Assignment2_2502026873
2502026873_Jasmine Mutia Alifa
2022-06-02
Exploratory Data Analysis
Libraries and Data
library(readr)## Warning: package 'readr' was built under R version 4.1.3library(dplyr)## Warning: package 'dplyr' was built under R version 4.1.3##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)## Warning: package 'ggplot2' was built under R version 4.1.3library(openintro)## Warning: package 'openintro' was built under R version 4.1.3## Loading required package: airports## Warning: package 'airports' was built under R version 4.1.3## Loading required package: cherryblossom## Warning: package 'cherryblossom' was built under R version 4.1.3## Loading required package: usdata## Warning: package 'usdata' was built under R version 4.1.3library(gapminder)## Warning: package 'gapminder' was built under R version 4.1.3cars <- read.csv("https://assets.datacamp.com/production/course_1796/datasets/cars04.csv")
comics <- read.csv("https://assets.datacamp.com/production/course_1796/datasets/comics.csv")
life <- read.csv("https://assets.datacamp.com/production/course_1796/datasets/life_exp_raw.csv")Exploring Categorical Data
a. Bar chart expectations
Bar charts with categorical variables on the x axis and in the fill are a common way to see a contingency table visually.
It essentialy what you would get if you used the
tablefunction with two variablesWhich way you show the data can change the perception.
Which variable you use for the fill or the position of the bars (fill, dodge, stack) all can give different perceptions
b. Contingency table review
# Print the first rows of the data
head(comics)## name id align eye hair
## 1 Spider-Man (Peter Parker) Secret Good Hazel Eyes Brown Hair
## 2 Captain America (Steven Rogers) Public Good Blue Eyes White Hair
## 3 Wolverine (James \\"Logan\\" Howlett) Public Neutral Blue Eyes Black Hair
## 4 Iron Man (Anthony \\"Tony\\" Stark) Public Good Blue Eyes Black Hair
## 5 Thor (Thor Odinson) No Dual Good Blue Eyes Blond Hair
## 6 Benjamin Grimm (Earth-616) Public Good Blue Eyes No Hair
## gender gsm alive appearances first_appear publisher
## 1 Male <NA> Living Characters 4043 Aug-62 marvel
## 2 Male <NA> Living Characters 3360 Mar-41 marvel
## 3 Male <NA> Living Characters 3061 Oct-74 marvel
## 4 Male <NA> Living Characters 2961 Mar-63 marvel
## 5 Male <NA> Living Characters 2258 Nov-50 marvel
## 6 Male <NA> Living Characters 2255 Nov-61 marvelExplanation : Dari dataset comics,
dapat dilihat bahwa ada 11 variables dengan tipe data yang berbeda.
Variabel appearances memiliki tipe data integer, sedangkan
10 variables lainnnya memiliki tipe data character. Selain itu, data
teratas pada variable gsm merupakan missing value.
comics$align <- as.factor(comics$align)
# Check levels of align
levels(comics$align)## [1] "Bad" "Good" "Neutral"
## [4] "Reformed Criminals"Explanation : Variable align pada
dataset comics, memiliki tipe data char, lalu diubah ke
factor untuk mengetahui levels pada variable nya. Ada 4 levels pada
variabel align yaitu Bad, Good, Neutral, dan Reformed
Criminals.
comics$gender <- as.factor(comics$gender)
# Check the levels of gender
levels(comics$gender)## [1] "Female" "Male" "Other"Explanation : Variable gender pada
dataset comics, memiliki tipe data char, lalu diubah ke
factor untuk mengetahui levels pada variable nya. Terdapat 3 levels pada
variabel gender yaitu Female, Male, dan Other.
# Create a 2-way contingency table
table(comics$align, comics$gender)##
## Female Male Other
## Bad 1573 7561 32
## Good 2490 4809 17
## Neutral 836 1799 17
## Reformed Criminals 1 2 0Explanation : Dengan menggunaka function
table, dapat dibuat tabel kontigensi 2 arah pada variable
align(sifat karakter) dan gender (jenis
kelamin). Berdasarkan tabel, dapat dilihat bahwa Male
(pria) pada dataset comics lebih banyak memerankan karakter
Bad, Good, Neutral, maupun Reformed Criminals dibandingkan
Female (perempuan). Selain pria dan wanita, kategori
Other paling sedikit memainkan keempat peran yang ada pada
dataset comics.
