Descriptive Statistics with agricolae

Felipe de Mendiburu1, Muhammad Yaseen2

2020-05-02

Source: vignettes/DescriptiveStats.Rmd

  1. Professor of the Academic Department of Statistics and Informatics of the Faculty of Economics and Planning.National University Agraria La Molina-PERU.

  1. Department of Mathematics and Statistics, University of Agriculture Faisalabad, Pakistan.

Descriptive statistics

The package agricolae provides some complementary functions to the R program, specifically for the management of the histogram and function hist.

Histogram

The histogram is constructed with the function graph.freq and is associated to other functions: polygon.freq, table.freq, stat.freq. See Figures: @ref(fig:DescriptStats2), @ref(fig:DescriptStats6) and @ref(fig:DescriptStats7) for more details.

Example. Data generated in R . (students’ weight).

weight<-c( 68, 53, 69.5, 55, 71, 63, 76.5, 65.5, 69, 75, 76, 57, 70.5, 71.5, 56, 81.5,
           69, 59, 67.5, 61, 68, 59.5, 56.5, 73, 61, 72.5, 71.5, 59.5, 74.5, 63)
print(summary(weight))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  53.00   59.88   68.00   66.45   71.50   81.50 
oldpar<-par(mfrow=c(1,2),mar=c(4,4,0,1),cex=0.6)
h1<- graph.freq(weight,col=colors()[84],frequency=1,las=2, ylim=c(0,12),ylab="Frequency")
x<-h1$breaks
h2<- plot(h1, frequency =2, axes= FALSE,ylim=c(0,0.4),xlab="weight",ylab="Relative (%)")
polygon.freq(h2, col=colors()[84], lwd=2, frequency =2)
axis(1,x,cex=0.6,las=2)
y<-seq(0,0.4,0.1)
axis(2, y,y*100,cex=0.6,las=1)
Absolute and relative frequency with polygon

Absolute and relative frequency with polygon 

par(oldpar)

Statistics and Frequency tables

Statistics: mean, median, mode and standard deviation of the grouped data.

$variance
[1] 51.37655

$mean
[1] 66.6

$median
[1] 68.36

$mode
       [-   -]     mode
[1,] 67.4 72.2 70.45455

Frequency tables: Use table.freq, stat.freq and summary

The table.freq is equal to summary()

Limits class: Lower and Upper

Class point: Main

Frequency: Frequency

Percentage frequency: Percentage

Cumulative frequency: CF

Cumulative percentage frequency: CPF

print(summary(h1),row.names=FALSE)
 Lower Upper Main Frequency Percentage CF   CPF
  53.0  57.8 55.4         5       16.7  5  16.7
  57.8  62.6 60.2         5       16.7 10  33.3
  62.6  67.4 65.0         3       10.0 13  43.3
  67.4  72.2 69.8        10       33.3 23  76.7
  72.2  77.0 74.6         6       20.0 29  96.7
  77.0  81.8 79.4         1        3.3 30 100.0

Histogram manipulation functions

You can extract information from a histogram such as class intervals intervals.freq, attract new intervals with the sturges.freq function or to join classes with join.freq function. It is also possible to reproduce the graph with the same creator graph.freq or function plot and overlay normal function with normal.freq be it a histogram in absolute scale, relative or density . The following examples illustrates these properties.

sturges.freq(weight)
$maximum
[1] 81.5

$minimum
[1] 53

$amplitude
[1] 29

$classes
[1] 6

$interval
[1] 4.8

$breaks
[1] 53.0 57.8 62.6 67.4 72.2 77.0 81.8
     lower upper
[1,]  53.0  57.8
[2,]  57.8  62.6
[3,]  62.6  67.4
[4,]  67.4  72.2
[5,]  72.2  77.0
[6,]  77.0  81.8
join.freq(h1,1:3) -> h3
print(summary(h3))
  Lower Upper Main Frequency Percentage CF   CPF
1  53.0  67.4 60.2        13       43.3 13  43.3
2  67.4  72.2 69.8        10       33.3 23  76.7
3  72.2  77.0 74.6         6       20.0 29  96.7
4  77.0  81.8 79.4         1        3.3 30 100.0
oldpar<-par(mfrow=c(1,2),mar=c(4,4,0,1),cex=0.8)
plot(h3, frequency=2,col=colors()[84],ylim=c(0,0.6),axes=FALSE,xlab="weight",ylab="%")
y<-seq(0,0.6,0.2)
axis(2,y,y*100,las=2)
axis(1,h3$breaks)
normal.freq(h3,frequency=2,col=colors()[90])
ogive.freq(h3,col=colors()[84],xlab="weight")
Join frequency and relative frequency with normal and Ogive

Join frequency and relative frequency with normal and Ogive 

  weight    RCF
1   53.0 0.0000
2   67.4 0.4333
3   72.2 0.7667
4   77.0 0.9667
5   81.8 1.0000
6   86.6 1.0000
par(oldpar)

hist() and graph.freq() based on grouped data

The hist and graph.freq have the same characteristics, only f2 allows build histogram from grouped data.

0-10 (3)

10-20 (8)

20-30 (15)

30-40 (18)

40-50 (6)

oldpar<-par(mfrow=c(1,2),mar=c(4,3,2,1),cex=0.6)
h4<-hist(weight,xlab="Classes (h4)")
table.freq(h4)
# this is possible
# hh<-graph.freq(h4,plot=FALSE)
# summary(hh)
# new class
classes <- c(0, 10, 20, 30, 40, 50)
freq <- c(3, 8, 15, 18, 6)
h5 <- graph.freq(classes,counts=freq, xlab="Classes (h5)",main="Histogram grouped data")
hist() function and histogram defined class

hist() function and histogram defined class 

par(oldpar)
print(summary(h5),row.names=FALSE)
 Lower Upper Main Frequency Percentage CF CPF
     0    10    5         3          6  3   6
    10    20   15         8         16 11  22
    20    30   25        15         30 26  52
    30    40   35        18         36 44  88
    40    50   45         6         12 50 100