# 611 Highlights in R (Part II)

611 Highlights in R (Part II)

The raw .R file is here and the Rmd file is here.

# Brief ‘Hello’ to R Markdown

Let me first introduce you to R markdown and kitr. This format allows you to integrate your analyses with text that can be automatically translated to html, word, and pdf formats. I just produced a supplementary materials document using this and it probably saved me a ridiculous number of hours. It’s easy to get started:

1. Save your file with extension .Rmd.
2. Place something like the following in the very top of your file:

---
author: John Flournoy
title: 611 Highlights in R (Part II)
output: html_document
---
3. Write as you normally would, using Markdown syntax for formatting. For example:

# This is a big heading

1. this is
2. a numbered list

- this is a bulleted list
- With **bold** and *italic*  text
4. When you want to throw in some R code, place it inside an R chunk by wrapping it in {r} at the beginning and  at the end. When you do, it comes out something like this:

# From Rose's presentation:
# a toy data set for us to work with
n <- 100
gender <- as.factor(c(rep("M", n/2), rep("F", n/2)))
IQ <- rnorm(n, mean=100, sd=15)
degree <- rep(c("HS", "BA", "MS", "PhD"), n/4)
height <- as.numeric(gender)-2 + rnorm(n, mean=5.5, sd=1)
RT1 <- rchisq(n, 4)
RT2 <- rchisq(n, 4)
DV <- 50 - 5*(as.numeric(gender)-1) + .1*IQ + rnorm(n)

df <- data.frame(awesome=DV, gender=gender, IQ=IQ, degree=degree, height=height, RT1=RT1, RT2=RT2)
head(df)
##    awesome gender        IQ degree   height      RT1      RT2
## 1 52.89486      M  79.40263     HS 6.292706 1.761990 2.228117
## 2 57.04782      M  96.31289     BA 4.759042 2.236027 7.363253
## 3 55.59594      M 104.95331     MS 5.560292 5.159114 7.126281
## 4 55.44397      M  84.23347    PhD 5.354595 7.652900 2.836956
## 5 55.45191      M 107.38754     HS 4.523997 7.768904 4.504664
## 6 54.70468      M 110.07096     BA 6.139368 7.786462 7.508488

Notice that in 4, the we see the output of the command head(df). This is useful for outputting tables and plots, as we’ll see.

Here are more resources on

# Streamlined Data Workflow with dplyr

Make sure you have the package (library(dplyr)), and if you don’t, install it (install.packages('dplyr')). Here’s an intro to dplyr straight from the horse’s (Hadley’s) mouth.

By way of data manipulation that I’m actually using for a real project, this tutorial will introduce you to

• %>%
• a function chaining operator
• mutate and transmute
• adds new variables and preserves existing (transmute drops existing variables)
• mutate_each
• adds new variables, applying functions in funs(...) to each column
• group_by
• groups data set according to some variable (e.g., gender) – other dplyr operations will be done on groups
• summarise
• summarizes multiple values to a single value
• left_join
• joins two data frames, returning all rows from x, and all columns from x and y
• select
• keeps the variables/columns that you mention (see ?select for special functions that help you select variables)
• filter
• returns rows with matching conditions (similar to selecting columns like: aDataFrame[variable == value,])
• group_by
• groups data set according to some variable (e.g., gender) – other dplyr operations will be done on groups
• summarise
• summarizes multiple values to a single value
• do
• use do to perform arbitrary computation, returning either a data frame or arbitrary objects which will be stored in a list (e.g., run the same lm or t.test separately for each gender, country)

# Biased and unbiased estimates

(This was really little more than an excuse to get me to learn a little about Markdown in R. I have been toying with the idea of trying to move the 302 labs away from SPSS and into R. One such advantage could be the relative ease of employing simulations in R to to illustrate some of the concepts that students often report as challenging. The distinction between biased and unbiased estimates was something that students questioned me on last week, so it’s what I’ve tried to walk through here.)

In 302, we teach students that sample means provide an unbiased estimate of population means. Of course, this doesn’t mean that sample means are PERFECT estimates of population means. We should expect that the mean of any sample, no matter how representative, will differ a bit from the mean of the population from which it was drawn. This is sampling error. We say the sample mean is an unbiased estimate because it doesn’t differ systemmatically from the population mean–samples with means greater than the population mean are as likely as samples with means smaller than the population mean.

Let’s simulate this.

### Creating a population

First, we need to create a population of scores. Let’s use IQ scores as an example. Here we’ll draw a million scores from a normal distribution with a mean of 100 and a standard deviation of 15. We’ll plot it as a histogram to show that everything is nice and normal.

# Define a few settings for our work today
popMean = 100; # The mean of our population
popSD = 15; # The standard deviation of our population
sampSize = 30; # The size of the samples we'll draw from the population

population <- rnorm(1000000, mean = popMean, sd = popSD)
hist(population)


Just to double check and make sure that R is doing its thing like it should, we can check some descriptive statistics for this population. If things have worked, these values should be pretty darn close to μ = 100 and σ = 15.

mean(population)
## [1] 100.0175
sd(population)
## [1] 14.99739

Yep.