Dropping Levels
# Load dplyr
# Print tab
tab <- table(comics$align, comics$gender)
tab##
## Female Male Other
## Bad 1573 7561 32
## Good 2490 4809 17
## Neutral 836 1799 17
## Reformed Criminals 1 2 0# Remove align level
comics <- comics %>%
filter(align != 'Reformed Criminals') %>%
droplevels()
levels(comics$align)## [1] "Bad" "Good" "Neutral"Explanation : Salah satu level pada variable
align dihapus, yaitu Reformed Criminals. Dilakukan
penghapusan karena data nya tidak terlalu banyak sehingga saat dihapus
tidak terlalu mempengaruhi proses analisis selanjutnya.
Side-by-side Barcharts
# Load ggplot2
# Create side-by-side barchart of gender by alignment
ggplot(comics, aes(x = align, fill = gender)) +
geom_bar(position = "dodge")
Explanation : Diagram diatas menunjukkan keterkaitan
antara variable align dan gender, menunjukkan
jumlah gender yang memerankan sifat karakter (Bad, Good,
Neutral) pada dataset comics. Tidak ada level Reformed
Criminals pada visualisasi align karena sudah dihapus.
# Create side-by-side barchart of alignment by gender
ggplot(comics, aes(x = gender, fill = align)) +
geom_bar(positio = "dodge") +
theme(axis.text.x = element_text(angle = 90))
Explanation : Diagram diatas menunjukkan keterkaitan
antara variable gender dan align, menunjukkan
gender (Female, Male, Other, dan missing value) yang
memerankan sifat karakter (Bad, Good, Neutral) pada dataset
comics.
Bar chart interpretation
Among characters with “Neutral” alignment, males are the most common.
In general, there is an association between gender and alignment.
There are more male characters than female characters in this dataset.
Counts vs. proportions
# simplify display format
options(scipen = 999, digits = 3)
## create table of counts
tbl_cnt <- table(comics$id, comics$align)
tbl_cnt##
## Bad Good Neutral
## No Dual 474 647 390
## Public 2172 2930 965
## Secret 4493 2475 959
## Unknown 7 0 2Explanation : Dari hasil table diatas, karakter
Bad biasanya memiliki identitas yang secret
(rahasia). Sedangkan karakter Good biasanya memiliki
identitas bersifat public (tidak rahasia / umum). Selain
itu, karater Neutral biasanya banyak bersifat umum. Semua
karakter paling sedikit bersifat unknown (tidak
diketahui).
# Proportional table
# All values add up to 1
prop.table(tbl_cnt)##
## Bad Good Neutral
## No Dual 0.030553 0.041704 0.025139
## Public 0.140003 0.188862 0.062202
## Secret 0.289609 0.159533 0.061815
## Unknown 0.000451 0.000000 0.000129Explanation : Dari table diatas, terlihat persentase
dari karakter Bad, Good, dan
Neutral. Karakter Bad biasanya bersifat
rahasia, dilihat dari persentasenya yang bernilai 28%. Karakter
Good biasanya bersifat tidak rahasia (umum), dengan
persentase 18%. Sedangkan karakter Neutral biasanya
bersifat tidak rahasia (umum).
sum(prop.table(tbl_cnt))## [1] 1Explanation : Output diatas menunjukkan hasil
penjumlahan semua nilai pada table tbl_cnt yaitu 1.
# All rows add up to 1
prop.table(tbl_cnt, 1)##
## Bad Good Neutral
## No Dual 0.314 0.428 0.258
## Public 0.358 0.483 0.159
## Secret 0.567 0.312 0.121
## Unknown 0.778 0.000 0.222Explanation : Table diatas menunjukkan nilai proportion berdasakan penjumlahan baris.
# Coluns add up to 1
prop.table(tbl_cnt, 2)##
## Bad Good Neutral
## No Dual 0.066331 0.106907 0.168394
## Public 0.303946 0.484137 0.416667
## Secret 0.628743 0.408956 0.414076
## Unknown 0.000980 0.000000 0.000864Explanation : Table diatas menunjukkan nilai proportion berdasakan penjumlahan kolom.
