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.