Basic Introduction to R

```
#######################################################
# CHAPTER 1: PROPAGANDA FOR R
#
# R is a programming language designed primarily for
# data analysis and statistics.
#
# The big advantages of R are:
#
# 1. It is free.
# 2. It is easy.
#
# Point #2 sometimes takes some convincing, especially
# if you haven't programmed before. But, trust me, R
# is WAY easier than ANY other programming language
# I have ever tried, which you could also do serious
# science with.
#
# MATLAB is probably the only other competitor for ease
# of use and scientific ability, but Matlab costs
# hundreds of dollars, and hundreds of dollars more for
# the various extensions (for e.g. statistics, image
# analysis, etc.). This works great when your institution
# has a site license for Matlab, but it suck when you
# move to a new school/job.
#
# R is easy because most of the "computer science
# details" -- how to represent numbers and other
# objects in the computer as binary bits/bytes,
# how to manage memory, how to cast and type variables,
# blah blah blah, are done automatically behind the
# scenes.
#
# This means almost anyone can get going with R in
# minutes, by just typing in commands and not having
# to spend days learning the difference between a
# short and long integer, blah blah blah.
#
# That said, the cost of this automation is that R
# is slower than other programming languages. However,
# this doesn't matter for common, basic sorts of
# statistical analyses -- say, linear regression with
# 1,000 data observations. It DOES matter if you are
# dealing with huge datasets -- say, large satellite
# images, or whole genomes.
#
# In these situations, you should use specialist
# software, which is typically written in Python
# (for manipulating textual data, e.g. genome files)
# or Java, C, or C++ (for high-powered computing).
#
# (Although, in many situations, the slow parts of
# R can be re-programmed in C++, and accessed from
# R.)
#
# R is also pretty bad for large, complex programming
# projects. Python and C++ are "object-oriented."
# In computer-programming, "objects" help organize
# your data and tasks. For example, if you are
# writing a video game, you might want to program
# many different monsters. However, you don't want to
# re-program the behavior of each monster from scratch.
# Instead, you create a general object, "monster", and
# give it attributes (speed, armor, etc.). The "monster"
# object takes inputs (like what enemies are close to
# it) and produces outputs (motion or attacks in a
# certain direction).
#
# Each specific type of monster would be an instance
# of the monster class of objects. Each individual
# monster of a specific type would be its own object,
# keeping track of hit points, etc.
#
# You can see that, for serious programming, this
# object-oriented style would be the way to go. Therefore,
# "real" computer-science classes teach you this way
# of programming. This is great if you want to
# go work in the video game industry and devote your
# life to coding.
#
# However, if you just want to plot some data and
# run some statistical tests and do some science,
# you don't want to have to go through a bunch of
# rigamarole first. You just want to load the data
# and plot it and be done. This is what R is for.
#
#######################################################
#######################################################
# CHAPTER 2: GETTING R
#######################################################
#
# R is free and available for all platforms. You can
# download it here.:
#
# http://www.r-project.org/
#
# Tip for free, scientific software:
#
# Unless you are doing something expert, you will want
# the "binary" file rather than the source code.
#
# Programmers write source code in text files.
#
# A compiler program turns this into a "binary" which
# actually executes (runs) on a computer.
#
# Compiling from source code can take minutes or hours,
# and sometimes will crash if your computer & compiler
# are not set up right.
#
# A binary should just work, once you have installed it,
# assuming you've got the binary for your machine.
#
# ASSIGNMENT: Once you have R installed (it appear in
# "Applications" on a Mac, or "Program Files" on a
# Windows machine), open it to make sure it works.
# Then, return to this tutorial.
#
########################################################
#######################################################
# CHAPTER 3: GET A *PLAIN*-TEXT EDITOR
#######################################################