Look at the proportion of bad characters in the secret and unknown groups
Note there are very few characters with id = unknown
ggplot(comics, aes(x = id, fill = align)) +
geom_bar(position = "fill") +
ylab("proportion")
Explanation : Visualisasi table diatas menunjukkan nilai proporsi (secara desimal/persentase) antara identitas karakter (No Dual, Public, Secret, Unknown) dengan sifat karakter(Bad, Good, Neutral). Selain itu, tabel diatas juga menunjukkan nilai proporsi dari missing value yang terdeteksi. Warna pada visualisasi diatas juga menunjukkan perbedaan sifat karakter yang ada.
Swap the x and fill variables. Notice the most bad cahracters are secret (not unknown).
Here you can see more clearly that there are very few characters at all with id = unknown
ggplot(comics, aes(x = align, fill = id)) +
geom_bar(position = "fill") +
ylab("proportion")
Explanation : Visualisasi table diatas menunjukkan nilai proporsi (secara desimal/persentase) antara sifat karakter (Bad, Good, Neutral) pada sumbu-x dengan identitas karakter pada sumbu-y (No Dual, Public, Secret, Unknown). Warna pada visualisasi diatas juga menunjukkan perbedaan identitas karakter yang ada.
Conditional proportions
tab <- table(comics$align, comics$gender)
options(scipen = 999, digits = 3) # Print fewer digits
prop.table(tab) # Joint proportions##
## Female Male Other
## Bad 0.082210 0.395160 0.001672
## Good 0.130135 0.251333 0.000888
## Neutral 0.043692 0.094021 0.000888Explanation : Output diatas menunjukkan nilai proporsi antara sifat dan identitas karakter
prop.table(tab, 2)##
## Female Male Other
## Bad 0.321 0.534 0.485
## Good 0.508 0.339 0.258
## Neutral 0.171 0.127 0.258Approximately what proportion of all female characters are good?
- 51%
Counts vs. proportions (2)
# Plot of gender by align
ggplot(comics, aes(x = align, fill = gender)) +
geom_bar()
# Plot proportion of gender, conditional on align
ggplot(comics, aes(x = align, fill = gender)) +
geom_bar(position = "fill")
Distribution of one variable
# Can use table function on just one variable
# This is called a marginal distribution
table(comics$id)##
## No Dual Public Secret Unknown
## 1511 6067 7927 9# Simple barchart
ggplot(comics, aes(x = id)) +
geom_bar()
You can also facet to see variables indidually
A little easier than filtering each and plotting.
This is a rearrangement of the bar chart we plotted earlier
We facte by alignment rather then coloring the stack.
This can make it a little easier to answer some questions.
ggplot(comics, aes(x = id)) +
geom_bar() +
facet_wrap(~align)
Marginal Barchart
It makes more sense to put neutral between Bad and Good
We need to reorder the levels so it will chart this way
Otherwise it will defult to alphabetical
# Change the order of the levels in align
comics$align <- factor(comics$align,
levels = c("Bad", "Neutral", "Good"))
# Create plot of align
ggplot(comics, aes(x = align)) +
geom_bar()
Conditional Barchart
# Plot of alignment broken down by gender
ggplot(comics, aes(x = align)) +
geom_bar() +
facet_wrap(~ gender)
c. Improve Piechart
pies <- data.frame(flavors = as.factor(rep(c("apple", "blueberry", "boston creme", "cherry", "key lime", "pumpkin", "strawberry"), times = c(17, 14, 15, 13, 16, 12, 11))))
# Put levels of flavor in descending order
lev <- c("apple", "key lime", "boston creme", "blueberry", "cherry", "pumpkin", "strawberry")
pies$flavor <- factor(pies$flavor, levels = lev)# Create barchart of flavor
ggplot(pies, aes(x = flavor)) +
geom_bar(fill = "chartreuse") +
theme(axis.text.x = element_text(angle = 90))
Exploring Numerical Data
# A dot plot shows all the datapoints
ggplot(cars, aes(x = weight)) +
geom_dotplot(dotsize = 0.4)## Bin width defaults to 1/30 of the range of the data. Pick better value with `binwidth`.## Warning: Removed 2 rows containing non-finite values (stat_bindot).
# A histogram groups the points into bins so it does not get overwhelming
ggplot(cars, aes(x = weight)) +
geom_histogram(dotsize = 0.4, binwidth = 500)## Warning: Ignoring unknown parameters: dotsize## Warning: Removed 2 rows containing non-finite values (stat_bin).
