FES 720 Introduction to R

Statistical Approaches

Three distinct goals for which one might use statistics:

  1. Hypothesis testing
  1. Prediction
  1. Exploration

Which of these you are up to should be determined before you start (collecting and) analyzing the data.

These goals overlap with the summary statistics provided for statistical models.

It is possible to do an approach using the same statistical techniques; but, some techniques are not appropriate for some approaches.

  1. p-value—used in a hypothetico-deductive framework telling us the probability the signal could have been observed by chance (e.g., does nitrogen increase crop yield?)
  2. coefficient estimate—the biological significance (e.g., how much does crop yield increase given a level of nitrogen addition?)
  3. R2—how much what we are studying explains vs the other sources of variation (e.g., how much of the variation in crop yield is due to nitrogen). How well/competely do we understand the system?

Much of science is focussed on p-values to the detriment of other information: A p < 0.05 with an effect size of 0.1% and R2 of 3% is not that useful!

Many ‘exploratory’ analysis are portrayed as hypothesis-testing. e.g.,

Example techniques

1. Hypothesis testing

2. Prediction

3. Exploration