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Lecture Notes - Correlation and Regression in Psychology Research

Psychology Research Basics

  • Definition of Psychology Research
  • Focuses on identifying and studying relationships between variables.
  • Aim is to build theories through analysis of variables.

Correlational Research

  • Purpose: To determine if a relationship exists between two variables (X and Y)
  • Method:
  • Observes and measures two or more variables without manipulation.
  • Examples of variables to study:
    • Anxiety vs. depression
    • Hours of TV-watching vs. reading ability
    • Shoe size vs. intellect

Understanding Relationships

  • A relationship is established if two variables covary:
  • As one variable increases, the other may also increase (Positive correlation) or decrease (Negative correlation).
  • No systematic changes between variables mean no correlation.

Characteristics of Correlational Research

  • Direction (Positive or Negative)
  • Form (Linear or Non-linear)
  • Strength: Measured by correlation coefficients, ranging from -1 to 1.
  • Correlation does NOT equal causation.
  • Possible scenarios:
    • A causes B
    • B causes A
    • A third variable (C) causes the relationship between A and B

Scatterplots and Correlation

  • Visual representation of relationships between two variables.
  • How to read Scatterplots:
  1. Each point represents an individual.
  2. The X-coordinate corresponds to one variable (X) and the Y-coordinate corresponds to another (Y).
  3. Analyze the plot for patterns indicating strength and direction of the relationship.

Correlation Coefficient (r)

  • Ranges from -1 to 1.
  • Indicates the strength and direction of a relationship:
  • Negative value: as X increases, Y decreases.
  • Positive value: as X increases, Y increases.
  • Squared value (r^2) shows the proportion of variance accounted for.

Testing Significance

  • Determine how likely the correlation found is a result of chance.
  • Generally use p-value < .05 to indicate significance.

Examples in Research

  • Studying the relationship between:
  • Time spent revising and exam performance.
  • Exam anxiety and exam performance.

Non-Parametric Correlations

  • Spearman’s Rho: Used when parametric assumptions are violated.
  • Kendall’s Tau: Preferable for small datasets with tied scores.

Regression Analysis

  • A method used to predict one variable based on another, enhancing predictive quality.
  • Simple Linear Regression: Predicts the outcome variable based on a single predictor variable.
  • Results in a straight line best fitting observed data.

Key Elements of Regression

  • Regression Coefficients:
  • Intercept (b0): Value at which the line crosses the Y-axis when X=0.
  • Slope (b1): Indicates the change in Y for a one-unit change in X.

Goodness of Fit

  • Assess how well the regression model predicts outcomes compared to the mean predictor.
  • Common metrics:
  • R-squared (R^2): Proportion of variance accounted for by the model.
  • F-statistic: Compares model’s predictive improvement against model error.

Example Model from Data

  • Regression Equation:
  • Exam Anxiety = 87.67 - 0.67(Time Spent Revising)
  • Interpretation: For every unit increase in revision time, exam anxiety decreases by 0.67 points.

Conclusion

  • Correlation and regression provide vital statistical tools in psychology research for analyzing and understanding the relationships between variables.
  • Always remember the principle: Correlation does not imply causation.