# A density plot gives a bigger picture representation of the distribution
# It more helpful when there is a lot of data
ggplot(cars, aes(x = weight)) +
geom_density()## Warning: Removed 2 rows containing non-finite values (stat_density).
# A boxplot is a good way to just show the summary info of the distriubtion
ggplot(cars, aes(x = 1, y = weight)) +
geom_boxplot() +
coord_flip()## Warning: Removed 2 rows containing non-finite values (stat_boxplot).
a. Faceted histogram
# Load package
library(ggplot2)
# Learn data structure
str(cars)## 'data.frame': 428 obs. of 19 variables:
## $ name : chr "Chevrolet Aveo 4dr" "Chevrolet Aveo LS 4dr hatch" "Chevrolet Cavalier 2dr" "Chevrolet Cavalier 4dr" ...
## $ sports_car : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ suv : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ wagon : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ minivan : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ pickup : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ all_wheel : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ rear_wheel : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ msrp : int 11690 12585 14610 14810 16385 13670 15040 13270 13730 15460 ...
## $ dealer_cost: int 10965 11802 13697 13884 15357 12849 14086 12482 12906 14496 ...
## $ eng_size : num 1.6 1.6 2.2 2.2 2.2 2 2 2 2 2 ...
## $ ncyl : int 4 4 4 4 4 4 4 4 4 4 ...
## $ horsepwr : int 103 103 140 140 140 132 132 130 110 130 ...
## $ city_mpg : int 28 28 26 26 26 29 29 26 27 26 ...
## $ hwy_mpg : int 34 34 37 37 37 36 36 33 36 33 ...
## $ weight : int 2370 2348 2617 2676 2617 2581 2626 2612 2606 2606 ...
## $ wheel_base : int 98 98 104 104 104 105 105 103 103 103 ...
## $ length : int 167 153 183 183 183 174 174 168 168 168 ...
## $ width : int 66 66 69 68 69 67 67 67 67 67 ...# Create faceted histogram
ggplot(cars, aes(x = city_mpg)) +
geom_histogram() +
facet_wrap(~ suv) ## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 14 rows containing non-finite values (stat_bin).
b. Boxplots and Density Plots
unique(cars$ncyl)## [1] 4 6 3 8 5 12 10 -1table(cars$ncyl)##
## -1 3 4 5 6 8 10 12
## 2 1 136 7 190 87 2 3# Filter cars with 4, 6, 8 cylinders
common_cyl <- filter(cars, ncyl %in% c(4,6,8))
# Create box plots of city mpg by ncyl
ggplot(common_cyl, aes(x = as.factor(ncyl), y = city_mpg)) +
geom_boxplot()## Warning: Removed 11 rows containing non-finite values (stat_boxplot).
# Create overlaid density plots for same data
ggplot(common_cyl, aes(x = city_mpg, fill = as.factor(ncyl))) +
geom_density(alpha = .3)## Warning: Removed 11 rows containing non-finite values (stat_density).
Compare distribution via plots
The highest mileage cars have 4 cylinders.
The typical 4 cylinder car gets better mileage than the typical 6 cylinder car, which gets better mileage than the typical 8 cylinder car.
Most of the 4 cylinder cars get better mileage than even the most efficient 8 cylinder cars.
Distribution of One Variable
a. Marginal and conditional histograms
# Create hist of horsepwr
cars %>%
ggplot(aes(horsepwr)) +
geom_histogram() +
ggtitle("Horsepower distribution")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# Create hist of horsepwr for affordable cars
cars %>%
filter(msrp < 25000) %>%
ggplot(aes(horsepwr)) +
geom_histogram() +
xlim(c(90, 550)) +
ggtitle("Horsepower distribtion for msrp < 25000")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 1 rows containing non-finite values (stat_bin).## Warning: Removed 2 rows containing missing values (geom_bar).
