Examining relationships between and among variables. Chapter 9. Biostatistics

What are the three possible relationships between variables?

1. Positive relationship: Variables move in the same direction.

2. Negative relationship: Variables move in opposite directions.

3. No association: No relationship exists between variables.

What is the difference between correlation and causality?

• Correlation indicates a relationship between variables but does not imply cause and effect.

• Causality can only be determined through experimental studies.

How can a bivariate relationship be visualized?

It can be shown in a scatter plot, which provides an idea of how variables might be related.

What is the simplest statistic to observe the relationship between variables?

Covariance

What are the limitations of covariance?

Covariance is not a standardized measure of relationship, making comparison of covariances difficult.

What is the Pearson Correlation Coefficient?

A standardized measure that allows comparison of coefficients, ranging between -1 and +1.

How is the Pearson Correlation Coefficient interpreted?

• 0 to 0.1: No relationship

• 0.1 to 0.3: Low relationship

• 0.3 to 0.5: Medium relationship

• 0.5 to 0.8: High relationship

• 0.8: Very high relationship

What does a significant p-value indicate in correlation analysis?

It indicates statistical evidence against the null hypothesis, suggesting a significant linear relationship between variables.

What is the Coefficient of Determination (R²)?

it is the square of the correlation coefficient, indicating the proportion of variability in one variable explained by the other.

When are non-parametric correlation coefficients like Spearman's rho and Kendall's tau used?

They are used when the assumptions for Pearson's correlation coefficient are not met, such as non-normal distribution or ordinal variables.

What is partial correlation?

It measures the relationship between two variables while controlling for the effect of a third variable.

How is the effect size interpreted in correlation analysis?

• Small effect: ±0.1

• Medium effect: ±0.3

• Large effect: ±0.5

What should be reported when presenting correlation coefficients?

• The size of the relationship between variables.

• The associated significance.

• The exact p-value.

• Confidence intervals.