included in a study.

• Also known as data units, these are the subjects from which data is collected.

Variables

• Definition: Characteristics of individuals being measured or observed.

• Referred to as data items, they can vary among subjects and are crucial for analysis.

Sources of Data

Primary Sources

• Collected firsthand by the researcher.

• Methods include:

  • Questionnaires

  • Surveys

  • Tests & Exams

  • Interviews

  • Observation

Secondary Sources

• Utilization of existing data obtained from:

  • Newspapers

  • Previous research studies

  • Census data

  • Academic journals

Types of Variables

Quantitative Variables

• Definition: Numerical; meaningful mathematical functions can be performed.

• Transformations: All data points can undergo the same unit change.

Qualitative Variables

• Definition: Categorical; mathematical operations do not yield meaningful results.

• Transformations: Must preserve uniqueness (nominal) or rank (ordinal).

Levels of Measurement (LOM)

Categorical Variables

• Nominal: Non-rankable categories (e.g., names, religion, gender).

• Ordinal: Rankable categories without numerical differences (e.g., grades, drink sizes).

Numerical Variables

• Interval: Rankable, but with no true zero (e.g., temperature scales).

• Ratio: Rankable with a true zero point (e.g., weight, height).

Types of Data

Discrete Data

• Countable values (e.g., number of cars).

Continuous Data

• Uncountable values; can include fractions (e.g., weight, time).

Target Groups

Population

• All individuals within the study’s target group.

Sample

• A subset of the population selected for the research.

Types of Statistics

Descriptive Statistics

• Techniques to organize and summarize data (e.g., averages, tables).

• Describe characteristics of the sample or population.

Inferential Statistics

• Techniques that allow inferences about a population based on a sample.

• Involve making generalized conclusions.

Units of Analysis

Individual Units

• Most common in social research (e.g., surveying individual student opinions).

Group Units

• Focuses on group behavior rather than individual entities (e.g., gangs in different environments).

Organizational Units

• Evaluation of behavior across organizations (e.g., school performance).

Sampling Concepts

Population vs. Sample

• Population: Entire group of interest.

• Sample: Subset selected for practical research constraints.

Accessible Population

• Elements of the population available for selection as a sample.

Sampling Frame

• A comprehensive list of all elements to choose from in a population.

Sampling Strategies

Representative Samples

• Samples should ideally represent broader populations.

• Law of Large Numbers: Larger sample sizes yield results closer to actual population behaviors.

Sampling Methods

Sampling with Replacement

• Samples drawn are returned; probabilities remain the same.

Sampling without Replacement

• Drawn samples are not returned; affects remaining selection probabilities.

Probability Sampling

Characteristics

• Each element has a defined chance of selection.

• Involves randomness, reducing biases.

Methods of Probability Sampling

Random Sampling

• Every population element has an equal chance of selection.

• Best method for minimizing bias.

Systematic Random Sampling

• Involves a defined starting point and a set interval for selection.

Stratified Random Sampling

• Divides population into subgroups; samples are selected from each group.

Cluster Sampling

• Involves selecting entire clusters or groups; useful for large populations.

Non-Probability Sampling

General Characteristics

• No defined probability for selection; more practical with no sampling frame available.

Methods of Non-Probability Sampling

Quota Sampling

• Participants chosen based on representation rates within the population.

Snowball Sampling

• Current participants help identify future subjects, useful for hidden populations.

Convenience Sampling

• Selecting based on ease of access at a specific time and place.

Purposive Sampling

• Researcher uses judgment to select representative units based on variation within the population.