Libraries and Data

#source('create_datasets.R')

library(readr)

## Warning: package 'readr' was built under R version 4.1.3

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(ggplot2)
library(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 4.1.3

library(gapminder)

## Warning: package 'gapminder' was built under R version 4.1.3

cars <- 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

– 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 table function with two variables
Which 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

- 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    marvel

There are 11 attributes in this comics dataset: name, id, align, eye, hair, gender, gsm, alive, appearances, first appear, and publisher. Except for the appearances property, all of the attributes in this dataset are of the character data type.

#Check levels of align
comics$align = as.factor(comics$align)
levels(comics$align)

## [1] "Bad"                "Good"               "Neutral"           
## [4] "Reformed Criminals"

To examine the align attribute’s level, first convert the align attribute’s data type from character to factor. After inspecting the levels of the align attribute in the comic dataset, it is discovered that there are four levels: “Bad”, “Good”, “Neutral”, and “Reformed Criminals.”

#Check the levels of gender
comics$gender = as.factor(comics$gender)
levels(comics$gender)

## [1] "Female" "Male"   "Other"

To examine the gender attribute’s level, first convert the gender attribute’s data type from character to factor. After inspecting the levels of the gender attribute in the comic dataset, it is discovered that there are three levels: “Female”, “Male”,and “Reformed Criminals.”

#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     0

Contingency table is use to represent the total counts of observations that fall into each combination of the levels of categorical variables. 1. According to the result above, the most common or most prevalent category is gender “Male” with align “Bad” with the value 7561. 2. The lowest category is gender “Other” with align “Reformed Criminals” with a value of 0. 3. Gender “Female” and align “Bad” have a total of 1573 instances in this comics data, Gender “Female” and align “Good” have a total of 2490 instances in this comics data, and so on. 4. The gender attribute has a low contingency on the align attribute with the “Reformed Criminals” level.

- 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

The output above is the original contingency table between the align and gender attributes in the data.

# Remove align level
comics <- comics %>% filter(align != 'Reformed Criminals') %>% droplevels()

levels(comics$align)

## [1] "Bad"     "Good"    "Neutral"

The output above is the result of the remaining levels in the align attribute after we removed the reformed criminal level in the align attribute by using filter(align != ‘Reformed Criminals’) %>% droplevels().
Dropping levels can used to simplify our analysis.

- 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")

The output above is the outcome of the visualization of the contingency table that was created earlier, with the x representing the align property, which is filled with the gender attribute to make it easier to understand. 1. According to the result, align “Bad” and gender “Male” have the largest number when compared to other align and gender combinations.Then, followed by align “Good” with the gender “Male,” and finally, align “Neutral” with the gender “Male.”

Furthermore, when compared to other align and gender combinations, align “Good” and gender “Female” have the highest number. Then, followed by align “Bad” with the gender “Female,” and finally align “Neutral” with the gender “Female.”
Also, when compared to other align and gender combinations, align “Bad” and gender “NA” have the highest number. Then, followed by align “Good” with the gender “NA,” and finally, align “Neutral” with the gender “NA.”
The number between align and gender “Other” has the fewest others until the bar is no longer visible.

# 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))

The output above is the outcome of the preceding visualization of the contingency table, but it differs from the prior visualization, where the x that has the gender property now and its contains the align attribute’s values. But, for the explanation is the same as the previous visualization explanation.

- 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       2

The output above is a table of the number of cases based on id and align. 1. From the output above, which has the highest number of cases is id “Secret” with align “Bad”, followed by id “Public” with align “Good”. Then id “Secret” and align “Good”, and so on.

From the output above, which has the lowest number of cases is id “Unknown” with align “Good” with the value of 0.
The number of cases between id “Unknown” and all align’s attribute level is small, with a value less than 10.

# 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 0.000129

The output above is the proportion of all cases that fall into each category. 1. The largest single category is id “Secret” and align “Bad,” which stand for around 29% of id.

The smallest single category is id “Unknown” and align “Good,” which stand for 0% of id.

sum(prop.table(tbl_cnt))

## [1] 1

The result above shows that the total of all the proportions in the whole dataset is worth 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   0.222

Following that, conditional proportions are needed to determine the systematic relationship between variables such as the output above. 1. From the output above, it can be seen that about 57% of all “Secret” id(s) have “Bad” align.

