Download Rosner data: http://academic.cengage.com/resource_uploads/downloads/0538733497_245020.zip
Extract the data file so that you can read in BONEDEN.DAT.txt.
bone <- read.csv("./BONEDEN.DAT.txt", quote = "'")
## Mean
mean(bone$age)
[1] 48.85
## SD
sd(bone$age)
[1] 11.77
## Median
median(bone$age)
[1] 47
## Quantiles:
quantile(bone$age)
0% 25% 50% 75% 100%
27 42 47 53 76
## Interquartile range
IQR(bone$age)
[1] 11
## Maximum
max(bone$age)
[1] 76
## Minimum
min(bone$age)
[1] 27
## Load e1071
library(e1071)
## Skewness
skewness(bone$age) # Type 3
[1] 0.6941
skewness(bone$age, type = 2) # Type 2: SAS-method
[1] 0.748
skewness(bone$age, type = 1) # Type 1: Stata-method
[1] 0.7203
## Kurtosis
kurtosis(bone$age) # Type 3
[1] -0.1392
kurtosis(bone$age, type = 2) # Type 2: SAS-method
[1] 0.1683
kurtosis(bone$age, type = 1) # Type 1: Stata-method
[1] 0.005628
summary(bone)
ID age zyg ht1 wt1 tea1 cof1
Min. :1002501 Min. :27.0 Min. :1.00 Min. :149 Min. : 47.0 Min. : 0.0 Min. : 0.0
1st Qu.:1273101 1st Qu.:42.0 1st Qu.:1.00 1st Qu.:159 1st Qu.: 57.0 1st Qu.: 1.0 1st Qu.: 0.0
Median :1528201 Median :47.0 Median :1.00 Median :162 Median : 61.0 Median :14.0 Median : 7.0
Mean :1476714 Mean :48.9 Mean :1.49 Mean :161 Mean : 65.4 Mean :19.3 Mean :14.6
3rd Qu.:1628601 3rd Qu.:53.0 3rd Qu.:2.00 3rd Qu.:165 3rd Qu.: 70.0 3rd Qu.:35.0 3rd Qu.:28.0
Max. :2609801 Max. :76.0 Max. :2.00 Max. :171 Max. :114.0 Max. :56.0 Max. :56.0
alc1 cur1 men1 pyr1 ls1 fn1 fs1
Min. : 0.00 Min. : 0.00 Min. :0.000 Min. : 0.00 Min. :0.500 Min. :0.420 Min. :0.70
1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.:0.000 1st Qu.: 0.00 1st Qu.:0.710 1st Qu.:0.600 1st Qu.:1.05
Median : 1.00 Median : 0.00 Median :1.000 Median : 0.00 Median :0.800 Median :0.660 Median :1.11
Mean : 4.07 Mean : 3.66 Mean :0.707 Mean : 4.36 Mean :0.795 Mean :0.665 Mean :1.10
3rd Qu.: 6.00 3rd Qu.: 3.00 3rd Qu.:1.000 3rd Qu.: 0.00 3rd Qu.:0.870 3rd Qu.:0.720 3rd Qu.:1.15
Max. :28.00 Max. :28.00 Max. :2.000 Max. :33.75 Max. :1.040 Max. :0.900 Max. :1.42
ht2 wt2 tea2 cof2 alc2 cur2 men2
Min. :150 Min. :43.0 Min. : 0.0 Min. : 0.0 Min. : 0.00 Min. : 0.00 Min. :0.000
1st Qu.:159 1st Qu.:54.0 1st Qu.: 0.0 1st Qu.: 7.0 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.:0.000
Median :162 Median :58.0 Median : 7.0 Median :21.0 Median : 0.00 Median : 1.00 Median :1.000
