Lecture 8

Testing for trends

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

Introduction to Biostatistics

By: Peter Kamerman    (view at painblogR)

Correlation vs regression


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


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

Association does not imply causality

“Bradford Hill” criteria for causality

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



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?


Always plot your data first