Univariate Designs in Research Methods

Univariate Designs - Key Concepts

  • Definition: Univariate designs analyze one dependent variable (DV) in relation to one or more independent variables (IVs).
Types of Research Designs:

  • Independent Measures Design (Between-Subjects): Compares different groups of participants.

    • Example: Comparing grades of undergraduates with laptops to those without.

  • Repeated Measures Design (Within-Subjects): Compares the same group of participants across different conditions.

    • Example: Measuring depression scores before and after therapy in the same individuals.

Transition from 2-Group to Multi-Group Designs

Key Steps:
  1. Deciding how many levels of the IV are needed:
    • 2 Groups: Use an Independent Samples t-test.
    • > 2 Groups: Use a One-way ANOVA.
  2. For repeated measures (same participants tested multiple times):
    • 2 Levels: Use a Paired Samples t-test.
    • > 2 Levels: Use a Repeated Measures ANOVA.
Interaction Effects:
  • In cases with both between-subjects and within-subjects IVs, a 2 Factor ANOVA is employed.
  • Example: Comparing the effects of treatment vs control groups over pre and post-treatments.

Important Design Lessons

  • Hypotheses determine design.
  • Design determines analysis.
  • The critical component of research methodology is the hypothesis.

Testing Hypotheses: Statistical Tests

Single IV, 2-Level Designs:
  • Independent Samples t-test
    • Hypotheses:
    • Null (H0): μ1 - μ2 = 0 (no difference my null hypothesis).
    • Alternative (H1): μ1 - μ2 ≠ 0 (indicates significant difference).
Formula:
  • t = (M1 - M2) / s(M1 – M2)
Single IV, >2 Level Designs:
  • One-way ANOVA:
  • ANOVA assesses variance between groups (systematic effects) versus within groups (error variance). Prospective ratio:
    • F = MSbetween / MSwithin.
Notable Criteria:
  • To find F values that indicate significance, matching with degrees of freedom.

Within-Subjects Designs: Repeated Measures ANOVA

  • Evaluates mean differences across treatment conditions using the same subjects. Measures are more reliable as individual differences are controlled.
  • F-Ratio Differences: Compared between-treatment variance and within-treatment error variance to assess significant differences.

Factorial Designs

  • Involves 2 or more IVs affecting 1 DV.
    • Example: Comparing the effects of different treatments in a factorial analysis:
    • 2 IVs: Drug vs placebo (IV1), Mindfulness vs Exercise (IV2).
  • Main Effects:
    • It refers to the effect of each IV.
    • Interaction effects indicate how the different levels of IVs interact to affect the DV.

Special Case - Covariates in ANOVA

  • Purpose of Including Covariates:
  1. To reduce within-group error variance.
  2. To eliminate confounding effects.
  • Key Assumptions:
    • Relationship between covariate and DV must be linear.
    • Homogeneity of regression coefficients must be assessed and met across groups, ensuring the adjustment applies uniformly to all groups.