Marginal and conditional histograms interpretation
- The highest horsepower car in the less expensive range has just under 250 horsepower.
b. Three binwidths
# Create hist of horsepwr with binwidth of 3
cars %>%
ggplot(aes(horsepwr)) +
geom_histogram(binwidth = 3) +
ggtitle("binwidth = 3")
# Create hist of horsepwr with binwidth of 30
cars %>%
ggplot(aes(horsepwr)) +
geom_histogram(binwidth = 30) +
ggtitle("binwidth = 30")
# Create hist of horsepwr with binwidth of 60
cars %>%
ggplot(aes(horsepwr)) +
geom_histogram(binwidth = 60) +
ggtitle("binwidth = 60")
Box plots
a. Box plots for outliers
# Construct box plot of msrp
cars %>%
ggplot(aes(x = 1, y = msrp)) +
geom_boxplot()
# Exclude outliers from data
cars_no_out <- cars %>%
filter(msrp < 100000)
# Construct box plot of msrp using the reduced dataset
cars_no_out %>%
ggplot(aes(x = 1, y = msrp)) +
geom_boxplot()
b. Plot selection
# Create plot of city_mpg
cars %>%
ggplot(aes(x = 1, y = city_mpg)) +
geom_boxplot()## Warning: Removed 14 rows containing non-finite values (stat_boxplot).
cars %>%
ggplot(aes(city_mpg)) +
geom_density()## Warning: Removed 14 rows containing non-finite values (stat_density).
# Create plot of width
cars %>%
ggplot(aes(x = 1, y = width)) +
geom_boxplot()## Warning: Removed 28 rows containing non-finite values (stat_boxplot).
cars %>%
ggplot(aes(x = width)) +
geom_density()## Warning: Removed 28 rows containing non-finite values (stat_density).
Visualization in higher dimensions
3 variable plot
# Facet hists using hwy mileage and ncyl
common_cyl %>%
ggplot(aes(x = hwy_mpg)) +
geom_histogram() +
facet_grid(ncyl ~ suv) +
ggtitle("hwy_mpg by ncyl and suv")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 11 rows containing non-finite values (stat_bin).
Interpret 3 var plot
- Across both SUVs and non-SUVs, mileage tends to decrease as the number of cylinders increases.
Numerical Summaries
Measures of center
What is a
typicalvalue for life expectancy?We will look at just a few data points here
And just the females
head(life)## State County fips Year Female.life.expectancy..years.
## 1 Alabama Autauga County 1001 1985 77.0
## 2 Alabama Baldwin County 1003 1985 78.8
## 3 Alabama Barbour County 1005 1985 76.0
## 4 Alabama Bibb County 1007 1985 76.6
## 5 Alabama Blount County 1009 1985 78.9
## 6 Alabama Bullock County 1011 1985 75.1
## Female.life.expectancy..national..years.
## 1 77.8
## 2 77.8
## 3 77.8
## 4 77.8
## 5 77.8
## 6 77.8
## Female.life.expectancy..state..years. Male.life.expectancy..years.
## 1 76.9 68.1
## 2 76.9 71.1
## 3 76.9 66.8
## 4 76.9 67.3
## 5 76.9 70.6
## 6 76.9 66.6
## Male.life.expectancy..national..years. Male.life.expectancy..state..years.
## 1 70.8 69.1
## 2 70.8 69.1
## 3 70.8 69.1
## 4 70.8 69.1
## 5 70.8 69.1
## 6 70.8 69.1x <- head(round(life$Female.life.expectancy..years.), 11)
x## [1] 77 79 76 77 79 75 77 77 77 78 77mean
balance point of the data
sensitive to extreme values
sum(x)/11## [1] 77.2mean(x)## [1] 77.2median
middle value of the data
robust to extreme values
most approrpriate measure when working with skewed data
sort(x)## [1] 75 76 77 77 77 77 77 77 78 79 79median(x)## [1] 77mode
- most common value
table(x)## x
## 75 76 77 78 79
## 1 1 6 1 2a. Calculate center measures
str(gapminder)## tibble [1,704 x 6] (S3: tbl_df/tbl/data.frame)
## $ country : Factor w/ 142 levels "Afghanistan",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ continent: Factor w/ 5 levels "Africa","Americas",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ year : int [1:1704] 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 ...
## $ lifeExp : num [1:1704] 28.8 30.3 32 34 36.1 ...
## $ pop : int [1:1704] 8425333 9240934 10267083 11537966 13079460 14880372 12881816 13867957 16317921 22227415 ...
## $ gdpPercap: num [1:1704] 779 821 853 836 740 ...# Create dataset of 2007 data
gap2007 <- filter(gapminder, year == 2007)
# Compute groupwise mean and median lifeExp
gap2007 %>%
group_by(continent) %>%
summarize(mean(lifeExp),
median(lifeExp))## # A tibble: 5 x 3
## continent `mean(lifeExp)` `median(lifeExp)`
## <fct> <dbl> <dbl>
## 1 Africa 54.8 52.9
## 2 Americas 73.6 72.9
## 3 Asia 70.7 72.4
## 4 Europe 77.6 78.6
## 5 Oceania 80.7 80.7# Generate box plots of lifeExp for each continent
gap2007 %>%
ggplot(aes(x = continent, y = lifeExp)) +
geom_boxplot()
Measures of variability
We want to know ‘How much is the data spread out from the middle?’
