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Introduction to Statistics - Lecture Flashcards

Statistics Fundamentals

  • Statistics is the collection, analysis, interpretation, and presentation of data.
    • Definitions:
    • Gravetter & Wallnau (2017): "Mathematical procedures used to organize, summarize, and interpret information."
    • Tokunaga (2016): "A branch of mathematics devoted to the collection, analysis, interpretation, and presentation of data."
    • Purpose: to help the researcher answer questions that initiated the research.

Populations & Samples

  • Population: the set of all individuals of interest in a study; often very large and diverse.
  • Sample: a subset of individuals selected from the population; usually intended to represent the population in a research study.
  • Practical tip: be specific when stating the population and the sample.

Relationship Between a Population & Samples

  • The population represents all individuals of interest.
  • The sample is the group actually studied.
  • Generalization: results from the sample are generalized to the population.
  • The sample is drawn from the population.

Population vs. Samples: Key Distinctions

  • Population vs. Sample:
    • Population: the complete set.
    • Sample: a subset of the population.
  • Measurable qualities:
    • Population parameter: denoted by a parameter (e.g., m, s).
    • Sample statistic: denoted by a statistic (e.g., M, s).
  • Population contains all members of a specified group; a sample is a subset that represents the population.
  • Concepts: true representation of data; margin of error.

Descriptive vs Inferential Statistics

  • Descriptive statistics:
    • Organize, summarize, and describe data.
    • Examples: graphs; measures of central tendency.
  • Inferential statistics:
    • Generalize from samples to populations; hypothesis testing; make predictions and inferences about data.
    • Examples: t-tests and ANOVAs.

A Demonstration of Sampling Error

  • Sampling error: the natural differences (discrepancies) that exist, by chance, between a sample statistic and a population parameter.

The Research Process

  • Core steps: Research question → Form a hypothesis → Design study → Collect data → Analyze data → Draw conclusions → Report findings.
  • Reference: Simplypsychology.org.

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

  • Goal: demonstrate a cause-and-effect relationship.
  • True experiment includes:
    • Manipulation of the IV (independent variable) by changing its value from one level to another.
    • Random assignment of participants to treatment conditions.
    • Inclusion of a control group.
  • Additional concepts:
    • Random Assignment: each participant has an equal chance of being assigned to each treatment condition.
    • Control Group: baseline for comparison with the experimental group.
    • Researchers control the research situation to minimize influence from extraneous variables.
    • Participant variables: age, gender, education level, IQ, etc. that vary across people.
    • Environmental variables: lighting, time of day, background noise, etc.
    • Extraneous variables: not of interest but could influence the dependent variable.

Controlling Variables: Examples from Research

  • Journals highlight the importance of controlling for time of day/testing, etc., in research studies.

Terminology in the Experimental Method

  • Independent Variable (IV): the variable manipulated by the researcher.
  • Manipulation: changing the IV to create different levels.
  • Dependent Variable (DV): the variable measured to observe the effect of IV.
  • Relationship: changes in the DV depend on the manipulation of the IV.
  • Operational Definition/Operationalization: defines a construct in terms of observable and measurable external behaviors.
    • Example: aggressive behaviors operationalized as the number of times a participant hits a punching bag during a simulated frustrating task.

Terminology in the Experimental Method (continued)

  • Control condition: participants do not receive the experimental treatment or receive a neutral/placebo treatment.
  • Experimental condition: participants do receive the experimental treatment.

Research Article Example: Learning in double time

  • Article: Murphy, Kuehn, Hoover, Agadzhanyan, Castel (DOI: 10.1002/acp.3899).
  • Research question and hypothesis framed around video speed and comprehension.
  • Procedure (Experiment 1): random assignment to video speeds 1\times, 1.5\times, 2\times, 2.5\times (n = 57, 58, 59, 57).
  • Tasks: watch short videos on real estate appraisals; predict immediate test performance; take a comprehension test; predict performance on a similar exam in 1 week.
  • Predictions: participants forecast how many of 20 questions they expect to answer correctly.
  • Findings: minimal costs to comprehension up to 2\times speed; performance declines beyond 2\times; watching twice at 2\times speed did not outperform once at 1\times one week earlier.
  • Takeaway: increasing video speed up to 2\times can be efficient if time is used for additional studying or rewatching shortly before a test; results may vary with speech rate, complexity, or audiovisual overlap.
  • Keywords: comprehension, metacognition, online learning, video speed.

Research Process - Example: Mood and Problem Solving

  • Example display: research question, hypothesis, IV, DV, and operationalization.
  • Mood induction: two conditions (positive vs neutral).
  • DV: problem-solving performance measured by the number of logic puzzles correctly solved.
  • Provide an explicit list of groups/conditions and the expected direction of effects based on prior research/theory.

Nonexperimental Methods

  • Nonexperimental (nonequivalent groups) design:
    • The researcher cannot control group assignment; groups are pre-existing.
    • Groups are non-equivalent before treatment.
    • Quasi-independent variable: the variable that creates the group differences without random assignment.
  • Other nonexperimental methods: survey research, correlational research, observational research.

