Research Methods and Statistical Analysis

Correlation

• Pearson’s r: Most commonly used correlation coefficient.
  • Requires both variables to be continuous (interval or ratio).
  • Factors affecting Pearson’s r:
  • Range restrictions:
    • Examining a limited portion of the scatter plot reduces r.
    • Reduced variability decreases r.
  • Coefficient of determination (R²):
    • Proportion of total variance in one variable accounted for by the other.
    • $R^2$ is obtained by squaring Pearson’s r.
• Spearman Rank-order Correlation:
  • Denoted as $r_{sp}$.
  • Used with two ranked/ordinal variables.
  • Same formula as Pearson’s r.
  • Advantages:
  • Does not require normal distribution.
  • Can handle outliers/extreme values.
  • Does not require linear association.
• Point-biserial correlation:
  • Denoted as $r_{pb}$.
  • Used with one continuous variable and one dichotomous variable.
  • Example:
  • Continuous variable: appetite (1 to 10).
  • Dichotomous variable: lunch break (0 = no, 1 = yes).

Regression

• Simple Regression:
  • Understand how to interpret each part of the regression equation.
  • Example for B:
    • If self-esteem $= 0.986$, for every 1 unit increase in predictor, outcome changes by the value under B.
    • If self-esteem increases by 1, life satisfaction increases by $0.99$.
• Beta:
  • e.g. $= 0.755$
  • For every standard deviation increase in self-esteem, life satisfaction increases by $0.76$ standard deviations on average.
• R² (coefficient of determination):
  • Proportion of variance in outcome explained by regression line (predictor).
• F Statistics:
  • Indicates whether the regression line explains a significant amount of variation in the outcome.
• Multiple regression:
  • Linear combination of multiple variables predicts an outcome.
  • Assess contributions of each predictor variable.
  • Types of multiple regression:
  1. Standard (simultaneous): All predictors entered at once.
  2. Stepwise: SPSS enters predictors one at a time.
     • Not theory driven; can be problematic.
  3. Hierarchical: Predictors entered based on theory/research.
     • Provide output for each block and assess change in R².
     • Examine additional variance accounted for by each predictor block.

Moderation

• Identify significant moderation from SPSS output.
• Visually depict moderation and interpret figures accurately.
• Concept of Moderation:
  • The relationship between $X$ and $Y$ varies depending on the level of the moderator.
  • Moderators are usually stable variables (e.g., personality traits, gender).

Mediation

• Conceptual clarity between mediators and moderators.
• Steps to establish mediation:
  1. Show causal variable is correlated with outcome (use $Y$ as criterion, $X$ as predictor).
  2. Show causal variable is correlated with the mediator (use $M$ as criterion, $X$ as predictor).
  3. Show mediator affects outcome (use $Y$ as criterion, $X$ and $M$ as predictors).
  4. Effect of $X$ on $Y$ controlling for $M$ should be weaker ( path $c' $).
  • Identify paths a, b, c, and c’ in mediation model.
  • Sobel’s test can be used to test the indirect effect.
• Understanding total effect vs. direct effect: Mediators change in relation to other variables (e.g., anxiety, social support).

Quasi-experimental Design

• Lacks control over assignment of participants or manipulation of causal variables.
• Goals: Assess causal relationships, despite some limits on internal validity.
• Common threats to internal validity: History, selection, maturation, biases.

Types of Quasi-Experimental Designs

1. Nonequivalent control group pretest-posttest: Assessment before and after intervention.
2. Nonequivalent control group post-test only: Assessment after intervention.
3. Interrupted time-series design: Collect data before and after intervention.
4. Regression discontinuity design: Strongest quasi-experimental design based on cut-off scores.

Qualitative Research

• Explores phenomena through words; focuses on context and meaning.
• Methods include observation, interviews, document reviews.
• Differences between qualitative and quantitative:
  • Qualitative: Idiographic (focus on uniqueness), inductive (research leads to theory).
  • Quantitative: Nomothetic (generalization), deductive (theory precedes research).

Characteristics of Qualitative Research

• Natural setting, researcher as key instrument (data collectors), multiple data sources.
• Emergent design allows for flexible research approaches.
• Engages with participants to understand their meanings and contexts.

Types of Qualitative Methods

1. Interviews: Structured and semi-structured formats.
2. Focus Groups: Discussion with respondents on specific issues.
3. Observation: Field notes and participant observation, understanding experience firsthand.
4. Case Study: In-depth study providing narrative descriptions based on various data sources.

Strengths and Weaknesses of Qualitative Research

• Strengths: Unique perspectives, sensitivity to context, flexibility.
• Weaknesses: Time-consuming, analysis challenges, potential biases.

Mixed Methods Research

• A combination of quantitative and qualitative methods.
• Purposes include triangulation, complementarity, and development of methods.

Community-Based Participatory Research (CBPR)

• Collaborative approach that involves community in the research process.
• Key components: equitable relationships, knowledge with action, and addressing local issues.
• Aims for social change and empowering communities.