PSYC 120: Quantitative Methods and Research Basics

Course Overview and Structure

• Course Identification: PSYC 120, Section 03, Fall 2026: Quantitative Methods and Research Basics.
• Instructor Profile:
  • Dr. Mann (she/her).
  • Background: Originally from just outside Philadelphia; spent 13 years at Penn Charter; earned an AB in Psychology from Bryn Mawr College; completed graduate education at Vanderbilt; previously served on the faculty at the medical school at East Tennessee State University (Quillen College of Medicine); currently in 6th year at Lafayette.
• Course Learning Outcomes:
  • Understand key terms and concepts related to quantitative statistical methods commonly used in Psychology and Neuroscience.
  • Understand and evaluate statistical analysis used to support arguments in empirical literature and popular publications.
  • Create and interpret charts, graphs, and tables containing descriptive and inferential statistics.
  • Capture, import, and transform data into forms appropriate for statistical analysis.
  • Perform descriptive and inferential statistical analysis both by hand and using statistical software (e.g., JASP).
  • Report results of descriptive and inferential statistical analysis using American Psychological Association (APA) style.
• Syllabus & Course Policies:
  • Syllabus is hosted digitally on Moodle.
  • Updates to the posted Moodle version are rare; if alterations occur, the Moodle document serves as the official reference.
• Weekly Class Schedule & Workflow:
  • Tuesday: Class dedicated to concluding new material, conducting in-class activities, and completing problem sets. Weekly problem sets are due at 8:00 PM; answer keys are posted at 8:00 PM.
  • Thursday: Class opens with a quiz covering prior material, followed immediately by the introduction of a new topic.
  • Preparation Recommendation: Assigned textbook readings should be completed prior to the class session in which the topic is introduced.
• Classroom Introductory Activity:
  1. Connect with an unfamiliar classmate.
  2. Share name.
  3. Share an activity completed over winter break.
  4. Share an aspect of the course anticipated for the semester.
  5. Share one target learning goal or expectation for the course.

Fundamentals of Quantitative Methods

• Quantitative Methods Definition: Statistical techniques utilized by researchers to collect, analyze, interpret, disseminate (share), and test empirical hypotheses using quantitative (numerical) data.
• Role in Behavioral Sciences: Serves as the numerical language of scientific research. Although mathematical operations and computations are required, the discipline is rooted in research design and statistical logic rather than theoretical mathematics.
• Practical Utility: Provides the foundational knowledge needed to understand how numerical claims, summary metrics, and figures presented in scientific publications are generated and validated.

Key Concepts in Psychological Research

• Variables and Operationalization:
  • Variable: Any characteristic, property, or condition that varies across individuals, observations, or entities within a dataset.
  • Independent Variable (IV): The variable manipulated, controlled, or categorized by researchers to assess its effect.
  • Dependent Variable (DV): The measured outcome variable hypothesized to change as a function of the independent variable.
  • Levels of a Variable: The specific conditions, groups, or values that a variable takes on (e.g., Experimental condition vs. Control condition).
  • Empirical Observation: Scientific inquiry grounded in direct, systematic observation.
  • Operational Definition: The precise process of translating an abstract concept or observation into concrete, quantifiable, and measurable variables.
• Classifications of Variables:
  • Qualitative Variables: Non-numerical variables representing categories, labels, or qualitative attributes that lack quantitative distinctions.
  • Quantitative Variables: Measured numerical variables representing distinct amounts or quantities.
  • Discrete Variables: Variables restricted to whole integer values or distinct units with no intermediate fractional values (e.g., frequency counts of events).
  • Continuous Variables: Variables defined by real limits that can take on an infinite continuum of fractional or decimal values (e.g., body weight in pounds recorded to the nearest pound).
• Measurement Reliability & Psychological Constructs:
  • Directly observable physical variables possess calibrated measurement instruments that yield reliable, consistent data.
  • Constructs: Internal, abstract psychological attributes or entities that cannot be directly observed (e.g., depression, intelligence, self-esteem).
  • Construct measurement requires careful operationalization to construct valid and reliable measuring tools.
• Populations, Samples, and Sampling Strategies:
  • Population: The entire group of individuals or instances to which research findings are intended to be generalized. Quantitative properties of populations are termed population parameters.
  • Sample: A defined subset of individuals selected from a target population to participate in a study. Quantitative properties of samples are termed sample statistics.
  • Sampling Bias: Systematic distortion occurring when a sample fails to accurately represent the target population, rendering results ungeneralizable.
  • Simple Random Sampling: A sampling method in which every individual in the population possesses an equal probability of selection, and selections are made independently such that selecting one individual does not alter the likelihood of selecting another.
  • Sample Size ($N$): Random sampling alone does not guarantee population representativeness; larger sample sizes ($N$) systematically reduce sampling variance and enhance representativeness.
  • Stratified Random Sampling: A sampling technique where the population is divided into meaningful sub-groups (strata) based on known characteristics, followed by random sampling within each stratum.
  • Convenience Sampling: A non-random sampling strategy selecting readily available participants; it lacks representative guarantees and carries higher risks of sampling bias.
• Research Designs:
  • Experimental Design: Involves random assignment of participants to experimental conditions alongside systematic manipulation of independent variables. This design provides the basis for establishing cause-and-effect relationships.
  • Quasi-Experimental Design: Features independent variable manipulation or group comparison without true random assignment due to logistical, practical, or ethical constraints.
  • Non-Experimental Design: Observational research assessing naturally occurring attributes or participant characteristics that cannot be manipulated or assigned.
  • Correlational Design: Evaluates the statistical relationship between two unmanipulated variables without experimental intervention. Common statistical tests include continuous numerical correlations (e.g., Pearson's $r$) and categorical tests (e.g., Chi-square). Demonstrates association or predictive power, but cannot establish causation.

