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.