Just looking at the data gives us a sense of this
- But we want break it down to one number so we can compare sample distributions
x## [1] 77 79 76 77 79 75 77 77 77 78 77# Look at the difference between each point and the mean
sum(x - mean(x))## [1] -0.0000000000000568So we can square the difference
But this number will keep getting bigger as you add more observations
We want something that is stable
# Square each difference to get rid of negatives then sum
sum((x - mean(x))^2)## [1] 13.6Variance
so we divide by n - 1
This is called the sample variance. One of the most useful measures of a sample distribution
sum((x - mean(x))^2)/(length(x) - 1)## [1] 1.36var(x)## [1] 1.36Standard Deviation
Another very useful metric is the sample standard deviation
This is just the square root of the variance
The nice thing about the std dev is that it is in the same units as the original data
In this case its 1.17 years
sqrt(sum((x - mean(x))^2)/(length(x) - 1))## [1] 1.17sd(x)## [1] 1.17Inter Quartile Range
The IQR is the middle 50% of the data
The nice thing about this one is that it is not sensitve to extreme values
All of the other measures listed here are sensitive to extreme values
summary(x)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 75.0 77.0 77.0 77.2 77.5 79.0IQR(x)## [1] 0.5Range
max and min are also interesting
as is the range, or the difference between max and min
max(x)## [1] 79min(x)## [1] 75diff(range(x))## [1] 4b. Calculate spread measures
str(gap2007)## tibble [142 x 6] (S3: tbl_df/tbl/data.frame)
## $ country : Factor w/ 142 levels "Afghanistan",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ continent: Factor w/ 5 levels "Africa","Americas",..: 3 4 1 1 2 5 4 3 3 4 ...
## $ year : int [1:142] 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 ...
## $ lifeExp : num [1:142] 43.8 76.4 72.3 42.7 75.3 ...
## $ pop : int [1:142] 31889923 3600523 33333216 12420476 40301927 20434176 8199783 708573 150448339 10392226 ...
## $ gdpPercap: num [1:142] 975 5937 6223 4797 12779 ...# Compute groupwise measures of spread
gap2007 %>%
group_by(continent) %>%
summarize(sd(lifeExp),
IQR(lifeExp),
n())## # A tibble: 5 x 4
## continent `sd(lifeExp)` `IQR(lifeExp)` `n()`
## <fct> <dbl> <dbl> <int>
## 1 Africa 9.63 11.6 52
## 2 Americas 4.44 4.63 25
## 3 Asia 7.96 10.2 33
## 4 Europe 2.98 4.78 30
## 5 Oceania 0.729 0.516 2# Generate overlaid density plots
gap2007 %>%
ggplot(aes(x = lifeExp, fill = continent)) +
geom_density(alpha = 0.3)