#
# Many people make the mistake of typing commands
# into R, but not saving those commands.
#
# *ALWAYS* SAVE YOUR COMMANDS IN A TEXT FILE!!
# *ALWAYS* SAVE YOUR COMMANDS IN A TEXT FILE!!
# *ALWAYS* SAVE YOUR COMMANDS IN A TEXT FILE!!
#
# Got it? Good.
#
# The next mistake people make is to use Word or
# some other monstrosity to save their commands.
# You can do this if you want, but the formatting
# etc. just gets in the way.
#
# Find or download a PLAIN-TEXT editor (aka ASCII
# text editor). Common examples:
#
# Mac: TextWrangler (free) or BBedit
#
# Windows: Notepad (free, search Programs) or Notetab
#
# Or: versions of R that have a GUI (GUI=Graphical User
# Interface) also have a built-in editor.
#
#
# WHY SAVE YOUR COMMANDS?
#
# Because you can come back in 6 months and run the
# same analysis again, just by pasting the commands
# back into R.
#
# Trust me, this is MUCH better than trying to remember
# what buttons to click in some software.
#
# And, anytime
# you need to do something more than a few times,
# it gets super-annoying to click all of the buttons
# again and again.
#
# This is why most serious scientific software is
# command-line, rather than menu-driven.
#
#
# HOW TO TAKE NOTES IN R SCRIPTS
#
# Put a "#" symbol in front of your comments. Like I
# did here. COMMENTS ARE GOOD! COMMENT EVERYTHING!
#
#
# ASSIGNMENT: Once you've found a plain-text editor,
# return to this tutorial.
#######################################################
#######################################################
# CHAPTER 4: R BASICS
#######################################################
#
# There are two major hurdles in learning R:
#
# 1. Getting/setting your working directory.
#
# 2. Loading your data
#
# 3. Learning the commands to do what you want.
#
# Points #1 and #2 are easy to learn -- just don't
# forget! You can never get anything significant
# done in R if you can't get your data loaded.
#
# Point #3 -- No one knows "all" of R's commands. As
# we see, every package and function creates
# additional commands.
#
# Your goal is just to learn the basics, and then learn
# how to find the commands you need.
#
# ASSIGNMENT: Type/paste in each of the commands below
# into your text file, then into R. Take notes as
# you go.
#######################################################
#######################################################
# Working directories:
#
# One of the first things you want to do, usually, is
# decide on your working directory.
#
# You should create a new directory using:
#
# Mac: Finder
# Windows: Windows Explorer (or File Manager or
# whatever it's called these days)
#
# ROOLZ FOR FILES AND DIRECTORIES IN R
#
# 1. Put the directory somewhere you will find it
# again.
#
# 2. Never use spaces in filenames.
#
# 3. Never use spaces in directory names.
#
# 4. Never use spaces in anything involving
# files/directories.
#
# 5. Never! It just causes problems later. The
# problems are fixable, but it's easier to
# just never use spaces.
#
# 6. Use underscore ("_") instead of spaces.
#
#
# FINDING MAC/WINDOWS DIRECTORIES IN R
#
# Usually, you can drag/drop the file or directory
# into R to see the full path to the file.
# Copy this into the 'here' in wd="here", below.
#
#
# CHANGE FILE SETTINGS IN MACS/WINDOWS
#
# Modern Macs/Windows hide a lot of information
# from you. This makes life easier for John Q. Public,
# but makes it harder for scientists.
#
# Good preferences for your file viewer:
#
# * Turn ON viewing file extensions (.txt, .docx, etc.)
# * Turn ON viewing of hidden files
# * Change file viewing to "list" format
#
# See Preferences in Mac Finder or Windows Explorer.
#
########################################################
# On my Mac, this is a working directory I have chosen
# (change it to be yours)
wd = "/Users/nickm/Desktop/Rintro/"
wd = "~/Desktop/Rintro/"
wd="/drives/GDrive/REU_example"
# On a PC, you might have to specify paths like this:
#wd = "c:\\Users\\nick\\Desktop\\_ib200a\\ib200b_sp2011\\lab03"
# setwd: set working directory
setwd(wd)
# getwd: get working directory
getwd()
# list.file: list the files in the directory
list.files()
#######################################################
# PLAYING WITH R
#######################################################
# (Preliminary: this might be useful; uncomment if so)
# options(stringsAsFactors = FALSE)
# concatentate to a list with c()
student_names = c("Nick", "Hillary", "Sonal")
# describe what the function "c" does:
#
grade1 = c(37, 100, 60)
grade2 = c(43, 80, 70)
grade3 = c(100, 90, 100)
grade1
grade2
grade3
print(grade3)
# column bind (cbind)
temp_table = cbind(student_names, grade1, grade2, grade3)
class(temp_table)
# convert to data frame
grade_data = as.data.frame(temp_table)
class(grade_data)
# Don't convert to factors
grade_data = as.data.frame(temp_table, stringsAsFactors=FALSE)
# add column headings
col_headers = c("names", "test1", "test2", "test3")
names(grade_data) = col_headers
print(grade_data)
# change the column names back
old_names = c("student_names", "grade1", "grade2", "grade3")
names(grade_data) = old_names
grade_data$grade1
# Let's calculate some means
# mean of one column
mean(grade_data$grade1)
