# Lesson 6: Working with Two Variables

Lesson 6: Working with Two Variables

## Overview

In this chapter we'll start working with more than one variable, using Chapter 6 in Essential R, and it will (hopefully) start to feel more like we are actually doing statistics. Note that while we'll introduce plotting functions a bit more here, we're just scratching the surface - in later chapters we'll go into plotting in much greater depth.

## Objectives

Upon completion of this lesson, you should be able to:

• Make frequency table and carry out chi-squared test for 2 factors
• Make barplots for 2 factors
• Explore correlation between 2 numeric variables
• Fit a regression between 2 numeric variable
• Compare group means for a continuous variable over levels of a factor

## Data and R Code Files

As always, you can access these files in the "Code Files" folders available from the Essential R page, of here: Chapter 6.R (R script)

# 6.1 - Two Factors: Frequency Tables

6.1 - Two Factors: Frequency Tables

In this screencast we'll demonstrate frequency tables and proportion tables for analyzing the relationship between two factors (qualitative or categorical variables).

# 6.2 - Two Factors: Chi-squared Tests

6.2 - Two Factors: Chi-squared Tests

Here we'll build on the last video by showing how a frequency table can be used to calculate a $$Chi^2$$ test for independence between two variables.

# 6.3 - Two Factors: Barplots and Mosaic Plots

6.3 - Two Factors: Barplots and Mosaic Plots

Here we will consider a couple of ways to visualize the relationship between two factors.

# 6.4 - Two Numeric Variables: Scatterplot

6.4 - Two Numeric Variables: Scatterplot

Here we'll begin with visualizing the relationship between two continuous variables.

# 6.5 - Two Numeric Variables: Correlation

6.5 - Two Numeric Variables: Correlation

Now we'll introduce the function cor() for correlations, and show how to derive both Pearson and Spearman correlations, and how to specify how missing values should be treated.

# 6.6 - Two Numeric Variables: Regression

6.6 - Two Numeric Variables: Regression

Now that we've explored correlation we'll take a brief look at using the "linear model" function lm() to fit regressions. We'll also look at how we can examine the residuals (stored inside the "lm object" created by lm()) to see if their distribution is approximagely normal. Note that we'll we explore regression in much more detail in a later chapter.

# 6.7 - Two Numeric Variables: Regression Diagnostics

6.7 - Two Numeric Variables: Regression Diagnostics

Here we'll briefly introduce the built-in regression diagnsitcs available by calling plot() on an lm object. The residual plot and the normal q-q plots are the most helpful.

# 6.8 - Comparing Group Means: t-tests and One-way tests

6.8 - Comparing Group Means: t-tests and One-way tests

We'll wind up this chapter by demonstraing comparison of group means using t-tests and one-way tests of means, and ANOVA.

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