# Lecture 8

## Testing for trends

• Correlation vs. regression
• Association vs causality
• Correlation
• Regression

### Introduction to Biostatistics

By: Peter Kamerman    (view at painblogR)

### Correlation

Correlation assesses the linear association or strength of relationship between two variables.

### Regression

Regression describes the relationship between x (independent) and y (dependent) variables.

### “Bradford Hill” criteria for causality

• Strength of association
• Consistency
• Specificity
• Temporality
• Coherence (scientific reasoning)
• Experiment (manipulate independent variable)
• Analogy

Correlation

### Pearson’s product-moment correlation

• Variables measured on interval or ratio scale
• There needs to be a linear relationship between the variables
• There are no outliers
• Both variables should be approximately normally distributed

### Spearman’s rank correlation

• Variables measured on an ordinal or interval or ratio scale
• There is a monotonic relationship between the variables

### Interpreting results of a correlation

$$~r~$$

• The strength and direction of relationship between variables. Values range from -1 (perfect inverse linear relationship) to 1 (perfect positive linear relationship).

$$~p$$

• Answers the question: what is the probability of obtaining a correlation coefficient $$(r)$$ as far from zero (no linear relationship) as observed in your experiment assuming the null hypothesis is true?