c. Choose measures for center and spread
# Compute stats for lifeExp in Americas
head(gap2007)## # A tibble: 6 x 6
## country continent year lifeExp pop gdpPercap
## <fct> <fct> <int> <dbl> <int> <dbl>
## 1 Afghanistan Asia 2007 43.8 31889923 975.
## 2 Albania Europe 2007 76.4 3600523 5937.
## 3 Algeria Africa 2007 72.3 33333216 6223.
## 4 Angola Africa 2007 42.7 12420476 4797.
## 5 Argentina Americas 2007 75.3 40301927 12779.
## 6 Australia Oceania 2007 81.2 20434176 34435.gap2007 %>%
filter(continent == "Americas") %>%
summarize(mean(lifeExp),
sd(lifeExp))## # A tibble: 1 x 2
## `mean(lifeExp)` `sd(lifeExp)`
## <dbl> <dbl>
## 1 73.6 4.44# Compute stats for population
gap2007 %>%
summarize(median(pop),
IQR(pop))## # A tibble: 1 x 2
## `median(pop)` `IQR(pop)`
## <dbl> <dbl>
## 1 10517531 26702008.Shape and transformations
4 chracteristics of a distribution that are of interest:
center
- already covered
spread or variablity
- already covered
shape
modality: number of prominent humps (uni, bi, multi, or uniform - no humps)
skew (right, left, or symetric)
Can transform to fix skew
outliers
a. Describe the shape
A: unimodal, left-skewed
B: unimodal, symmetric
C: unimodal, right-skewed
D: bimodal, symmetric
b. Transformations
# Create density plot of old variable
gap2007 %>%
ggplot(aes(x = pop)) +
geom_density()
# Transform the skewed pop variable
gap2007 <- gap2007 %>%
mutate(log_pop = log(pop))
# Create density plot of new variable
gap2007 %>%
ggplot(aes(x = log_pop)) +
geom_density()
Outliers
a. Identify outliers
# Filter for Asia, add column indicating outliers
str(gapminder)## tibble [1,704 x 6] (S3: tbl_df/tbl/data.frame)
## $ country : Factor w/ 142 levels "Afghanistan",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ continent: Factor w/ 5 levels "Africa","Americas",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ year : int [1:1704] 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 ...
## $ lifeExp : num [1:1704] 28.8 30.3 32 34 36.1 ...
## $ pop : int [1:1704] 8425333 9240934 10267083 11537966 13079460 14880372 12881816 13867957 16317921 22227415 ...
## $ gdpPercap: num [1:1704] 779 821 853 836 740 ...gap_asia <- gap2007 %>%
filter(continent == "Asia") %>%
mutate(is_outlier = lifeExp < 50)
# Remove outliers, create box plot of lifeExp
gap_asia %>%
filter(!is_outlier) %>%
ggplot(aes(x = 1, y = lifeExp)) +
geom_boxplot()
Case Study
Introducing the data
a. Spam and num_char
# ggplot2, dplyr, and openintro are loaded
# Compute summary statistics
email %>%
group_by(spam) %>%
summarize(
median(num_char),
IQR(num_char))## # A tibble: 2 x 3
## spam `median(num_char)` `IQR(num_char)`
## <fct> <dbl> <dbl>
## 1 0 6.83 13.6
## 2 1 1.05 2.82str(email)## tibble [3,921 x 21] (S3: tbl_df/tbl/data.frame)
## $ spam : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ to_multiple : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 2 2 1 1 ...
## $ from : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ cc : int [1:3921] 0 0 0 0 0 0 0 1 0 0 ...
## $ sent_email : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 2 2 1 1 ...
## $ time : POSIXct[1:3921], format: "2012-01-01 13:16:41" "2012-01-01 14:03:59" ...
## $ image : num [1:3921] 0 0 0 0 0 0 0 1 0 0 ...
## $ attach : num [1:3921] 0 0 0 0 0 0 0 1 0 0 ...
## $ dollar : num [1:3921] 0 0 4 0 0 0 0 0 0 0 ...
## $ winner : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
## $ inherit : num [1:3921] 0 0 1 0 0 0 0 0 0 0 ...
## $ viagra : num [1:3921] 0 0 0 0 0 0 0 0 0 0 ...
## $ password : num [1:3921] 0 0 0 0 2 2 0 0 0 0 ...
## $ num_char : num [1:3921] 11.37 10.5 7.77 13.26 1.23 ...
## $ line_breaks : int [1:3921] 202 202 192 255 29 25 193 237 69 68 ...
## $ format : Factor w/ 2 levels "0","1": 2 2 2 2 1 1 2 2 1 2 ...
## $ re_subj : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ exclaim_subj: num [1:3921] 0 0 0 0 0 0 0 0 0 0 ...
## $ urgent_subj : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ exclaim_mess: num [1:3921] 0 1 6 48 1 1 1 18 1 0 ...
## $ number : Factor w/ 3 levels "none","small",..: 3 2 2 2 1 1 3 2 2 2 ...table(email$spam)##
## 0 1
## 3554 367email <- email %>%
mutate(spam = factor(ifelse(spam == 0, "not-spam", "spam")))
# Create plot
email %>%
mutate(log_num_char = log(num_char)) %>%
ggplot(aes(x = spam, y = log_num_char)) +
geom_boxplot()
b. Spam and num_char interpretation
- The median length of not-spam emails is greater than that of spam emails
c. Spam and !!!