Scales and Levels of Measurement

• Nominal Scale:
  • Characteristics: Categorizes or labels data into distinct qualitative groups. Provides no quantitative distinctions, order, or numerical value.
  • Examples: Gender identity, diagnostic categories, experimental condition assignment (e.g., Experimental vs. Control).
• Ordinal Scale:
  • Characteristics: Categorizes observations into ordered groups organized by relative size, rank, or magnitude. Distance between adjacent categories is unequal or unknown.
  • Examples: Class rank, standardized clothing sizes ($S$, $M$, $L$, $XL$), Likert agreement scales (e.g., Strongly disagree to strongly agree).
• Interval Scale:
  • Characteristics: Ordered categories with equal interval distances between adjacent scale points, but featuring an arbitrary or absent true zero point (a score of $0$ does not indicate the total absence of the measured variable).
  • Examples: Temperature scales (Fahrenheit and Celsius), Standardized IQ test scores, Golf scores measured relative to par.
• Ratio Scale:
  • Characteristics: Ordered categories separated by equal interval distances with an absolute, true zero point (a score of $0$ signifies total absence of the variable).
  • Examples: Number of correct test items, task completion duration in seconds, monetary amounts, physical growth metrics (e.g., height or weight gain since baseline).

Statistical Classification and Notation

• Definition of Data: A plural noun (e.g., "data are…") referring to the collection of information, observations, or measurement values gathered during research.
• Main Branches of Statistics:
  • Descriptive Statistics: Statistical procedures used to organize, summarize, simplify, and present raw sample data in an accessible format.
  • Inferential Statistics: Mathematical procedures that utilize sample statistics to draw generalized conclusions, estimate parameters, and test hypotheses regarding unobserved target populations.
• Sampling Error & True Differences:
  • Sampling Error: The natural, expected statistical variance that exists between a sample statistic and the underlying true population parameter. In statistics, "error" does not signify a mistake, but rather natural sampling variability.
  • Margin of Error: An estimated numerical range encompassing the expected difference between a sample statistic and the true population parameter.
  • Differentiating Effects: Observed score differences between groups arise either from random sampling error (chance fluctuations) or genuine experimental treatment effects (statistically significant differences). Inferential tests evaluate these possibilities.
  • Hypothetical Example: An experiment evaluates two groups on an outcome variable measured on a scale from $1$ to $10$. The control group yields a mean score of $6$ ($\text{Control Mean} = 6$), while the experimental group yields a mean score of $8$ ($\text{Experimental Mean} = 8$). Inferential statistics determine whether the $2$-point mean difference reflects a true manipulation effect or chance sampling variation.
• Statistical Notation Rules:
  • Individual Scores: Raw scores or observed measurements for a variable are designated as $X$ or $Y$.
  • Sample Size ($N$): The symbol $N$ denotes the total number of individual participants or observations within a sample dataset.
  • Summation Operator ($\Sigma$): The uppercase Greek letter sigma ($\Sigma$) represents the mathematical command to calculate the sum of a series of values.
  • Sum of Scores ($\Sigma X$): Instructs the addition of all individual $X$ values in the dataset.
  • Order of Operations Guidelines:
    • $\Sigma X^2$ vs. $(\Sigma X)^2$: $\Sigma X^2$ requires squaring each raw $X$ score individually before summing the squared values. Conversely, $(\Sigma X)^2$ requires summing all raw $X$ scores first, then squaring that total sum.
    • $\Sigma XY$ vs. $(\Sigma X)Y$: $\Sigma XY$ requires multiplying each paired $X$ and $Y$ value together individually before summing the products. Conversely, $(\Sigma X)Y$ multiplies the total sum of $X$ scores by a constant or separate $Y$ metric.