### Sample means are unbiased estimates of population means

Now, we need to create a sampling distribution. We will draw a sample from this population and find its mean. Then, we do that same thing over and over again a whole mess ’a times. This distribution of sample means is a sampling distribution.

Let’s give it a whirl. We’ll start with a little snippet that just gives us a single sample of 30 participants, using random sampling with replacement. When we take a peek at its mean, we should find that it is pretty darn close to 100, but with a little sampling error.

sampChamp <- sample(population, sampSize, replace=TRUE)
mean(sampChamp)
## [1] 96.36024

A quick aside: Just how close should it be to the population mean? Well, the expected deviation between any sample mean and the population mean is estimated by the standard error: σ2M = σ / √(n). So, in this case, we’d have a σ2M = 15 / √30 = 2.7386128

Let’s return to our simulation. We’ll now draw a whole bunch of samples and enter their means into a sampling distribution.

sampDist <- replicate(10000,mean(sample(population, sampSize, replace=TRUE)))
hist(sampDist)

Let’s get a few descriptive statistics here, too.

mean(sampDist)
## [1] 99.96665
sd(sampDist)
## [1] 2.743161

Note that the mean of the sampling distribution is a pretty darn good match for the original population mean. So, looky there, the sample mean is an unbaised estimator! Replications of the sampling procedure yield means that are just as likely to be above the population mean as below (in a symmetrical distribution like this, the mean and median are pretty much the same. If you’re interested, the actual value for the median is 99.950235. Also: The standard deviation of the sampling distribution is the standard error, so we see a pretty good match between the SD here (2.7431614) and the standard error calculated earlier (2.7386128).

### Uncorrected sample standard deviations are biased estimates of population standard deviations

Okay, let’s put together a different sampling distribution. Rather than collecting means from each sample we’ll collect uncorrected sample standard deviations. This is the square root of the sample variance, where the sample variance is the sum of the squared deviations from the mean divided by the sample size (SS/n).

R uses the corrected sample standard devaition (and variance), by default. So I use some cheap tricks to get it to give me the uncorrected standard deviation.

sdDist <- replicate(10000,(((sqrt(var(sample(population, sampSize, replace=TRUE)))*(sampSize-1))/(sampSize))))
hist(sdDist)

Let’s grab a mean of this sampling distribution of standard deviations.

mean(sdDist)
## [1] 14.35129

Notice that it is an underestimate of the population variance. The deviation between this estimate (14.3512925) and the true population standard deviation (15) is 0.6487075. Uncorrected sample standard deviations are systemmatically smaller than the population standard deviations that we intend them to estimate.

Now, let’s try it again with the corrected sample standard deviation.

sdDist_2 <- replicate(10000,sd(sample(population, sampSize, replace=TRUE)))
hist(sdDist_2)

And its mean.

mean(sdDist_2)
## [1] 14.88884

Here, the deviation between the estimate from the sample(14.8888407) and the true population standard deviation (15) is reduced to 0.1111593. Sample standard deviations are less systemmatically underrepresenting the population standard deviation.

# A Catty Intro to R

The website R for cats and cat lovers is further proof that R users have more fun (the voice of statistical reason asks: compared to what, though?).

Just look at this photo that appears at the beginning of the tutorial:

If you’re just getting started with R, you could do worse.

# Welcome to the wonderful world of R!

### Getting started

Slides on R basics (including installation):
www.ats.ucla.edu/stat/r/seminars/intro.htm (you may want to toggle the format using the button in the bottom right)

The way to learn R is by using it, so jump into some practice problems. You can use the “practice with datasets” code copied below, or download swirl and play around with that. Or both!

### Learning with Swirl

To install swirl, first install R if you haven’t already (see instructions in the slides above), and open it. In the command line, type
 install.packages("swirl")
and hit Enter. You need a working internet connection. Once R has installed the package, you also need to load it. Type
 library(swirl)
and hit Enter. Once you do that, swirl will take over and start giving you instructions (and peppy feedback!) to take you though the basics of R. Have fun!

### Practice with datasets

This is some code for you to work through to practice using datasets in R.

This coordinates (roughly) with the [Intro to R slides from UCLA](http://www.ats.ucla.edu/stat/r/seminars/intro.htm“>www.ats.ucla.edu/stat/r/seminars/intro.htm).

https://www.dropbox.com/s/cw5hrw62exn3lvx/rclub1_data1.txt
https://www.dropbox.com/s/zvw58hhel8bu3gh/rclub1_data2.sav

Make a note of where these data files get saved when you download them (your downloads folder, maybe? Or the desktop?). You’ll need to know where they are to be able to access them from R.

Note: this is meant to provide practice moving data in and out of R. suggested functions are provided, but you need to fill in the arguments, etc. For help on how to use the functions, enter ?function.name in the command window (e.g. ?read.table).

To save your work, I recommend copying your code into an R script and working from there. In R Studio, go to File > New File > R Script. In R, go to File > New Document. In either case, this will open up a blank text file. You can copy-paste this code there, and then fill in your answers as work through the problems. Any line of text that begins with # is a comment.