Types of Variables

  • Before data collection, define and measure variables.
  • Discrete variables:
    • Separate, indivisible categories; no values between neighboring categories.
    • Measured in whole units or categories.
    • Examples: number of children, number of siblings, number of pets.
  • Continuous variables:
    • Infinite number of possible values between observed values.
    • Measured along a continuum; can be fractional.
    • Examples: height (e.g., 180.34\,\text{cm}), weight (e.g., 65.4\,\text{lbs} or 70.222\,\text{lbs}), skull circumference.

4 SCALES OF MEASUREMENT (NOIR)

  • Nominal: non-numerical, qualitative; categorical; examples include brand of computer (e.g., Apple, Acer, Dell, Samsung) or degree type (e.g., BA, BSc).
  • Ordinal: ordered attributes; categories have an order but not equal intervals; examples include rank (1st, 2nd, 3rd), Likert scales (Strongly Agree to Strongly Disagree).
  • Interval: ordered categories with equal intervals between values; no true zero point; examples include temperature scales (Celsius, Fahrenheit) and IQ scores.
  • Ratio: ordered categories with equal intervals and a true zero point; examples include percent correct, height, weight, time to complete task, speed.
  • NOIR relationship: each scale builds on the previous one; you must have at least nominal data to consider ordinal, and so on.

NOIR Summary Table (Characteristics and Examples)

  • Nominal: labels/categories; no quantitative distinctions; examples: eye color; type of program; political orientation.
  • Ordinal: ordered by size/magnitude; examples: race results; clothing sizes; Olympic medals; Likert ratings.
  • Interval: ordered with equal intervals; no true zero; examples: Celsius/Fahrenheit temperatures; IQ; GRE/SAT scores.
  • Ratio: ordered with equal intervals; true zero; examples: number of correct answers; time to complete task; height; speed; weight; Kelvin temperature.
  • NOIR: Each scale level adds new properties; the four scales are NOIR.

SCALES OF MEASUREMENT (NOIR) – Visual Summary

  • A quick reference showing which properties each scale has (order, equal distance, absolute zero) across Nominal, Ordinal, Interval, Ratio.
  • Note: It’s common to summarize NOIR with a NOIR (Nominal, Ordinal, Interval, Ratio) framework to guide appropriate analyses.

SCALES OF MEASUREMENT – JAMOVI SPECIFICATION (Overview)

  • In jamovi, you specify:
    • Variables: Measure type (Nominal, Ordinal, Interval, Ratio) and Data type (e.g., Integer, Continuous).
    • Analyses: List includes T-Tests, ANOVA, Regression, Frequencies, Factor, etc.
  • This UI helps ensure you choose appropriate tests based on the measurement level.

PRACTICE PROBLEMS (TEXTBOOK)

  • Chapter 1, Questions: #1-4, 6-15, 17, 18-23 (math review).
  • Appendix A provides additional math review.
  • Note: The textbook provides solutions to odd-numbered questions at the back; for even-numbered questions, contact TAs to check solutions.

Connections to Previous Lectures and Real-World Relevance

  • Core concept: measurement scales (NOIR) guide the choice of statistical analyses in real research and practice.
  • Distinction between population and sample underpins poll reporting, clinical trials, and social science research.
  • Descriptive vs. inferential statistics: essential for summarizing data and making informed decisions in fields from psychology to public policy.
  • Experimental vs. nonexperimental designs highlight the importance of internal validity and causal inference in interpreting results.
  • Operational definitions connect abstract constructs (e.g., aggression, mood) to observable behaviors, enabling replication and measurement across studies.

Ethical, Philosophical, or Practical Implications

  • Random assignment and control groups raise ethical considerations in study design when withholding treatment or exposing participants to potentially harmful conditions.
  • Operationalization affects construct validity; overly narrow or biased definitions can distort findings.
  • Mindful interpretation of sampling error is essential to avoid overgeneralization from a non-representative sample.
  • Transparency about scales of measurement and data type helps ensure reproducibility and proper analysis.

Notation and Formulas Used in This Overview

  • Population parameter examples (as presented): m,\ s
  • Sample statistic examples (as presented): M,\ s
  • Video speeds in the sample article: 1\times,\ 1.5\times,\ 2\times,\ 2.5\times
  • Sample sizes from the article: n=57,\ 58,\ 59,\ 57
  • Notes: all other numerical references are described in their textual context within the transcript.

Quick Recap for Exam Prep

  • Distinguish population vs. sample; know parameter vs. statistic.
  • Identify descriptive vs. inferential statistics in a study.
  • Describe the role of sampling error and why random assignment is used.
  • Explain the basics of control groups and operational definitions.
  • Recognize the four scales of measurement and their implications for data analysis.
  • Be familiar with basic research process steps and common examples from lectures.

References Mentioned

  • Gravetter, F. J., & Wallnau, L. B. (2017). Introduction to Statistics.
  • Tokunaga, 2016. [Definition reference]
  • Murphy, D. H., Kuehn, J. C., Hoover, K. M., Agadzhanyan, K., Castel, A. D. (2021). Learning in double time: The effect of lecture video speed on immediate and delayed comprehension. doi: 10.1002/acp.3899
  • Simplypsychology.org (general research process reference)