Facts from real world !!
YAYA DIALLO
September 20, 2019
1 - Basic Statistics.
1.1 - Crosstabs, distribution, marginal distribution.
#Read data file
setwd("C:/Users/MamadouYaya/Dropbox/Fall2019/TA_Fall2019/Data")
LFSCanada<- read.csv2("Can0718.txt", sep="")
LFSCanada$hrlyearn=LFSCanada$hrlyearn/100The function table() to create frequencies
It is possible to generate frequency tables using the table( ) function :
- The following table display the population by gender for each province.
#Average wage by age group
table1<-table(LFSCanada$prov,LFSCanada$sex)
table1##
## Female Male
## Alberta 5476 5359
## British Columbia 6228 5928
## Manitoba 4614 4496
## New Brunswick 2682 2511
## Newfoundland 1972 1772
## Nova Scotia 2871 2594
## Ontario 14234 13297
## Prince Edward Island 1446 1331
## Québec 8931 8577
## Saskatchewan 3891 3680The function pro.table() to create tables of proportions.
- The option 1 will display row percentages: The sum of each row will be 1. In each province, we will have the proportion of Male and Female.
# Distribution of workers by gender for each province
tablepro1<-prop.table(table1,1)
round(tablepro1,digits = 2)##
## Female Male
## Alberta 0.51 0.49
## British Columbia 0.51 0.49
## Manitoba 0.51 0.49
## New Brunswick 0.52 0.48
## Newfoundland 0.53 0.47
## Nova Scotia 0.53 0.47
## Ontario 0.52 0.48
## Prince Edward Island 0.52 0.48
## Québec 0.51 0.49
## Saskatchewan 0.51 0.491.2 - Statistics : Mean, median, min, max.
The function tapply() to create table of statistics
tapply() computes a measure (mean, median, min, max, etc..) or a function for each factor variable in a vector. The following example calculate the sample mean wage for each age group in Canada. We applied the special function tapply():
- x is a vector of the continuous variable : Individual wage.
- INDEX : list of factors : Age group.
- FUN : Is a function of statistics we want to display : Here we are looking mean. But it is possible also other statistics like median, percentiles.
#Average wage by age group
table3 <- tapply(LFSCanada$hrlyearn,INDEX = LFSCanada$age_12,FUN=mean,na.rm =TRUE)
round(table3,digits = 2)## 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70+
## 13.44 17.36 24.18 27.60 29.08 30.01 29.94 29.29 28.29 26.61 25.29 22.57The function barplot to represent the previous table.
- Create the table you want to plot.
- Plot the table.
barplot command has many options : look at the help.
#Average wage by age group
barplot(table3,las=2,ylab = "Hourly wage",xlab = "Age group")
Represent cross-tablebarplot with two variables
- Create the table you want to plot.
- Plot the table.
barplot command has many options : look at the help.
Table
#Average wage by age group
table4= tapply(LFSCanada$hrlyearn,INDEX=list(LFSCanada$sex,LFSCanada$age_12),FUN=mean,na.rm =TRUE)
round(t(table4),digits = 2)## Female Male
## 15-19 13.08 13.80
## 20-24 16.59 18.10
## 25-29 22.97 25.31
## 30-34 25.87 29.23
## 35-39 27.01 31.06
## 40-44 27.73 32.27
## 45-49 27.46 32.40
## 50-54 26.77 32.02
## 55-59 25.50 31.11
## 60-64 23.91 29.03
## 65-69 23.39 26.78
## 70+ 20.53 24.09Barplot
#Average wage by age group
barplot(table4,las=2,beside = TRUE)
legend("topleft",legend = rownames(table4) , pch =c(15,15), col=c("gray10","gray70"))
2- Plotting Graphs.
One of the most frequently used plotting functions in R is the plot() function. This is a generic function: the type of plot produced is dependent on the type or class of the first argument.
Two continuous variables.
If x and y are vectors, plot(x, y) produces a scatterplot of y against x :
x=seq(0,20,0.5)
e=rnorm(length(x),0,2)
y=2+0.6*x+1.4*e
plot(x,y)
Select individuals living in Quebec province
#Read data file
setwd("C:/Users/MamadouYaya/Dropbox/Fall2019/TA_Fall2019/Data")
TSCanada <- read.csv2("TSCanada.txt", sep="")
TSQuebec <-subset(TSCanada,prov=='Quebec')Plotting number of employed against wage during the period 2000-2017 for Quebec province :
plot(TSQuebec$Employed,TSQuebec$hrlyearn,pch=24)
Time-series : Trend of employment in Quebec from 2000 to 2017
plot(TSQuebec$year,TSQuebec$Employed, type = "l")
Time-series : Trend (colored) of employment in Quebec from 2000 to 2017
plot(TSQuebec$year,TSQuebec$Employed, type = "l",col="blue",xlab="years", ylab="Number of employed")
Time Series using ts() function
The ts() function will convert a numeric vector into an R time series object. We have to specify the start date, the end and the frequency
- Start date: 2000
- End date: 2017
- Frequency: 1 if annual, 4 if quartly and 12 if monthly
myts<-ts(TSQuebec$Employed, start=c(2000, 1), frequency=1)
plot(myts,las=2)
Plot several time series on a common plot using ts.plot().
-First: Create the time series.
mytsON=ts(subset(TSCanada,prov=='Ontario')$hrlyearn,start=c(2000,1),frequency=1)
mytsQC=ts(subset(TSCanada,prov=='Quebec')$hrlyearn,start=c(2000, 1),frequency=1)
mytsBC=ts(subset(TSCanada,prov=='BritishColumbia')$hrlyearn,start=c(2000,1),frequency=1)
myts=cbind(mytsQC,mytsON,mytsBC)
myts## Time Series:
## Start = 2000
## End = 2017
## Frequency = 1
## mytsQC mytsON mytsBC
## 2000 30 49 56
## 2001 35 59 61
## 2002 40 65 69
## 2003 46 72 73
## 2004 55 82 77
## 2005 62 89 78
## 2006 68 97 88
## 2007 79 109 98
## 2008 90 120 116
## 2009 102 130 127
## 2010 105 136 133
## 2011 113 142 138
## 2012 121 147 146
## 2013 129 154 150
## 2014 137 159 156
## 2015 145 166 164
## 2016 152 170 167
## 2017 161 172 169
- Second: Plot the evolution of average wage in Quebec, British Columbia and Ontario.
require(graphics)
ts.plot(myts,gpars=list(ylab="Hourly wagee", lty=c(1:3)))
legend("topleft",legend =c("Ontario","Quebec","British Columbia"), lty=c(1:3))