psyc

Comprehensive Study Guide: Regression, ANOVA, and Experimental Design

🧩 1. Regression (from “08_Regression (3).pptx”)

08_Regression (3)

Goal:

  • Predict outcomes (Y) from predictors (X).

Core Concepts:

  • Linear Regression Equation:
    Y^=bX+aŶ = bX + aY^=bX+a

    • b (slope): Change in Y per unit change in X.

    • a (intercept): Y when X = 0.

Steps to Create a Regression Equation:

  1. Compute SP (Sum of Products)

  2. Compute SSx (Sum of Squares for X)

  3. Calculate slope (b = SP / SSx)

  4. Calculate intercept (a = My - bMx)

Error and Variability:

  • Residual: Difference between predicted and actual Y.

  • Standard Error of Estimate: Average prediction error.

  • Sum of Squares:

    • SSY = Total variability in Y

    • SSRegression = Predicted variability

    • SSResidual = Unexplained variability

Significance Testing:

  • Use r² (coefficient of determination) to assess effect size.

    • r2=SSregression/SSYr^2 = SS_{regression} / SS_Yr2=SSregression​/SSY​

    • Represents the % of variance explained by X.

Multiple Regression:

  • Includes 2+ predictors.

  • Each predictor’s b coefficient shows its unique contribution to Y.

  • Larger b → stronger predictor.

🧪 2. Experimental & Quasi-Experimental Design (from “10_Experimental.pptx”)

10_Experimental

Goal:

  • Establish causation (not just correlation).

Three Conditions for Causation:

  1. Temporal Precedence: Cause occurs before effect.

  2. Covariation: Cause and effect are related.

  3. No Alternative Explanations: Random assignment controls for confounds.

Types of Designs:

  • Pre-experimental: Minimal control, weak validity.

    • One-shot case study (X → O)

    • One-group pre/post-test (O → X → O)

    • Static-group comparison (X → O / O)

  • True Experimental: Uses random assignment (R).

    • Posttest-only: R → X O / R → O

    • Pretest-posttest: R → O X O / R → O O

    • Solomon Four-Group Design combines both.

  • Quasi-Experimental: No random assignment.

    • Nonequivalent groups (O X O / O O)

    • Time series (O O O X O O O)

    • Multiple time series adds a comparison group.

Threats to Internal Validity:

  • Selection bias, history, maturation, testing, instrumentation, mortality, regression to mean.

  • Social threats: Demand characteristics, placebo effect, diffusion, compensatory rivalry.

Threats to External Validity:

  • Realism:

    • Mundane realism (how real the setting is)

    • Experimental realism (how engaging the task is)

  • Reactivity: Hawthorne effect.

📊 3. Analysis of Variance (from “10_ANOVA(4100).pptx”)

10_ANOVA(4100)

Purpose:

  • Compare two or more means to test group differences.

  • Used in independent single-factor designs.

Key Terms:

  • Factor: Independent variable (e.g., group type).

  • Levels: Number of groups or conditions.

  • Between-treatments variance: Due to treatment effects.

  • Within-treatments variance: Due to random or individual differences.

Hypotheses:

  • H0:ÎĽ1=ÎĽ2=ÎĽ3H_0: ÎĽ_1 = ÎĽ_2 = ÎĽ_3H0​:ÎĽ1​=ÎĽ2​=ÎĽ3​

  • H1:H_1:H1​: At least one mean differs.

ANOVA Statistic:
F=MSbetweenMSwithinF = \frac{MS_{between}}{MS_{within}}F=MSwithin​MSbetween​​

  • Large F → significant group differences.

Sum of Squares (SS):

  • SS Total = SS Between + SS Within

  • df Total = N – 1

  • df Between = k – 1

  • df Within = N – k

  • MS=SS/dfMS = SS / dfMS=SS/df

Post Hoc Tests:

  • Used when F is significant.

  • Tukey’s HSD and ScheffĂ© test compare specific means.

Assumptions:

  1. Independence of observations.

  2. Normality.

  3. Homogeneity of variance (equal variances).