Graphical Representation of Qualitative Data

• Qualitative Graphics Overview: Visual displays suited for non-numeric, categorical data (words representing categories, names, or discrete groups).
• Frequency Tables: Tabular arrangements showing discrete category labels alongside their respective counts ($n$).
• Pie Charts:
  • Best Uses: Displaying relative proportions or percentages of a categorical whole when working with a small number of mutually exclusive categories.
  • Limitations: Ineffective when applied to small sample sizes ($N$) or datasets containing overlapping, non-mutually exclusive categories.
  • Empirical Study Preferences Dataset ($N = 94$ total participants):
    • Listen to notes via text to speech: $n = 30$ ($31.9\%$)
    • Re-read notes: $n = 20$ ($21.3\%$)
    • Study group discussion: $n = 14$ ($14.9\%$)
    • Practice problems: $n = 10$ ($10.6\%$)
    • Flash cards: $n = 10$ ($10.6\%$)
    • Re-read text: $n = 10$ ($10.6\%$)

• Bar / Column Charts: Displays discrete qualitative categories along the horizontal axis and frequencies or values along the vertical axis, allowing straightforward visual comparisons across groups.
• Principles of Ethical and Effective Graphing:
  • Keep graphic designs simple: Avoid heavy background shading, 3D effects, or decorative pictorial overlays that degrade visual accuracy.
  • Explicitly label all axes: Clearly describe variables and measurement units.
  • Avoid truncated vertical scale ranges: Vertical axes ($Y$-axis) displaying quantitative amounts should originate at $0$ to prevent visual exaggeration of minor numerical differences.

Graphical Representation of Quantitative Data

• Stem-and-Leaf Plots:
  • Purpose: Displays small numerical datasets by preserving raw individual score values while providing a visual outline of distribution shape.
  • Structure: Deconstructs each number into a "stem" (leading digits, such as tens place) and a "leaf" (trailing digits, such as ones place).
  • Endurance Test Dataset ($N = 18$ raw scores): $55, 29, 21, 11, 19, 12, 23, 23, 88, 72, 50, 13, 15, 89, 70, 59, 67, 50$
  • Stem-and-Leaf Formatting:
    • Stem $1$: $1, 2, 3, 5, 9$ (representing $11, 12, 13, 15, 19$)
    • Stem $2$: $1, 3, 3, 9$ (representing $21, 23, 23, 29$)
    • Stem $3$: (empty)
    • Stem $4$: (empty)
    • Stem $5$: $0, 0, 5, 9$ (representing $50, 50, 55, 59$)
    • Stem $6$: $7$ (representing $67$)
    • Stem $7$: $0, 2$ (representing $70, 72$)
    • Stem $8$: $8, 9$ (representing $88, 89$)
• Histograms:
  • Structure: Displays continuous quantitative variables divided into contiguous class intervals along the horizontal axis ($X$-axis), with class frequencies plotted on the vertical axis ($Y$-axis).
  • Class Intervals & Bin Width: Class intervals define score ranges. The distance spanning an interval is defined as bin width.

• Frequency Polygons:
  • Structure: Continuous line graphs created by plotting data points at the exact midpoint and frequency height of each class interval, connecting adjacent midpoints with straight line segments.
  • Overlay Capability: Well-suited for superimposing multiple frequency distributions onto a single set of axes to compare different groups or experimental conditions.

• Box Plots (Box-and-Whisker Plots):
  • Purpose: Visual tool used to compare central tendency, spread, and quartile distributions across independent groups.
  • Box Anatomy: The central box encompasses the middle $50\%$ of data spanning the interquartile range from the $25\text{th}$ percentile (first quartile, $Q_1$) to the $75\text{th}$ percentile (third quartile, $Q_3$). A solid line inside the box marks the $50\text{th}$ percentile (median).
  • Whiskers & Outliers: Whiskers extend outward from the box to the minimum and maximum data values located within calculated adjacent bounds. Data points falling beyond these boundaries are classified as outside values (outliers) and are plotted individually as open circles.
  • Empirical Example: BDI Ia depression scores evaluated across gender groups (Men vs. Women) based on published findings by Sherchand, Sapkota, Chaudhari, Khan, Baranwal, Niraula, and Lamsal (2018) in Psychiatry Journal.

• Quantitative Bar Charts:
  • Application: Applied to quantitative data to illustrate summary metrics (such as group means) across discrete experimental conditions or time intervals.
  • Maze Completion Dataset: Displays mean maze completion duration in seconds across conditions: Baseline condition (~$75\,\text{s}$), Condition 1 (~$40\,\text{s}$), Condition 2 (~$35\,\text{s}$).
• Line Graphs:
  • Application: Illustrates continuous functional changes or tracking over time by connecting ordered data points.
  • Usage Constraint: Must not be applied when the ordering of categories along the horizontal axis is arbitrary or unordered.

Characteristics of Data Distributions

• Normal Distribution: A symmetrical, bell-shaped distribution curve where the mean, median, and mode coincide at the central peak.
• Bimodal Distribution: A distribution displaying two distinct local frequency peaks ("humps").
• Skewed Distributions:
  • Direction of Skew: Distribution skewness is defined by the direction in which the long, tapered tail extends, not where the primary cluster of data points is concentrated.
  • Positive Skew (Right-Skewed): The elongated tail extends toward higher positive values on the right side of the graph, while the majority of scores cluster on the lower left side.

*   **Negative Skew (Left-Skewed):** The elongated tail extends toward lower negative values on the left side of the graph, while the majority of scores cluster on the higher right side.