# R can be very annoying in certain situations, e.g. treating numbers as character data
# What does as.numeric do?
#
as.numeric(grade_data$grade1)
grade_data$grade1 = as.numeric(as.character(grade_data$grade1))
grade_data$grade2 = as.numeric(as.character(grade_data$grade2))
grade_data$grade3 = as.numeric(as.character(grade_data$grade3))
print(grade_data)
# mean of one column
mean(grade_data$grade1)
# apply the mean function over the rows, for just the numbers columns (2, 3, and 4)
apply(X=grade_data[ , 2:4], MARGIN=2, FUN=mean)
# Why doesn't this work?
mean(grade_data)
# What caused the warning message in mean(grade_data)?
# How about this?
colMeans(grade_data[,2:4])
# How about this?
colMeans(grade_data[,2:4])
# More functions
sum(grade_data$grade1)
median(grade_data$grade1)
# standard deviation
apply(X=grade_data[ , 2:4], MARGIN=1, FUN=sd)
# store st. dev and multiply by 2
mean_values = apply(grade_data[ , 2:4], 1, mean)
sd_values = apply(grade_data[ , 2:4], 1, sd)
2 * sd_values
# print to screen even within a function:
print(sd_values)
# row bind (rbind)
grade_data2 = rbind(grade_data, c("means", mean_values), c("stds", sd_values))
#######################################################
# GETTING DATA
#######################################################
#
# Let's download some data. Francis Galton was one
# of the founders of statistics. He was also
# the cousin of Charles Darwin. Galton invented the
# term "regression". These days, "regression" means
# fitting the best-fit line to a series of x and y
# data points.
#
# But, why is the weird term "regression" used for this?
# What is regressing?
#
# Let's look at Galton's original dataset: the heights
# of parents and children.
#
# Use your web browser to navigate here:
#
# http://www.randomservices.org/random/data/Galton.html
#
# ...and save "Galton's height data" as Galton.txt
# (right-click, save) to your
# working directory.
#
# After doing this, double-click on Galton.txt and
# view the file, just to see what's in there.
#
#######################################################
# Before proceeding, double-check that your data file
# is in the working directory:
getwd()
list.files()
# Let's store the filename in a variable
#
# Note: In Nick's head:
#
# "wd" means "working directory"
# "fn" means "filename"
#
#wd = "/drives/Dropbox/_njm/__packages/Rintro/"
#setwd(wd)
fn = "Galton.txt"
# Now, read the file into a data.frame
heights = read.table(file=fn, header=TRUE, sep="\t")
# Now, look at "heights"
heights
# Whoops, that went by fast! Let's just look at the
# top of the data table
head(heights)
# Let's get other information on the data.table
# Column names
names(heights)
# Dimensions (rows, columns)
dim(heights)
# Class (data.frame, matrix, character, numeric, list, etc.)
class(heights)
# The heights data is the adult height of a child (in inches),
# and the "midparent" height -- the mean of the two parents.
# QUESTION: Do the means of parent and child height differ?
# Means
colMeans(heights)
colMeans(heights[,-4])
# Standard deviations
apply(X=heights[,-4], MARGIN=2, FUN=sd)
# Min & Max
apply(X=heights[,-4], MARGIN=2, FUN=min)
apply(X=heights[,-4], MARGIN=2, FUN=max)
# They seem pretty close, but let's do a test
# Make sure numbers columns are numeric
heights$Family = as.numeric(heights$Family)
heights$Father = as.numeric(heights$Father)
heights$Height = as.numeric(heights$Height)
heights$Kids = as.numeric(heights$Kids)
# Let's add the Midparent column
heights[,c("Father","Mother")]
# Take the mean of Father and Mother columns, store in column "Midparent"
heights$Midparent = apply(X=heights[,c("Father","Mother")], MARGIN=1, FUN=mean)
# View the new column
head(heights)
# Population Mean Between Two Independent Samples
# http://www.r-tutor.com/elementary-statistics/inference-about-two-populations/population-mean-between-two-independent-samples
# (change "Child" to "Height")
ttest_result1 = t.test(x=heights$Midparent, y=heights$Height, paired=FALSE, alternative="two.sided")
ttest_result1
# But wait, this test assumes that the samples from each population
# are independent. Do you think parent heights and child heights are
# independent?
# Probably not. Actually, these samples are paired, so let's
# check that:
# Population Mean Between Two Matched Samples
# http://www.r-tutor.com/elementary-statistics/inference-about-two-populations/population-mean-between-two-matched-samples
ttest_result2 = t.test(x=heights$Midparent, y=heights$Height, paired=TRUE, alternative="two.sided")