# Columns 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 0.000864

We add 1 to each row to condition the id property. Instead, we add argument 2 to prop.table() to condition the column. 1. According to the result above, the proportion of align “Bad” whose ID is “hidden”Secret” is roughly 63 percent.

There are very few align(s) with id “Unknown”.

ggplot(comics, aes(x = id, fill = align)) + geom_bar(position = "fill") + ylab("proportion")

The proportion is visualized above to help you comprehend it. Above is a visualization with x as the id attribute filled with align attribute.

ggplot(comics, aes(x = align, fill = id)) + geom_bar(position = "fill") +ylab("proportion")

Above is a visualization with x as the align attribute filled with id attribute. 1. According to both visualization findings above, the id “Secret” has the worst alignment (align “Bad”). Id “No Dual” and Id “Public” have good alignment

From the output above, id “Unknown” only has “Bad” or “Neutral” align

- 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 0.000888

The output above is the proportion of all cases that fall into each category between align attribute and gender attribute.

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 0.258

From the output above, there are 51% proportion of all female characters are good.
The highest proportion are 53% that all male characters are Bad.
The lowest proportion are 13% that all male characters are Neutral.

– Counts vs. proportions (2)

# Plot of gender by align
ggplot(comics, aes(x = align, fill = gender)) + geom_bar()

The output above is the outcome of the visualization with the x representing the align attribute, which is filled with the gender attribute but with no position “fill”.

# Plot proportion of gender, conditional on align
ggplot(comics, aes(x = align, fill = gender)) + geom_bar(position = "fill")

The output above is the outcome of the visualization with the x representing the align attribute, which is filled with the gender attribute but with position “fill”. The result is the same but only the difference is that the bar is full or not with a different y value. If given the attribute position=“fill” the value on the y-axis will be decimal, but if not then vice versa.

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)

– 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 decending order
lev <- c("apple", "key lime", "boston creme", "blueberry", "cherry", "pumpkin", "strawberry")
pies$flavor <- factor(pies$flavor, levels = lev)

head(pies$flavor)

## [1] apple apple apple apple apple apple
## Levels: apple key lime boston creme blueberry cherry pumpkin strawberry

#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).

– 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).

- Boxplots and density plots

unique(cars$ncyl)

## [1]  4  6  3  8  5 12 10 -1

table(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

– 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. ### – 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

– 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()

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 typical value 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                                69.1

x <- head(round(life$Female.life.expectancy..years.), 11)
x

##  [1] 77 79 76 77 79 75 77 77 77 78 77

mean

balance point of the data
sensitive to extreme values

sum(x)/11

## [1] 77.2

mean(x)

## [1] 77.2

median

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 79

median(x)

## [1] 77

mode

most common value

table(x)

## x
## 75 76 77 78 79 
##  1  1  6  1  2

– 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 wnat 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

##  [1] 77 79 76 77 79 75 77 77 77 78 77

We could just take the differnce between all points and the mean and add it up
- But that would equal 0. Thats the idea of the mean.

# Look at the difference between each point and the mean
sum(x - mean(x))

## [1] -0.0000000000000568

So 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] 13.6

Variance

so we divide by n - 1
This is called the sample variance. One of the most useful measures of a sample distriution

sum((x - mean(x))^2)/(length(x) - 1)

## [1] 1.36

var(x)

## [1] 1.36

Standard 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] 1.17

sd(x)

## [1] 1.17

Inter 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    79.0

IQR(x)

## [1] 0.5

Range

max and min are also interesting
as is the range, or the difference between max and min

max(x)

## [1] 79

min(x)

## [1] 75

diff(range(x))

## [1] 4

– 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)

– 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 ## – Describe the shape There are 4 types of shape : - A: unimodal, left-skewed - B: unimodal, symmetric - C: unimodal, right-skewed - D: bimodal, symmetric

– 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

– 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

– Spam and num_char

# ggplot2, dplyr, and openintro are loaded
#library(openintro)
email = read.csv("D:/KULIAH SEMESTER 2/DATA MINING AND VISUALIZATION/1. FIN SESSION/email.csv")
email$spam <- factor(email$spam, labels = c("not-spam", "spam"))