First, check out the file: open the file rclub1_data1.txt in a text editor or excel. you’ll see it’s tab-deliminated. now we want to bring it into R so we can use it. before we tell R which file to open, we need to know what folder R is currently set to look in (working directory). If you’re trying unsucessfully to open a file, the first thing you should check is that your wd is correct.

getwd()
## [1] "/Users/TARDIS/Dropbox/RClub/rclub_code"
# if necessary, change wd so it matches the folder where you've got your data files
setwd("/Users/TARDIS/Dropbox/RClub")

# we want to read in the data file, so first you need to learn about the appropriate function (read.table) so you know how to structure the command. You'll want to do this for each new function you use.

# now we can tell R to open the file, and save it as an object called df (short for dataframe). you could name it whatever you want, though. the name of the file ("rclub_data1.txt" must be in quotes, so R knows to look for a string matching that rather than to look for an existing object with that name).
df <- read.table("rclub1_data1.txt", header = T, sep = "\t")

# look at the first part of your dataframe, to eyeball the data.
head(df)
##   gender HowSmartTheyAre HowManyPointsTheyGot DidTheyEatBreakfast
## 1      M              95                    3                   Y
## 2      F              85                    3                   Y
## 3      F             114                    1                   Y
## 4      M             108                    2                   Y
## 5      M              98                    3                   Y
## 6      F              86                    3                   Y
# check the last chunk of the dataset, too, just because you're curious.
tail(df)
##    gender HowSmartTheyAre HowManyPointsTheyGot DidTheyEatBreakfast
## 45      F              87                    5                   N
## 46      M             108                    2                   N
## 47      F              91                    3                   N
## 48      M              95                    4                   N
## 49      F             112                    1                   N
## 50      F             104                    1                   N
# actually, let's look at it in a new window.
View(df)

# get basic information about your dataframe (dimensions, variable types, etc.)
dim(df)
## [1] 50  4
str(df)
## 'data.frame':    50 obs. of  4 variables:
##  $gender : Factor w/ 2 levels "F","M": 2 1 1 2 2 1 2 1 2 1 ... ##$ HowSmartTheyAre     : int  95 85 114 108 98 86 85 107 100 97 ...
##  $HowManyPointsTheyGot: int 3 3 1 2 3 3 3 5 2 3 ... ##$ DidTheyEatBreakfast : Factor w/ 2 levels "N","Y": 2 2 2 2 2 2 2 2 1 1 ...
# what are the variable names (column names)?
colnames(df)
## [1] "gender"               "HowSmartTheyAre"      "HowManyPointsTheyGot"
## [4] "DidTheyEatBreakfast"
# you don't like these column names. rename several of the variables.
colnames(df) <- c("gender", "IQ", "Score", "Breakfast?")

# rename just one variable: change "gender" to "male".
colnames(df)[1] <- "male"

# change the coding scheme for "male" from M/F to Y/N. Remeber that "male" is currently a factor variable. Use str() and View() to check how the coding scheme is applied when you change the levels of the variable.
levels(df$male) # check what they are originally first ## [1] "F" "M" levels(df$male) <- c("N","Y") # change them to what you want

# you notice a typo (the first subject should actually be female, not male). damn RAs and their sloppy data entry! edit just that cell.
df$male[1] <- "N" # save this dataframe in csv format, so you can open it in other software: # write.csv() # open that csv file back in R, because you're fickle. (note that you can also just use read.table to read csv files - they're actually the same function, just with different defaults) # read.csv() # and now save it again, but this time as tab-deliminated. or try using other deliminators, if you like (e.g spaces). # write.table() # open the file rclub1_data2.sav (an SPSS file). first, learn about read.spss: ?read.spss ## No documentation for 'read.spss' in specified packages and libraries: ## you could try '??read.spss' # if R can't find the function, use two ?'s to conduct a boarder search: ??read.spss #read.spss is in the package "foreign". do you have the foreign package attached already? sessionInfo() ## R version 3.0.2 (2013-09-25) ## Platform: x86_64-apple-darwin10.8.0 (64-bit) ## ## locale: ## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8 ## ## attached base packages: ## [1] stats graphics grDevices utils datasets methods base ## ## loaded via a namespace (and not attached): ## [1] digest_0.6.4 evaluate_0.5.5 formatR_0.10 htmltools_0.2.4 ## [5] knitr_1.6 rmarkdown_0.3.10 stringr_0.6.2 tools_3.0.2 # if not, load the foreign library. library(foreign) # now try ?read.spss again, then open the fie rclub1_data2.sav df <- read.spss("rclub1_data2.sav") ## Warning: rclub1_data2.sav: Unrecognized record type 7, subtype 18 ## encountered in system file ## re-encoding from latin1 # check out the dataframe to see what variables you have, how many cases you have, etc. You can use the same functions you used before. # add a new column on the end with average test score by taking the mean of each person's scores for the three tests df$TestAve <- (df$Test1 + df$Test2 + df\$Test3)/3