Univariate Data Exploration and Analysis

source “K-MOOC 오세종 교수님의 강좌의 4. 일변량 자료의 탐색 중 (http://www.kmooc.kr/courses/course-v1:DKUK+DKUK0003+2020_T3)"

Basic Statistics

By data chracteristics Qualitative Data: (Categorical Data) Data that is not composed of numbers, or expressible by any kind of size.

Quantitative Data: Data that has been quantified to numbers with specific sizes.

Discrete Data: Data in integers. Continuous Data: Data with decimals.

By number of variables Univariate Data: Data with one variable. Stored in vector.

Multivariate Data: Data with more than two variables. Stored in matrix, data frame.

Terminology

Population: the entirety of groups that we are interested in, and would like to analyze. Sample: part of the population that could represent the entire group. Subset of the population. Error: wrongness of sampling Population parameters: standards that show the characteristics of specific population. Means, standard divisions.

Number of variable	Variable type	Graph
Univariate	Continuous data	Histogram kernel Densisty Curve Box Plot Violin Plot
Categorical data	Bar Chart Pie Chart
Multivariate	Continuous data	Scatter Plot Line Plot Time Series Plot
Categorical data	Mosaic Chart

Univariate Qualitative Data Analysis

For qualitative data, counting is the first step.

1. table(): create Frequency Distribution Table length(): length of vector (total number) table()/length(): ratio of data

ans=c("Y", "Y", "N", "Y", "Y")
table(ans)
table(ans)/length(ans) # returns N, Y ratio

1. Create Bar Graph Store data as vector

Store frequency distribution table using table()

barplot(): create bar graph

favorite.color<- c("red", "green", "yellow", "red", "green", "red", "red")
sum<- table(favorite.color)
sum # frequency distribution table
barplot(sum, main="Favorite color") # main: graph title

Bar Graph

head(mtcars)
carb<- mtcars[,"carb"] # extract number of carburetors
table(carb) # carb is a vector. As we can COUNT the models with one carburetors, even though carb is quantitative data, we can use it for bar graph
barplot(table(carb), main="Barplot of Carburetors", xlab="#of carburetors", ylab="frequency")
# xlab: x axis label, ylab: y axis label

barplot() parameters

instance	explanation
angle, density, col	slope, density of shading lines, colors of bars
legend	legend for the plot
names	label for each bar
width	bar widths
space	space between bars
beside	TURE: columns are portrayed as juxtaposed bars
horiz	TRUE: horizontal bar

Multiple Graphs in one Screen

par(mfrow=c(1,3)) # divide the screen virtually, divide to 1*3
barplot(table(mtcars$carb),
main="Barplot of Carburetors",
xlab="#of carburetors",
ylab="frequency",
col="blue")

Create Pie Graph

favorite.color<- c("red", "green", "yellow", "red", "green", "red")
sum<- table(favorite.color)
pie(sum, main="Favorite color")

Assignment

1. Extract education column of infert dataset. Store it to edu, and show value of edu.

2. Show value of edu without overlaps

3. Show frequency distributed table of edu values

4. Show bar graph of edu values

edu<- infert[,"education"]
edu
unique(edu)
table(edu)
barplot(table(edu), main="Bar Plot of Education")

Univariate Quantitative Data Analysis

Quantitative data has various analysis methods. First step is to calculate mean/median

Mean (or Median): Characteristics of data Trimmed Mean: Mean of (100-2n)%. Calculated after sorting out the values that are too high or too low. Median is useful for when it is not nomal distribution.

Quartile: Q1, Q2(=Median), Q3

mydata = c(50, 60, 100, 75, 200)
mydata.big= c(mydata, 50000)
mean(mydata)
mean(mydata.big)
median(mydata)
median(mydata.big)
mean(mydata, trim=0.2)
mean(mydata.big, trim=0.2)
quantile(mydata)
quantile(mydata, (0:10)/10)
summary(mydata) # min, max, mean, median
fivenum(mydata)

Distribution

The way the data is dispersed, or spread.

Variance and Standard deviations

How far from the mean?

Large variance or standard deviation \(\rightarrow\) data well away from the average.

diff(): DIfference var(): Variance sd(): Standard deviation

diff(range(mydata)) # range(): max, min of the data. Small diff() value means data dispersed over a small area
var(mydata) # 
sd(mydata) # 

Box Plot

head(state.x77)
st.income<- state.x77[, "Income"]
boxplot(st.income, ylab="Income value")
boxplot(Petal.Width~Species, data=iris, ylab="Petal.Width") # ~Species: Petal.Width by Species

Histogram

Approximate representation of the distribution of numerical data

st.income<- state.x77[,"Income"]
hist(st.income, main="Histogram for Income",
xlab="income",
ylab="frequency",
border="blue",
col="green",
las=2, # x axis range
breaks=5) # number of bars

Stem-and-Leaf Plot

score<- c(30, 40, 50, 100, 90)
stem(score, scale=2) # number of data by score range. scale: number of stem

Assignment

Course Score |KOR|ENG|MATH|HIST|SOC|MUSIC|BIO|EARTH|PHY|ART| |–|–|–|–|–|–|–|–|–|–| |90|85|73|80|85|65|78|50|68|96|

1. Store the data into score vector (course names as data name)

2. Show score vector

3. Mean of score

4. Median of score

5. Show standard deviation of score

6. Show the name of course with highest score

7. Draw boxplot for score. Show an outlier course.

8. Draw histogrem for score. Title: Hong’s score, Color of bar: Purple

mtcars dataset

1. Mean, Median, Trimmed Mean(15%), Standard Division of weight(wt)

2. summary() of weight(wt)

3. Frequency distribution table for number of cylinders (cyl)

4. Draw a frequency distribution table into bar graph

5. Draw a histogrem of weight(wt), bar graphs for cylinder(cyl), gear(gear) in one screen

6. Draw a boxplot of weight(wt). What can you observe from the boxplot?

7. Draw a boxplot for displacement(disp). What can you observe from the boxplot?

score<-c(90,85,73,80,85,65,78,50,68,96)
names(score)<-c("KOR", "ENG", "MATH", "HIST", "SOC", "MUSIC", "BIO", "EARTH", "PHY", "ART")
score
mean(score)
median(score)
sd(score)
colnames(max(score))
boxplot(score, main="Hong's score",
        col="Purple")

wt<- mtcars[,"wt"]
mean(wt)
median(wt)
mean(wt, trim=0.15)
sd(wt)
summary(wt)
cyl<- mtcars[,"cyl"]
table(cyl)
barplot(table(cyl))
gear<- mtcars[,"gear"]
par(mfrow=c(1,3))
hist(score)
barplot(cyl)
barplot(gear)
boxplot(wt)
disp<- mtcars[,"disp"]
boxplot(disp)

Tips

paste(): combines a number of characters to create a unified sentence sep: separator substr(): substring. Split the strings. nchar(): number of character. Length of a string. gsub(): replace

paste("Good", "Mornig", "Tom", sep=" ")
paste(1:10, "is good", sep=" ") # 1 is good, 2 is good, 3 is good, etc
str<- "Good Morning"
substr(str, 1, 4) # "Good" 
substr(str, 6, nchar(str)) # "Morning"
gsub("Good", "nice", str) # "nice Morning"
str<- gsub(" ", "/", str) # store change to str
str # "Good/Morning"

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