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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.