# 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 not-spam               6.83           13.6 
## 2 spam                   1.05            2.82

str(email)

## 'data.frame':    3921 obs. of  21 variables:
##  $ spam        : Factor w/ 2 levels "not-spam","spam": 1 1 1 1 1 1 1 1 1 1 ...
##  $ to_multiple : int  0 0 0 0 0 0 1 1 0 0 ...
##  $ from        : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ cc          : int  0 0 0 0 0 0 0 1 0 0 ...
##  $ sent_email  : int  0 0 0 0 0 0 1 1 0 0 ...
##  $ time        : chr  "2012-01-01T06:16:41Z" "2012-01-01T07:03:59Z" "2012-01-01T16:00:32Z" "2012-01-01T09:09:49Z" ...
##  $ image       : int  0 0 0 0 0 0 0 1 0 0 ...
##  $ attach      : int  0 0 0 0 0 0 0 1 0 0 ...
##  $ dollar      : int  0 0 4 0 0 0 0 0 0 0 ...
##  $ winner      : chr  "no" "no" "no" "no" ...
##  $ inherit     : int  0 0 1 0 0 0 0 0 0 0 ...
##  $ viagra      : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ password    : int  0 0 0 0 2 2 0 0 0 0 ...
##  $ num_char    : num  11.37 10.5 7.77 13.26 1.23 ...
##  $ line_breaks : int  202 202 192 255 29 25 193 237 69 68 ...
##  $ format      : int  1 1 1 1 0 0 1 1 0 1 ...
##  $ re_subj     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ exclaim_subj: int  0 0 0 0 0 0 0 0 0 0 ...
##  $ urgent_subj : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ exclaim_mess: int  0 1 6 48 1 1 1 18 1 0 ...
##  $ number      : chr  "big" "small" "small" "small" ...

table(email$spam)

## 
## not-spam     spam 
##     3554      367

email = read.csv("D:/KULIAH SEMESTER 2/DATA MINING AND VISUALIZATION/1. FIN SESSION/email.csv")
email <- 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()

-Spam and num_char interpretation

-The median length of not-spam emails is greater than that of spam emails ## Spam and !!!

# Compute center and spread for exclaim_mess by spam
email = read.csv("D:/KULIAH SEMESTER 2/DATA MINING AND VISUALIZATION/1. FIN SESSION/email.csv")
email <- email %>% mutate(spam = factor(ifelse(spam == 0, "not-spam", "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                   1

table(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).

– 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 ## – 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")

– Image and spam interpretation

An email without an image is more likely to be not-spam than spam ## – 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

– 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)`
##         <int>              <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    3

email %>% 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

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

– What’s in a number?

email$number = as.factor(email$number)
levels(email$number)

## [1] "big"   "none"  "small"

table(email$number)

## 
##   big  none small 
##   545   549  2827

# 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)

– 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.

nnn

Gabrielle Felicia Ariyanto

2022-06-02

Libraries and Data

Exploring Categorical Data

– Bar chart expectations

- Contingency table review

- Dropping levels

- Side-by-side barcharts

- Bar chart interpretation

Counts vs. proportions

- Conditional proportions

– Counts vs. proportions (2)

Distribution of one variable

- Marginal barchart

- Conditional barchart

– Improve piechart

Exploring Numerical Data

– Faceted histogram

- Boxplots and density plots

– Compare distribution via plots

Distribution of one variable

– Marginal and conditional histograms

– Marginal and conditional histograms interpretation

Box plots

– Box plots for outliers

Plot selection

Visualization in higher dimensions

– 3 variable plot

– Interpret 3 var plot

Numerical Summaries

Measures of center

mean

median

mode

– Calculate center measures

Measures of variability

Variance

Standard Deviation

Inter Quartile Range

Range

– Calculate spread measures

– Choose measures for center and spread

Shape and transformations

– Transformations

Outliers

– Identify outliers

Case Study

Introducing the data

– Spam and num_char

-Spam and num_char interpretation

– Spam and !!! interpretation

Check-in 1

– Image and spam interpretation

– Answering questions with chains

Within non-spam emails, is the typical length of emails shorter for

those that were sent to multiple people?

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?

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?

Check-in 2

– What’s in a number?

– What’s in a number interpretation