Introduction to Statistics Review

INTRODUCTION TO STATISTICS

Instructor: RACHEL RABI, PHD

What is Statistics?

• Definition:

  • Statistics is a set of mathematical procedures used to organize, summarize, and interpret information.

  • Reference: Gravetter & Wallnau, 2017

  • It is a branch of mathematics devoted to the collection, analysis, interpretation, and presentation of data.

  • Reference: Tokunaga, 2016

• Importance:

  • Assists researchers in answering questions that initiated their studies.

Populations vs. Samples

1. Population

• Definition:

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

  • Populations can vary widely in size, often being quite large.

2. Sample

• Definition:

  • A set of individuals selected from a population, usually intended to represent that population in a research study.

• Clarification:

  • It is essential to specify the population and the sample accurately in the study.

Relationship Between Population & Sample

• The Population:

  • Comprises all individuals of interest.

  • The results derived from a sample are generalized to this population.

• The Sample:

  • Individuals selected to participate in the research study, representing the population.

Differences Between Population and Sample

Two Branches of Statistics

1. Descriptive Statistics

• Purpose:

  • Organize, summarize, simplify, and describe data.

  • Techniques include graphs and measures of central tendency.

2. Inferential Statistics

• Purpose:

  • Generalize from samples to populations through hypothesis testing.

  • Enable predictions and inferences about data utilizing methods such as t-tests and ANOVAs.

A Demonstration of Sampling Error

• Definition:

  • Sampling Error refers to the natural discrepancies that occur by chance between a sample statistic and the corresponding population parameter.

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

• Reference: Simplypsychology.org

The Role of Statistics

Research Question Example

• Research Question:

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

The Experimental Method

• Goal:

  • To demonstrate a cause-and-effect relationship between variables.

Components of a True Experiment

1. Manipulation:

   • The researcher alters one variable by changing its value across different levels (manipulation of the independent variable).

2. Control:

   • Involves using random assignment and inclusion of a control group, while controlling for effects of extraneous variables.

   • Random Assignment: Each participant has an equal chance of being assigned to each treatment condition or group.

   • Control Group: Serves as a baseline for comparison against the experimental group outcomes.

   • Extraneous Variables: Factors outside the research interest that could potentially affect the dependent variable, including:

     • Participant Variables: Age, gender, education level, IQ.

     • Environmental Variables: Environmental characteristics such as lighting, time of day, background noise, and distractions.

Controlling Variables: Examples from Research

• Importance highlighted through journal articles regarding the timing of testing in research studies.

Terminology in the Experimental Method

Key Terms:

• Independent Variable (IV):

  • The variable manipulated by the researcher.

  • Manipulation: The purposeful change made in the independent variable.

• Dependent Variable (DV):

  • The variable being measured to observe effects of changes in the independent variable.

  • Changes in this variable are dependent upon the manipulations of the independent variable.

• Operational Definition/Operationalization:

  • Define constructs in terms of measurable and observable behaviors.

  • Example: Studying aggressive behaviors operationalized as the number of times a participant hits a punching bag during a simulated frustrating situation.

Control Conditions in Experimental Method

• Individuals in the control condition

  • Do not receive the experimental treatment.

  • May receive no treatment or a neutral placebo treatment, providing a baseline for comparison with the experimental condition.

• Individuals in the experimental condition receive the experimental treatment.

Example Research Design

• Research Question:

  • Does mood influence problem-solving abilities?

• Hypothesis:

  • Participants in a positively induced mood will perform better on logic puzzles than those in a neutral mood.

• Independent Variable (IV):

  • Mood state (Positive vs. Neutral).

• Dependent Variable (DV):

  • Problem-solving task performance measured by the number of puzzles correctly solved.

• Operationalization:

  • Number of puzzles solved correctly as the measure of problem-solving ability.

• Includes consideration of prior research indicating a positive mood improves memory recall.

Nonexperimental Methods

• Definition of Nonexperimental Methods:

  • In non-equivalent groups studies, the researcher cannot control how subjects are assigned to groups.

  • These studies compare pre-existing groups without random assignment.

  • Quasi-Independent Variable:

  • An independent variable in nonexperimental studies that differentiates the groups being compared without manipulation.

• Other Non-experimental Methods Include:

  • Survey research, correlational research, and observational research.

Types of Variables

• Discrete Variable:

  • Comprises distinct, indivisible categories; no values exist between neighboring categories.

  • Examples:

  • Number of children, siblings, pets, etc.

• Continuous Variable:

  • Comprises an infinite number of potential values between observed values.

  • Examples:

  • Height (e.g., 180.34 cm), Weight (e.g., 65.4 lbs).

Scales of Measurement

1. Nominal Scale

• Characteristics:

  • Non-numerical (qualitative); categorical.

  • Items belong to a specific class or category.

  • Examples:

  • Brand of computer (e.g., Apple, Acer), Degree type (e.g., BA, BSc).

2. Ordinal Scale

• Characteristics:

  • Stands for “order”; presents ordered attributes.

  • Cannot determine exact differences between values.

  • Examples:

  • Race results (e.g., 1st, 2nd, 3rd), Survey Scale (Strongly agree to Strongly disagree).

3. Interval Scale

• Characteristics:

  • Equal intervals between categories; however, has no true zero point.

  • Examples:

  • Temperature in Celsius (0 does not imply the absence of temperature).

4. Ratio Scale

• Characteristics:

  • Includes all characteristics of the interval scale plus a true zero point.

  • Examples:

  • Percent correct on an exam, height, and weight measurements.

Summary Table of Scales of Measurement

Properties of Scales of Measurement

Note: NOIR (Nominal, Ordinal, Interval, Ratio)

• Each scale builds on the preceding one.

Practice Problems Textbook

• Textbook Chapters for Reference:

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

• Additional Math Review:

  • Consult Appendix A.

  • Reminder: The textbook provides solutions only for odd-numbered questions at the back. For checking even-numbered questions, contact TAs.