Let’s load again Mice data:

## clear memory
rm(list = ls())
## load data
Mice=read.table("http://edu.sablab.net/data/txt/mice.txt",header=T,sep="\t")
str(Mice)
## 'data.frame':    790 obs. of  14 variables:
##  $ ID                  : int  1 2 3 368 369 370 371 372 4 5 ...
##  $ Strain              : Factor w/ 40 levels "129S1/SvImJ",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ Sex                 : Factor w/ 2 levels "f","m": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Starting.age        : int  66 66 66 72 72 72 72 72 66 66 ...
##  $ Ending.age          : int  116 116 108 114 115 116 119 122 109 112 ...
##  $ Starting.weight     : num  19.3 19.1 17.9 18.3 20.2 18.8 19.4 18.3 17.2 19.7 ...
##  $ Ending.weight       : num  20.5 20.8 19.8 21 21.9 22.1 21.3 20.1 18.9 21.3 ...
##  $ Weight.change       : num  1.06 1.09 1.11 1.15 1.08 ...
##  $ Bleeding.time       : int  64 78 90 65 55 NA 49 73 41 129 ...
##  $ Ionized.Ca.in.blood : num  1.2 1.15 1.16 1.26 1.23 1.21 1.24 1.17 1.25 1.14 ...
##  $ Blood.pH            : num  7.24 7.27 7.26 7.22 7.3 7.28 7.24 7.19 7.29 7.22 ...
##  $ Bone.mineral.density: num  0.0605 0.0553 0.0546 0.0599 0.0623 0.0626 0.0632 0.0592 0.0513 0.0501 ...
##  $ Lean.tissues.weight : num  14.5 13.9 13.8 15.4 15.6 16.4 16.6 16 14 16.3 ...
##  $ Fat.weight          : num  4.4 4.4 2.9 4.2 4.3 4.3 5.4 4.1 3.2 5.2 ...

6.1. Measures of the center

summary(Mice)
##        ID                  Strain    Sex      Starting.age  
##  Min.   :   1.0   C57BR/cdJ   : 28   f:396   Min.   :46.00  
##  1st Qu.: 310.2   MA/MyJ      : 23   m:394   1st Qu.:64.00  
##  Median : 537.5   CAST/EiJ    : 21           Median :66.00  
##  Mean   : 526.8   A/J         : 20           Mean   :66.21  
##  3rd Qu.: 799.8   BTBR_T+_tf/J: 20           3rd Qu.:71.00  
##  Max.   :1012.0   C3H/HeJ     : 20           Max.   :82.00  
##                   (Other)     :658                          
##    Ending.age    Starting.weight Ending.weight   Weight.change  
##  Min.   : 93.0   Min.   : 8.70   Min.   :10.00   Min.   :0.000  
##  1st Qu.:109.0   1st Qu.:17.20   1st Qu.:18.80   1st Qu.:1.059  
##  Median :114.0   Median :21.20   Median :23.50   Median :1.105  
##  Mean   :114.3   Mean   :21.38   Mean   :23.69   Mean   :1.107  
##  3rd Qu.:119.0   3rd Qu.:25.38   3rd Qu.:28.10   3rd Qu.:1.164  
##  Max.   :140.0   Max.   :39.10   Max.   :49.60   Max.   :2.109  
##  NA's   :2                                                      
##  Bleeding.time Ionized.Ca.in.blood    Blood.pH     Bone.mineral.density
##  Min.   : 14   Min.   :1.000       Min.   :6.810   Min.   :0.03980     
##  1st Qu.: 43   1st Qu.:1.200       1st Qu.:7.160   1st Qu.:0.04860     
##  Median : 55   Median :1.240       Median :7.200   Median :0.05300     
##  Mean   : 61   Mean   :1.237       Mean   :7.199   Mean   :0.05331     
##  3rd Qu.: 73   3rd Qu.:1.280       3rd Qu.:7.250   3rd Qu.:0.05785     
##  Max.   :522   Max.   :1.410       Max.   :7.430   Max.   :0.07140     
##  NA's   :30    NA's   :2           NA's   :2       NA's   :3           
##  Lean.tissues.weight   Fat.weight    
##  Min.   : 7.30       Min.   : 1.800  
##  1st Qu.:13.80       1st Qu.: 3.500  
##  Median :17.30       Median : 4.800  
##  Mean   :17.27       Mean   : 6.073  
##  3rd Qu.:20.85       3rd Qu.: 7.500  
##  Max.   :29.90       Max.   :23.300  
##  NA's   :3           NA's   :3
## mean and median. We should exclude NA from consideration
mn = mean(Mice$Ending.weight, na.rm=T)
md = median(Mice$Ending.weight, na.rm=T)
## for mode you should add a library:
library(modeest)
## 
## This is package 'modeest' written by P. PONCET.
## For a complete list of functions, use 'library(help = "modeest")' or 'help.start()'.
mo = mlv(Mice$Ending.weight, method = "shorth")$M

## let us plot them
plot(density(Mice$Ending.weight, na.rm=T),lwd=2,main="Ending weight")
abline(v = mn,col="red")
abline(v = md,col="blue")
abline(v = mo ,col="cyan")
legend(x="topright",c("mean","median","mode"),col=c("red","blue","cyan"),pch=19)

6.2. Measures of variation

## quantiles, percentiles and quartiles
quantile(Mice$Bleeding.time,prob=c(0.25,0.5,0.75),na.rm=T)
## 25% 50% 75% 
##  43  55  73
## standard deviation and variance
sd(Mice$Bleeding.time, na.rm=T)
## [1] 31.91943
var(Mice$Bleeding.time, na.rm=T)
## [1] 1018.85
## stable measure of variation - MAD
mad(Mice$Bleeding.time, na.rm=T)
## [1] 20.7564
mad(Mice$Bleeding.time, constant = 1, na.rm=T)
## [1] 14

S6.3. Measures of dependency

## covariation
cov(Mice$Starting.weight,Mice$Ending.weight)
## [1] 39.84946
## correlation
cor(Mice$Starting.weight,Mice$Ending.weight)
## [1] 0.9422581
## coefficient of determination, R2
cor(Mice$Starting.weight,Mice$Ending.weight)^2
## [1] 0.8878503
## kendal correlation
cor(Mice$Starting.weight,Mice$Ending.weight,method="kendal")
## [1] 0.8188964
## spearman correlation
cor(Mice$Starting.weight,Mice$Ending.weight,method="spearman")
## [1] 0.9423666

Excercises.

  1. Use mice dataset. Calculate the number of mice with bleeding time bigger than 2 minutes

read.table, sum b. Report a 5-numer summary for each column of “mice” data

summary

  1. For dataset “mice” replace starting weight of any mouse by 1000 (assume, there is a mistype). Calculate mean, median, standard deviation and median absolute deviation (MAD) of this weight. Compare the results with original measures.

mean, median, sd, mad

LIH