S2.4. Correlational analysis 2023-24

Page 1: Introduction to Correlational Analysis

  • Topics Covered: 12, 14, 16, 18, 20, 22, 24

  • Course Code: PS11300/SC11300

  • Focus: Cost

Page 2: Lecture Outline

  • Recap Last Lecture

  • Preparing Data for Correlation in SPSS

  • Parametric Assumptions of Correlation

  • Introduction to Correlational Analysis

    • Running Correlation Tests

    • Interpreting Results

  • Types of Correlation

    • Pearson’s Correlation

    • Spearman’s Rho Correlation

  • Presenting Findings

Page 3: Review of Key Concepts

  • Research Questions: Developing quantitative questions and hypotheses.

  • Data Types: Understanding different data types.

  • Raw Data Overview: Viewing to analyze center, shape, and spread.

  • Role of Correlation: Understanding relationships between variables.

  • Positive vs Negative Correlations: Differences explained.

  • Scatter Graphs: Visualization of relationships.

Page 4: Purpose of Correlational Analysis

  • Aim: To determine significant linear relationships between two variables.

  • Questions:

    • Do variables co-vary?

    • Consistency in change between variables?

  • Types of Relationships:

    • Positive correlation: Increase in one leads to increase in another.

    • Negative correlation: Increase in one leads to decrease in another.

Page 5: Examples of Correlations

  • Positive Correlation:

    • Example: More months in Welsh lessons leads to more sentences in vocabulary.

  • Negative Correlation:

    • Example: More time since contact with phobic stimulus leads to lower heart rate.

Page 6: Hypotheses Formation

  • Hypothesizing Relationships: Direction and significance need to be stated.

  • Positive Hypothesis: Significant relationship between Welsh lessons and vocabulary.

  • Negative Hypothesis: Significant relationship between time with phobic stimulus and heart rate.

Page 7: Nature of Relationships

  • Conclusive vs Tentative Relationships: Definitions of each.

  • Direction of Relationships: Positive or negative.

  • Statistical Tests: Determine significance (significant, non-significant) and strength (weak, moderate, strong).

Page 8: Principles of Correlation

  • Data Points: Each context (e.g., individual participant) provides a data point for analysis.

  • Examples:

    • Anxiety levels and exam marks.

    • Town temperature and ice cream sales.

  • Scatter Graphs: Visual representation of data points indicating linear patterns.

Page 9: Data Entry in SPSS

  • Data Type:

    • Attendance and Marks both numeric.

  • Data Presentation: Importance of clarity in rows and columns (e.g., width, decimals, labels).

Page 10: Parametric Assumptions

  • Parameter Assumptions include:

    • Data must be interval or ratio.

    • Relationships identified must be linear.

    • Variables should be normally distributed.

Page 11: Checking Linearity

  • Role of Scatter Graphs:

    • Provide preliminary checks for expected linearity.

    • Elements to Check:

      • Linearity indication

      • Direction of pattern

      • Level of scatter

Page 12: Scatter Graph Utility

  • Relationship Direction: Indicates if correlation is positive or negative.

  • Strength of Relationship: Assessing how closely data points cluster.

  • Identifying Outliers: Importance in analysis.

Page 13: Checking Normality with Histograms

  • Histograms: Useful for checking distributions of data.

  • Examples Provided:

    • Gametime and Attention.

Page 14: Statistical Normality Checks

  • Methodologies:

    • Shapiro-Wilk Test: Best for small samples (n<50).

    • Kolmogorov-Smirnov Test: Better for larger samples (n>50).

Page 15: SW & KS Test Interpretations

  • Significance Values:

    • p<0.05 indicates not normally distributed.

    • p>0.05 indicates normally distributed.

  • Example Interpretation: Reporting normality results of game time and attention data.

Page 16: Analyzing Correlational Data

  • Types of Analyses:

    • Chi-Square: For categorical variables.

    • Pearson Correlation: Continuous variables with parametric data.

    • Spearman Correlation: Non-parametric continuous data.

    • Regression Analysis: Predictive relationships.

Page 17: Overview of Correlation Types

  • Parametric vs Non-parametric: Clarifying distinctions.

  • Types of Correlations: Pearson’s and Spearman’s correlation types.

Page 18: Pearson’s Correlation Details

  • Usage Conditions:

    • For linear relationships in normally distributed data.

    • Data must be interval/ratio.

Page 19: Recap of Correlation Types

  • Reinforcement of Concepts: Parametric vs Non-parametric types of correlation reiterated.

Page 20: Non-parametric Data Considerations

  • Definition: Ordinal/categorical or non-normally distributed interval/ratio.

  • Linear Assumption: Even non-parametric data must meet linearity assumption.

Page 21: Reiteration of Correlation Types

  • Continued Focus: Highlighting parametric vs non-parametric correlations.

Page 22: Spearman’s Correlation Explanation

  • Usage: Determining relationships without parametric assumptions.

  • Ranking Data: Spearman uses ranked scores, losing sensitivity when data is ranked.

Page 23: Output Correlations

  • Output Characteristics: Correlation coefficient (r or rs), significance, direction, and participant count.

  • Importance of Interpretation: Assessing significance and strength of relationships.

Page 24: Matrix Output Description

  • Key Elements in Output:

    • Correlation coefficient, direction, significance value, and participant number.

    • Understanding relationships through output.

Page 25: Correlation Coefficient Insights

  • Interpreting 'r' Values:

    • Range from -1 to 1, with thresholds for strength and direction.

  • Strength Indicators: Definitions of weak, moderate, and strong correlations.

Page 26: Presenting Correlational Findings

  • APA Formatting Requirements:

    • Incorporating scatter plots, means, and SDs.

    • Report normality checks and outcome of correlation analysis.

Page 27: APA Guidelines for Figures and Tables

  • Scatter Graphs: Includes labeling of figures, titles, and axes.

  • Tables: Clear presentation required, including titles and table number labeling.

Page 28: Reporting Correlation in APA Format

  • Format Specifications: r (df, N-2)) = test statistic, p = significance value format detailed.

Page 29: Example of Reporting Correlation

  • Case Study Example: Reporting significant results between game time and dexterity, as well as attentiveness.

Page 30: Summary of Key Points

  • Correlational Hypotheses: Describe anticipated relationships.

  • Types of Relationships: Understanding linear relationships through visualization.

  • Statistical Tools: Pearson’s for parametric, Spearman’s for non-parametric data.

  • Interpretation of r: Effect sizes and relationship strengths analyzed.