ttest_result2
# Compare the two:
ttest_result1
ttest_result2
# Interestingly, it looks like parents are slightly taller than the children!
#
# Is this statistically significant?
#
# But is it a large effect? Is it *practically* significant?
#
# Let's plot the histograms
hist(heights$Midparent)
hist(heights$Height)
# That's a little hard to compare, due to the different
# automated scaling of the x-axis.
# Let's fix the x-axis to be (5 feet, 7 feet)
xlims = c(5*12, 7*12)
hist(heights$Midparent, xlim=xlims)
hist(heights$Height, xlim=xlims)
# And fix the y-axis
# Let's fix the y-axis to be (0, 220)
ylims = c(0, 220)
hist(heights$Midparent, xlim=xlims, ylim=ylims)
hist(heights$Height, xlim=xlims, ylim=ylims)
# Let's plot the means and 95% confidence intervals on top
# Midparent values
hist(heights$Midparent, xlim=xlims, ylim=ylims)
# Plot the mean
abline(v=mean(heights$Midparent), lty="dashed", lwd=2, col="blue")
# Plot the 95% confidence interval (2.5% - 97.5%)
CI_025 = mean(heights$Midparent) - 1.96*sd(heights$Midparent)
CI_975 = mean(heights$Midparent) + 1.96*sd(heights$Midparent)
abline(v=CI_025, lty="dotted", lwd=2, col="blue")
abline(v=CI_975, lty="dotted", lwd=2, col="blue")
# Child values
hist(heights$Height, xlim=xlims, ylim=ylims)
# Plot the mean
abline(v=mean(heights$Height), lty="dashed", lwd=2, col="blue")
# Plot the 95% confidence interval (2.5% - 97.5%)
CI_025 = mean(heights$Height) - 1.96*sd(heights$Height)
CI_975 = mean(heights$Height) + 1.96*sd(heights$Height)
abline(v=CI_025, lty="dotted", lwd=2, col="blue")
abline(v=CI_975, lty="dotted", lwd=2, col="blue")
# Let's put it all in a nice PDF format to save it
# Open a PDF for writing
pdffn = "Galton_height_histograms_v1.pdf"
pdf(file=pdffn, width=8, height=10)
# Do 2 subplots
par(mfrow=c(2,1))
# Midparent values
hist(heights$Midparent, xlim=xlims, ylim=ylims, xlab="height (inches)", ylab="Count", main="Midparent heights")
# Plot the mean
abline(v=mean(heights$Midparent), lty="dashed", lwd=2, col="blue")
# Plot the 95% confidence interval (2.5% - 97.5%)
CI_025 = mean(heights$Midparent) - 1.96*sd(heights$Midparent)
CI_975 = mean(heights$Midparent) + 1.96*sd(heights$Midparent)
abline(v=CI_025, lty="dotted", lwd=2, col="blue")
abline(v=CI_975, lty="dotted", lwd=2, col="blue")
# Child values
hist(heights$Height, xlim=xlims, ylim=ylims, xlab="height (inches)", ylab="Count", main="Child heights")
# Plot the mean
abline(v=mean(heights$Height), lty="dashed", lwd=2, col="blue")
# Plot the 95% confidence interval (2.5% - 97.5%)
CI_025 = mean(heights$Height) - 1.96*sd(heights$Height)
CI_975 = mean(heights$Height) + 1.96*sd(heights$Height)
abline(v=CI_025, lty="dotted", lwd=2, col="blue")
abline(v=CI_975, lty="dotted", lwd=2, col="blue")
# Close the PDF writing
dev.off()
# Write a system command as a text string
cmdstr = paste("open ", pdffn, sep="")
cmdstr
# Send the command to the computer system's Terminal/Command Line
system(cmdstr)
# The PDF should hopefully pop up, e.g. if you have the free Adobe Reader
# The difference in means is very small, even though it appears to be
# statistically significant.
#
# This is a VERY IMPORTANT lesson:
#
# "statistically significant" DOES NOT ALWAYS MEAN "practically "significant",
# "interesting", "scientifically relevant", etc.
#
#
# The difference may have to do with:
#
# * Galton's 'method' of dealing with the fact that
# male and female children have different average heights --
# he multiplied the female heights by 1.08!
#
# * Different nutrition between the generations
#
# * Maybe the adult children weren't quite all fully grown
#
# * Chance rejection of the null
#
# Who knows?
# You may have noticed that the standard deviations look to be
# a lot different. Can we test for this?
# Yes! The null hypothesis is that the ratio of the
# variances is 1:
Ftest_result = var.test(x=heights$Midparent, y=heights$Height, ratio=1, alternative="two.sided")
