R Tutorial

What is Cluster Analysis? Cluster analysis is a grouping technique that aims to put in the same group (or cluster) objects that are more similar to each other. The intent is very similar to what our brain does when we try to recognise a pattern and group elements based on similarity.

Often, when implementing statistical analysis we ignore variability, and focus on systematic effects of independent variables. This is possible because we assume that variability occurs at random and equally across variables, stimuli , participants, and time points - that it is homogeneous.

Regression (and multilevel/mixed models) gives an estimate of the effect of an independent variable on the dependent variable. When estimating the effect of a categorical independent variable, the mixed model will estimate the effect of each of its levels, and tell us if each effect is significantly different from zero.

At one of my first lab meetings as a postdoc, I started advertising multilevel/mixed models to my colleagues to convince them to give up multiple testing. On that occasion, my supervisor struck me with the question:

The example we have looked at before only included two variables, so we are going to add a third variable, and we are going to investigate the interaction between the independent variable (Days) and this newly generated variable (Lunch):

Understanding a multilevel model in R is one thing, but interpreting the output, plotting the results is another story. Let’s go through all the steps of fitting and interpreting the model with some example data.

In the previous post, we examined the relationship between a dependent variable and a couple of independent variables from the example ‘Chickweight’ dataset. Upon checking of the assumptions, we found that the data did not follow a linear pattern, and residuals were heteroscedastic.

T-tests and ANOVAs are all special cases of Linear Regression. A Linear Regression is an equation defined by the essential formula of a straight line: y = a + bx

This is based on my notes of the statistics course given by Prof. Brian Dillon (UMass Amherst). Introduction Anova is the analysis of variance based on differences among means of more than 2 samples, by comparing 2 estimates of population variance.