# Compute center and spread for exclaim_mess by spam
email %>%
group_by(spam) %>%
summarize(
median(exclaim_mess),
IQR(exclaim_mess)) ## # A tibble: 2 x 3
## spam `median(exclaim_mess)` `IQR(exclaim_mess)`
## <fct> <dbl> <dbl>
## 1 not-spam 1 5
## 2 spam 0 1table(email$exclaim_mess)##
## 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
## 1435 733 507 128 190 113 115 51 93 45 85 17 56 20 43 11
## 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
## 29 12 26 5 29 9 15 3 11 6 11 1 6 8 13 12
## 32 33 34 35 36 38 39 40 41 42 43 44 45 46 47 48
## 13 3 3 2 3 3 1 2 1 1 3 3 5 3 2 1
## 49 52 54 55 57 58 62 71 75 78 89 94 96 139 148 157
## 3 1 1 4 2 2 2 1 1 1 1 1 1 1 1 1
## 187 454 915 939 947 1197 1203 1209 1236
## 1 1 1 1 1 1 2 1 1# Create plot for spam and exclaim_mess
email %>%
mutate(log_exclaim_mess = log(exclaim_mess)) %>%
ggplot(aes(x = log_exclaim_mess)) +
geom_histogram() +
facet_wrap(~ spam)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 1435 rows containing non-finite values (stat_bin).
d. Spam and !!! interpretation
The most common value of exclaim_mess in both classes of email is zero (a log(exclaim_mess) of -4.6 after adding .01).
Even after a transformation, the distribution of exclaim_mess in both classes of email is right-skewed.
The typical number of exclamations in the not-spam group appears to be slightly higher than in the spam group.
Check-in 1
Zero inflation in the exclaim_mess variable
you can analyze the two part separatly
or turn it into a categorical variable of is-zero, not-zero
Could make a barchart
- need to decide if you are more interested in counts or proportions
a. Collapsing levels
table(email$image)##
## 0 1 2 3 4 5 9 20
## 3811 76 17 11 2 2 1 1# Create plot of proportion of spam by image
email %>%
mutate(has_image = image > 0) %>%
ggplot(aes(x = has_image, fill = spam)) +
geom_bar(position = "fill")
b. Image and spam interpretation
- An email without an image is more likely to be not-spam than spam
c. Data Integrity
# Test if images count as attachments
sum(email$image > email$attach)## [1] 0- There are no emails with more images than attachments so these most be counted as attachments also
d. Answering questions with chains
## Within non-spam emails, is the typical length of emails shorter for
## those that were sent to multiple people?
email %>%
filter(spam == "not-spam") %>%
group_by(to_multiple) %>%
summarize(median(num_char))## # A tibble: 2 x 2
## to_multiple `median(num_char)`
## <fct> <dbl>
## 1 0 7.20
## 2 1 5.36- Yes
# Question 1
## For emails containing the word "dollar", does the typical spam email
## contain a greater number of occurences of the word than the typical non-spam email?
table(email$dollar)##
## 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
## 3175 120 151 10 146 20 44 12 35 10 22 10 20 7 14 5
## 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32
## 23 2 14 1 10 7 12 7 7 3 7 1 5 1 1 2
## 34 36 40 44 46 48 54 63 64
## 1 2 3 3 2 1 1 1 3email %>%
filter(dollar > 0) %>%
group_by(spam) %>%
summarize(median(dollar))## # A tibble: 2 x 2
## spam `median(dollar)`
## <fct> <dbl>
## 1 not-spam 4
## 2 spam 2- No
# Question 2
## If you encounter an email with greater than 10 occurrences of the word "dollar",
## is it more likely to be spam or not -spam?
email %>%
filter(dollar > 10) %>%
ggplot(aes(x = spam)) +
geom_bar()
- Not-spam, at least in this dataset
Check-in 2
a. What’s in a number?
levels(email$number)## [1] "none" "small" "big"table(email$number)##
## none small big
## 549 2827 545# Reorder levels
email$number <- factor(email$number, levels = c("none","small","big"))
# Construct plot of number
ggplot(email, aes(x = number)) +
geom_bar() +
facet_wrap( ~ spam)
b. What’s in a number interpretation
Given that an email contains a small number, it is more likely to be not-spam.
Given that an email contains a big number, it is more likely to be not-spam.
Within both spam and not-spam, the most common number is a small one.
Note that the echo = FALSE parameter was added to the
code chunk to prevent printing of the R code that generated the
plot.