INTRODUCTION TO STATISTICS

Rachel Rabi, PhD

What is Statistics?

• Definition:

  • Statistics is defined as:

  • Mathematical procedures used to organize, summarize, and interpret information (Gravetter & Wallnau, 2017).

  • A branch of mathematics devoted to the collection, analysis, interpretation, and presentation of data (Tokunaga, 2016).

• Importance:

  • Statistics aids researchers in answering foundational questions that initiate research.

Populations and Samples

Population

• Definition:

  • The complete set of all individuals of interest in a particular study.

  • Varies in size; often quite large.

Sample

• Definition:

  • A set of individuals selected from a population.

  • Intended to represent the population in a research study.

• Important Note:

  • Be specific when stating the population and sample!

Relationship Between Populations & Samples

• The Population:

  • Comprises all individuals of interest.

• The Sample:

  • Individuals selected to participate in the research study.

  • Results from the sample are generalized to the population.

Population vs. Sample Comparison

Two Branches of Statistics

• Descriptive Statistics:

  • Purpose:

  • Organize, summarize, and simplify data.

  • Example tools include graphs and measures of central tendency.

• Inferential Statistics:

  • Purpose:

  • Generalize from samples to populations, conduct hypothesis testing, and make predictions/inferences about data.

  • Example tools include t-tests and ANOVAs.

A Demonstration of Sampling Error

• Definition:

  • Sampling Error refers to the natural differences (discrepancy) that exist, by chance, between a sample statistic and a population parameter.

The Research Process

Steps in the Research Process:

1. Research question

2. Form a hypothesis

3. Design study

4. Collect data

5. Analyze data

6. Draw conclusions

7. Report findings

The Role of Statistics

• Example Research Question:

  • Do college students learn better by studying text on printed pages or a computer screen?

The Experimental Method

Goals:

• Demonstrate cause-and-effect relationships.

• A true experiment includes:

1. Manipulation of the Independent Variable (IV).

2. Random assignment.

3. Inclusion of a control group.

Key Components:

1. Manipulation:

   • Researchers change the value of the independent variable.

2. Control:

   • Involves:

     • Random assignment, where each participant has an equal chance of being assigned to treatment conditions/groups.

     • Control group serves as a baseline for comparison.

     • Efforts to manage extraneous variables.

3. Variables: Types

• Participant Variables:

  • Characteristics like age, gender, education level, etc.

• Environmental Variables:

  • Aspects of the environment such as lighting or background noise.

• Extraneous Variables:

  • Unrelated variables that could influence dependent variable results.

Controlling Variables: Examples from Research

• Importance of controlling for time when testing in research studies highlighted through various journal articles.

Terminology in the Experimental Method

• Independent Variable (IV):

  • The variable manipulated by the researcher.

• Dependent Variable (DV):

  • The variable measured to observe changes. Changes in this variable depend on the manipulation of the IV.

• Operational Definition/Operationalization:

  • Defines a construct in terms of observable behaviors.

  • Example: Aggression operationalized by the frequency of hitting a punching bag during frustration simulations.

• Control Condition:

  • Participants do not receive the experimental treatment; serve as a baseline.

Research Process Example

• Research Question:

  • Does mood influence problem-solving abilities?

• Hypothesis:

  • Participants in a positively induced mood will outperform those in a neutral mood on logic puzzles.

• Variables Defined:

  • IV: Mood state (Positive vs. Neutral)

  • DV: Problem-solving task performance (measured by the number of correctly solved puzzles).

• Operationalization:

  • Measured by the number of logic puzzles completed correctly in the given task.

Nonexperimental Methods

Non-equivalent Groups Study:

• Definition:

  • Researcher cannot randomly assign participants, leading to groups being pre-existing and not equivalent.

• Terminology:

  • The independent variable in this context is referred to as a quasi-independent variable.

• Types of Non-Experimental Methods Include:

  • Survey research, correlational research, and observational research.

Types of Variables

Definitions:

• Discrete Variable:

  • Comprised of separate, indivisible categories (whole units).

  • Examples: Number of children, siblings, pets.

• Continuous Variable:

  • It can take an infinite number of values between two observed values.

  • Measured along a continuum, allowing fractional units.

  • Examples: Height (e.g., 180.34 cm), weight (e.g., 65.4 lbs).

Scales of Measurement

Four Scales:

1. Nominal Scale:

   • Non-numerical (qualitative), categorizing items into classes or categories.

   • Examples include brands of computers or degree types.

2. Ordinal Scale:

   • Organizes attributes in order, but does not determine exact differences.

   • Examples: Race results or survey responses (strongly agree to disagree).

3. Interval Scale:

   • Equal spacing between categories, but no true zero point.

   • Example: Temperature in Celsius.

4. Ratio Scale:

   • All properties of an interval scale, plus true zero point.

   • Examples: Exam percentage, height, weight.

Summary Table of Scales of Measurement

Classification of Scales (NOIR)

Scales of Measurement Exploration in Software

• Software such as jamovi can be used to specify variable types and scales for data analysis.

Practice Problems from the Textbook

1. Chapter 1 Questions: #1-4, 6-15, 17, 18-23 (math review).

2. Consult Appendix A for additional math review.

3. Note: The textbook solutions only provide answers for odd-numbered questions at the back. For solutions to even-numbered questions, students are encouraged to contact TAs.