Mean :162 Mean :61.8 Mean :15.1 Mean :23.1 Mean : 5.29 Mean : 5.07 Mean :0.634
3rd Qu.:165 3rd Qu.:68.0 3rd Qu.:21.0 3rd Qu.:35.0 3rd Qu.: 9.00 3rd Qu.: 8.00 3rd Qu.:1.000
Max. :170 Max. :94.0 Max. :91.0 Max. :99.0 Max. :35.00 Max. :30.00 Max. :2.000
pyr2 ls2 fn2 fs2
Min. : 5.0 Min. :0.470 Min. :0.380 Min. :0.64
1st Qu.:14.0 1st Qu.:0.650 1st Qu.:0.610 1st Qu.:1.01
Median :25.5 Median :0.770 Median :0.660 Median :1.08
Mean :27.5 Mean :0.759 Mean :0.664 Mean :1.07
3rd Qu.:39.0 3rd Qu.:0.860 3rd Qu.:0.740 3rd Qu.:1.16
Max. :64.5 Max. :0.980 Max. :0.880 Max. :1.33
library(psych)
## describe all variables except for the first (ID)
describe(bone[,-1], type = 2) # Type 2: SAS-method for skewness and kurtosis
var n mean sd median trimmed mad min max range skew kurtosis se
age 1 41 48.85 11.77 47.00 47.94 8.90 27.00 76.00 49.00 0.75 0.17 1.84
zyg 2 41 1.49 0.51 1.00 1.48 0.00 1.00 2.00 1.00 0.05 -2.10 0.08
ht1 3 41 161.41 5.23 162.00 161.82 4.45 149.00 171.00 22.00 -0.71 0.22 0.82
wt1 4 41 65.39 14.89 61.00 63.18 10.38 47.00 114.00 67.00 1.77 3.83 2.32
tea1 5 41 19.32 18.11 14.00 17.64 20.76 0.00 56.00 56.00 0.58 -0.88 2.83
cof1 6 41 14.56 15.80 7.00 12.36 10.38 0.00 56.00 56.00 1.00 0.04 2.47
alc1 7 41 4.07 6.72 1.00 2.45 1.48 0.00 28.00 28.00 2.20 4.66 1.05
cur1 8 41 3.66 6.77 0.00 1.91 0.00 0.00 28.00 28.00 2.36 5.09 1.06
men1 9 41 0.71 0.64 1.00 0.64 0.00 0.00 2.00 2.00 0.35 -0.62 0.10
pyr1 10 41 4.36 9.33 0.00 2.04 0.00 0.00 33.75 33.75 1.98 2.62 1.46
ls1 11 41 0.79 0.13 0.80 0.80 0.13 0.50 1.04 0.54 -0.21 -0.12 0.02
fn1 12 41 0.66 0.10 0.66 0.66 0.09 0.42 0.90 0.48 0.05 0.11 0.02
fs1 13 41 1.10 0.13 1.11 1.10 0.09 0.70 1.42 0.72 -0.58 2.09 0.02
ht2 14 41 161.59 4.67 162.00 161.82 4.45 150.00 170.00 20.00 -0.49 -0.24 0.73
wt2 15 41 61.83 11.89 58.00 60.58 7.41 43.00 94.00 51.00 0.97 0.51 1.86
tea2 16 41 15.07 21.17 7.00 10.67 10.38 0.00 91.00 91.00 2.41 6.68 3.31
cof2 17 41 23.15 21.09 21.00 20.73 20.76 0.00 99.00 99.00 1.29 2.94 3.29
alc2 18 41 5.29 8.14 0.00 3.76 0.00 0.00 35.00 35.00 1.93 4.08 1.27
cur2 19 41 5.07 7.55 1.00 3.52 1.48 0.00 30.00 30.00 1.87 3.42 1.18
men2 20 41 0.63 0.66 1.00 0.55 1.48 0.00 2.00 2.00 0.57 -0.61 0.10
pyr2 21 41 27.51 14.82 25.50 26.80 18.24 5.00 64.50 59.50 0.43 -0.53 2.31
ls2 22 41 0.76 0.14 0.77 0.77 0.16 0.47 0.98 0.51 -0.45 -0.62 0.02
fn2 23 41 0.66 0.12 0.66 0.67 0.12 0.38 0.88 0.50 -0.24 -0.17 0.02
fs2 24 41 1.07 0.15 1.08 1.08 0.10 0.64 1.33 0.69 -1.01 1.42 0.02