Ftest_result
# We get extremely significant rejection of the null. What is
# the likely cause of the lower variance in the midparent data?
#
# For the complex story of Galton's original data, see:
#
# http://www.medicine.mcgill.ca/epidemiology/hanley/galton/
#
# James A. Hanley (2004). 'Transmuting' women into men:
# Galton's family data on human stature. The American Statistician, 58(3) 237-243.
# http://www.medicine.mcgill.ca/epidemiology/hanley/reprints/hanley_article_galton_data.pdf
#
# BTW, Galton was both a genius, and promoted some deeply flawed ideas
# like eugenics:
# http://isteve.blogspot.com/2013/01/regression-toward-mean-and-francis.html
#
# We noted before that child and parent heights might not be
# independent. Let's test this!
# QUESTION: is there a relationship?
# Start by plotting the data:
plot(x=heights$Midparent, y=heights$Height)
# It looks like there is a positive relationship:
# taller parents have taller children.
# However, it's a little bit hard to tell for
# sure, because Galton's data is only measured
# to the half-inch, so many dots are plotting
# on top of each other. We can fix this by
# "jittering" the data:
# Plot the data, with a little jitter
plot(x=jitter(heights$Midparent), y=jitter(heights$Height))
# It looks like there's a positive relationship, which makes
# sense. Can we confirm this with a statistical test?
# Let's build a linear model (lm)
lm_result = lm(formula=Height~Midparent, data=heights)
lm_result
# This just has the coefficients, this doesn't tell us much
# What's in the linear model? A list of items:
names(lm_result)
# See the statistical results
summary(lm_result)
# Analysis of variance (ANOVA)
anova(lm_result)
# You can get some standard diagnostic regression plots with:
plot(lm_result)
# Let's plot the regression line on top of the points
intercept_value = lm_result$coefficients["(Intercept)"]
slope_value = lm_result$coefficients["Midparent"]
# Plot the points
plot(x=jitter(heights$Midparent), y=jitter(heights$Height))
# Add the line
abline(a=intercept_value, b=slope_value, col="blue", lwd=2, lty="dashed")
# It's a little hard to tell if the slope is 1:1 or not,
# Because the x-axis and y-axis aren't the same
# Let's fix this
# Plot the points
xlims = c(5*12, 6.5*12)
ylims = c(5*12, 6.5*12)
plot(x=jitter(heights$Midparent, factor=3), y=jitter(heights$Height, factor=3), xlab="Midparent height", ylab="Child height", xlim=xlims, ylim=ylims)
title("Galton's height data")
# Add the regression line
abline(a=intercept_value, b=slope_value, col="blue", lwd=2, lty="dashed")
# Add the 1:1 line
abline(a=0, b=1, col="darkgreen", lwd=2, lty="dashed")
# Is the slope statistically different from 1:1?
# We can test this by subtracting a 1:1 relationship from the data, and seeing if
# the result has a slope different from 0
child_minus_1to1 = heights$Height - (1/1*heights$Midparent)
heights2 = heights
heights2 = cbind(heights2, child_minus_1to1)
# Let's build a linear model (lm)
lm_result2 = lm(formula=child_minus_1to1~Midparent, data=heights2)
lm_result2
# This just has the coefficients, this doesn't tell us much
# What's in the linear model? A list of items:
names(lm_result2)
# See the statistical results
summary(lm_result2)
# Analysis of variance (ANOVA)
anova(lm_result2)
# You can get some standard diagnostic regression plots with:
plot(lm_result2)
# Let's plot the regression line on top of the points
intercept_value = lm_result2$coefficients["(Intercept)"]
slope_value = lm_result2$coefficients["Midparent"]
# Plot the points
plot(x=jitter(heights2$Midparent), y=jitter(heights2$child_minus_1to1), xlim=xlims, xlab="Midparent heights", ylab="Child heights minus 1:1 line", main="Relationship after subtracting 1:1 line")
# Add the regression line
abline(a=intercept_value, b=slope_value, col="blue", lwd=2, lty="dashed")
# Add the expected line if the relationship was 1:1
abline(a=0, b=0, col="darkgreen", lwd=2, lty="dashed")
# Yep, the relationship is definitely different than 1:1
# Why is the relationship between parent height and offspring
# height LESS THAN 1:1???
#
# Why do tall parents tend to produce offspring shorter
# than themselves? Why does height seem to "regress"?
# What about the children of short parents? Do they
# 'regress'?
#
# What are possible statistical consequences/hazards of this?
#
# Why is all of this rarely explained when regression
# is taught?
#
```