# Analyzing Grouped Data

In this unit, you will learn classical statistical tests and how to compare means between groups.

## Lesson 1. How to choose a statistical test

Lectures:

Which test? Which assumptions?

Formulae

Learning Goals:

• Understand the different arrangements and distributions of data,
• Understand what tests are appropriate for what questions and data,
• Test assumptions such as normality, homogeneity of variance, outliers,
• Plot data to examine distributions.

Lab: Unit 3: Lab 1

Zuur et al. 2010. A protocol for data exploration to avoid common statistical problems. Methods in Ecology & Evolution 1, 3–14.

Läärä, E. 2009. Statistics: reasoning on uncertainty, and the insignificance of testing null. Ann. Zool. Fennici 46: 138–157.

Functions: `qqplot()`, `ks.test()`, `shapiro.test()`, `bartlett.test()`

## Lesson 2. How to compare counts between groups

Learning Goals:

• Use of `table()` and `hist()`,
• Convert continuous data to groups,
• Run simple sign, proportion, binomial, and Chi-square tests.

SWIRL: Testing Ratios

Lab: Unit 3: Lab 2

Functions: `table()`, `prop.test()`, `binom.test()`, `chisq.test()`

## Lesson 3. How to calculate group-level stats in dataframes

Lecture: The Split-Apply-Combine approach

Learning Goals:

• Understand and use `tapply()`, `sapply()`, `lapply()`, `apply()`.
• Calculate and plot group-level means and sd.

SWIRL: The *apply() group of functions:

Lab: Unit 3: Lab 3

Reading: Wickham, H. 2001. The Split-Apply-Combine Strategy for Data Analysis. Journal of Statistical Software 40.

• (This paper describes the idea and principles, but also a specific R package (plyr) that we do not cover).

Functions: `apply()`, `tapply()`, `sapply()`, `lapply()`

## Lesson 4. How to compare means from different groups or populations

Lecture: t-tests and ANOVAS

Best Practice: Writing

Learning Goals:

• Run t-tests and ANOVAs,
• Test assumptions of normality, homogeneity of variance
• Extract details from model output,
• Plot these data with boxplots and barplots.

SWIRL: Testing Populations

Lab: Unit 3: Recap

Functions: `t.test()`, `aov()`,