## item name
## item number
## number of valid cases
## mean
## standard deviation
## trimmed mean (with trim defaulting to .1)
## median (standard or interpolated
## mad: median absolute deviation (from the median)
## minimum
## maximum
## skew
## kurtosis
## standard error
## describeBy()
## Same except for grouping by zyg status
describeBy(bone[,-1], bone$zyg, type = 2)
group: 1
var n mean sd median trimmed mad min max range skew kurtosis se
age 1 21 51.38 10.74 49.00 50.71 7.41 36.00 73.00 37.00 0.85 0.16 2.34
zyg 2 21 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00 NaN NaN 0.00
ht1 3 21 160.76 5.66 162.00 161.12 4.45 149.00 169.00 20.00 -0.64 -0.40 1.23
wt1 4 21 66.95 13.63 66.00 65.71 7.41 48.00 112.00 64.00 1.69 5.30 2.97
tea1 5 21 19.29 20.50 14.00 17.24 20.76 0.00 56.00 56.00 0.79 -0.82 4.47
cof1 6 21 15.67 15.79 14.00 13.59 20.76 0.00 56.00 56.00 1.00 0.53 3.45
alc1 7 21 3.62 6.05 1.00 2.29 1.48 0.00 23.00 23.00 2.12 4.47 1.32
cur1 8 21 3.62 6.05 1.00 2.29 1.48 0.00 22.00 22.00 1.98 3.49 1.32
men1 9 21 0.76 0.62 1.00 0.71 0.00 0.00 2.00 2.00 0.20 -0.36 0.14
pyr1 10 21 7.70 11.71 0.00 5.88 0.00 0.00 33.75 33.75 1.12 -0.35 2.55
ls1 11 21 0.77 0.09 0.75 0.76 0.07 0.58 0.95 0.37 0.30 -0.09 0.02
fn1 12 21 0.67 0.10 0.66 0.67 0.09 0.42 0.85 0.43 -0.11 0.51 0.02
fs1 13 21 1.08 0.11 1.11 1.10 0.07 0.70 1.22 0.52 -1.99 5.60 0.02
ht2 14 21 162.38 4.35 163.00 162.76 2.97 153.00 169.00 16.00 -0.79 0.12 0.95
wt2 15 21 65.19 12.99 62.00 64.59 11.86 43.00 94.00 51.00 0.53 -0.25 2.84
tea2 16 21 13.67 20.47 7.00 9.88 10.38 0.00 91.00 91.00 2.88 10.42 4.47
cof2 17 21 23.95 22.85 28.00 21.29 20.76 0.00 99.00 99.00 1.70 4.88 4.99
alc2 18 21 5.10 6.46 0.00 4.53 0.00 0.00 16.00 16.00 0.66 -1.52 1.41
cur2 19 21 4.86 5.69 2.00 4.06 2.97 0.00 20.00 20.00 1.10 0.68 1.24
men2 20 21 0.71 0.64 1.00 0.65 0.00 0.00 2.00 2.00 0.33 -0.51 0.14
pyr2 21 21 28.21 12.73 30.00 28.15 14.46 6.00 56.00 50.00 0.09 -0.24 2.78
ls2 22 21 0.75 0.11 0.76 0.75 0.12 0.51 0.96 0.45 -0.23 0.06 0.02
fn2 23 21 0.67 0.11 0.65 0.67 0.09 0.46 0.88 0.42 0.17 -0.27 0.02
fs2 24 21 1.07 0.13 1.09 1.08 0.10 0.66 1.24 0.58 -1.67 4.87 0.03
---------------------------------------------------------------------------------------
group: 2
var n mean sd median trimmed mad min max range skew kurtosis se
age 1 20 46.20 12.48 44.00 44.81 6.67 27.00 76.00 49.00 1.01 0.86 2.79
