Lecture Notes: Correlation and Analytical Tests

Overview

• Discussion on analytical tests for data across different groups or populations.
• Focus on continuous numerical data associated with categories (e.g., time periods, species, gender).
• Importance of assessing relationships between data without specific groups.

Key Concepts

Hypothesis Testing and Chi-Squared Test

• Example: Hypothesis on temperature's effect on phytoplankton biomass.
  • Null hypothesis: Same mean biomass across temperatures.
  • Alternative hypothesis: Increased temperature leads to more biomass.
• Importance of treating temperature as a continuous variable.

Data Visualization

• Use of scatter plots to represent two continuous numerical variables.
• Examples include relationships between length and weight of animals and their prey.

Correlation

• Measures strength of association between two continuous, numerical variables.
• Variables measured in x-y pairs for each data point.
• Determine if a relationship exists and its strength.

Examples

• Positive direct relationship: More humans, more pollution.
• Negative relationship: Higher temperatures lead to fewer sharks in South Florida.

Correlation vs. Regression

• Correlation: Determines degree of association.
• Regression: Determines level of dependence (cause and effect relationship).
• Key terms: Response variable and predictor variable.

Correlation Focus

• Determine if variables are related and how strongly.
• Examples: Body size and prey size relationship.

Strength of Relationship

• Correlation coefficient (r): Indicates strength of linear relationship.
• Values range from -1 (strong negative) to 1 (strong positive).
• r=0 indicates no linear relationship.

Pearson’s Correlation Coefficient

• Used for population parameters, often estimated using sample data.
• Represents test statistic for correlation.

Important Notes

• Slope of line is not crucial; focus on clustering of data points around the line.
• Next lecture will cover calculation of correlation coefficient.

Preparatory Work

• Review section 13.1 of the textbook for background information.