zyg 2 20 2.00 0.00 2.00 2.00 0.00 2.00 2.00 0.00 NaN NaN 0.00
ht1 3 20 162.10 4.79 162.50 162.50 2.97 150.00 171.00 21.00 -0.76 1.60 1.07
wt1 4 20 63.75 16.29 58.50 60.50 5.93 47.00 114.00 67.00 2.06 4.48 3.64
tea1 5 20 19.35 15.75 21.00 18.94 20.76 0.00 42.00 42.00 0.11 -1.53 3.52
cof1 6 20 13.40 16.12 7.00 11.06 10.38 0.00 49.00 49.00 1.11 -0.02 3.61
alc1 7 20 4.55 7.50 1.00 2.62 1.48 0.00 28.00 28.00 2.29 5.14 1.68
cur1 8 20 3.70 7.62 0.00 1.50 0.00 0.00 28.00 28.00 2.63 6.37 1.70
men1 9 20 0.65 0.67 1.00 0.56 1.48 0.00 2.00 2.00 0.55 -0.55 0.15
pyr1 10 20 0.85 3.69 0.00 0.00 0.00 0.00 16.50 16.50 4.47 19.96 0.82
ls1 11 20 0.83 0.16 0.84 0.84 0.15 0.50 1.04 0.54 -0.76 0.06 0.04
fn1 12 20 0.66 0.11 0.66 0.66 0.08 0.47 0.90 0.43 0.19 0.11 0.02
fs1 13 20 1.11 0.14 1.12 1.12 0.16 0.81 1.42 0.61 -0.01 0.38 0.03
ht2 14 20 160.75 4.96 161.50 160.81 5.19 150.00 170.00 20.00 -0.22 -0.11 1.11
wt2 15 20 58.30 9.70 56.00 57.06 5.19 43.00 88.00 45.00 1.67 3.92 2.17
tea2 16 20 16.55 22.32 10.50 12.38 15.57 0.00 91.00 91.00 2.20 5.85 4.99
cof2 17 20 22.30 19.63 21.00 20.12 20.76 0.00 68.00 68.00 0.67 -0.01 4.39
alc2 18 20 5.50 9.78 0.50 2.94 0.74 0.00 35.00 35.00 2.24 4.59 2.19
cur2 19 20 5.30 9.26 0.00 3.00 0.00 0.00 30.00 30.00 1.93 2.92 2.07
men2 20 20 0.55 0.69 0.00 0.44 0.00 0.00 2.00 2.00 0.89 -0.24 0.15
pyr2 21 20 26.79 17.05 20.75 25.64 15.57 5.00 64.50 59.50 0.65 -0.67 3.81
ls2 22 20 0.77 0.17 0.84 0.78 0.12 0.47 0.98 0.51 -0.63 -1.00 0.04
fn2 23 20 0.66 0.12 0.68 0.67 0.11 0.38 0.87 0.49 -0.55 0.00 0.03
fs2 24 20 1.06 0.18 1.06 1.07 0.19 0.64 1.33 0.69 -0.71 0.30 0.04
## item name
## item number
## number of valid cases
## mean
## standard deviation
## median
## mad: median absolute deviation (from the median)
## minimum
## maximum
## skew
## standard error
## Density plot of age (outliers of the higher side)
library(lattice)
densityplot(bone$age)
## mean is affected by the outliers
mean(bone$age)
[1] 48.85
## trimmed mean: top 10% and bottom 10% of observations are removed before mean
mean(bone$age, trim = 0.1)
[1] 47.94
## trimmed mean is closer to median (less affected by the outliers)
median(bone$age)
[1] 47
Compute the median absolute deviation, i.e., the (lo-/hi-) median of the absolute deviations from the median, and (by default) adjust by a factor for asymptotically normal consistency.
mad(bone$age)
[1] 8.896