Descriptive Data Analysis
Abdul Samad
June 12, 2021
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Introduction
This article explains how to compute the main descriptive statistics in R and how to present them graphically. To learn more about the reasoning behind each descriptive statistics, how to compute them by hand and how to interpret them. descriptive statistics (in the broad sense of the term) is a branch of statistics aiming at summarizing, describing and presenting a series of values or a dataset. Descriptive statistics is often the first step and an important part in any statistical analysis. It allows to check the quality of the data and it helps to "understand"" the data by having a clear overview of it. If well presented, descriptive statistics is already a good starting point for further analyses. There exists many measures to summarize a dataset. They are divided into two types:
- location measures and
- dispersion measures
Location measures give an understanding about the central tendency of the data, whereas dispersion measures give an understanding about the spread of the data.
Data
In this section, the aim is just showing the sample of data. How this data looks? What are the variables? How values in the variable looks? etc. Below is the preview of this data and its structure.
f <- read.xlsx("Data.xlsx",sheetIndex = 1,header = T)
f$Groups <- factor(f$Groups)
f$Groups.1 <- factor(f$Groups.1)
f$Material <- factor(f$Material)
f$Material.1 <- factor(f$Material.1)
head(f)## Groups Groups.1 Material Material.1 DE.0 DE.1 DE7 DE14 TP.0 TP.14
## 1 Control 1 CS 1 0.31 0.53 1.46 1.40 5.653053 6.540023
## 2 Control 1 CS 1 0.37 0.52 1.37 1.87 5.674346 7.200251
## 3 Control 1 CS 1 0.03 0.49 1.04 1.24 5.521978 5.860185
## 4 Control 1 CS 1 0.04 0.47 1.36 1.76 5.625432 5.966271
## 5 Control 1 CS 1 0.19 0.47 1.21 1.82 5.499675 8.995576
## 6 Control 1 CS 1 0.14 0.58 1.09 1.32 4.906897 6.457343
## VHN.0 VHN.14
## 1 79.2 72.4
## 2 80.0 76.5
## 3 83.3 76.7
## 4 86.1 74.0
## 5 83.7 76.2
## 6 82.9 75.1str(f)## 'data.frame': 360 obs. of 12 variables:
## $ Groups : Factor w/ 3 levels "Control","Regular dentifrice",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Groups.1 : Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
## $ Material : Factor w/ 5 levels "CS","GB","RC",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Material.1: Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...
## $ DE.0 : num 0.31 0.37 0.03 0.04 0.19 0.14 0.19 0.34 0.23 0.31 ...
## $ DE.1 : num 0.53 0.52 0.49 0.47 0.47 0.58 0.78 0.79 0.85 0.93 ...
## $ DE7 : num 1.46 1.37 1.04 1.36 1.21 1.09 1.63 1.79 1.52 1.16 ...
## $ DE14 : num 1.4 1.87 1.24 1.76 1.82 1.32 1.24 1.27 1.32 1.76 ...
## $ TP.0 : num 5.65 5.67 5.52 5.63 5.5 ...
## $ TP.14 : num 6.54 7.2 5.86 5.97 9 ...
## $ VHN.0 : num 79.2 80 83.3 86.1 83.7 82.9 80.9 83.5 81.9 78.8 ...
## $ VHN.14 : num 72.4 76.5 76.7 74 76.2 75.1 76.2 75.6 76.2 74.1 ...There are 360 observations of 12 variables, representing the groups and material. There are 4 variables are factor variables (i.e., groups, group1, material and material1), while, other 8 variables are numeric. In addition, group variable have 3 levels of factor, while, material have 4.
Summary of the Data
In the summary, for each numeric varible, we have presented the minimum, maximum, mean, median, 1st quantile and 3rd quantile value. While, for each factor variable, we have presented number of observations for each factor.
summary(f)## Groups Groups.1 Material Material.1 DE.0
## Control :120 1:120 CS :90 1:90 Min. :0.030
## Regular dentifrice :120 2:120 GB :90 2:90 1st Qu.:0.470
## Whitening dentifrice:120 3:120 RC :60 3:90 Median :0.825
## RC :30 4:90 Mean :0.820
## VE :90 3rd Qu.:1.170
## Max. :1.840
##
## DE.1 DE7 DE14 TP.0
## Min. :0.3800 Min. :0.550 Min. :0.660 Min. : 2.927
## 1st Qu.:0.9975 1st Qu.:1.367 1st Qu.:1.760 1st Qu.: 6.671
## Median :1.4400 Median :1.995 Median :3.170 Median : 6.879
## Mean :1.6821 Mean :2.332 Mean :3.161 Mean : 7.016
## 3rd Qu.:2.3850 3rd Qu.:3.342 3rd Qu.:4.237 3rd Qu.: 7.502
## Max. :3.9700 Max. :4.990 Max. :6.610 Max. :10.205
## NA's :296
## TP.14 VHN.0 VHN.14
## Min. :3.094 Min. : 78.8 Min. : 72.1
## 1st Qu.:5.381 1st Qu.:146.4 1st Qu.:128.3
## Median :6.137 Median :187.8 Median :170.4
## Mean :6.279 Mean :204.3 Mean :176.4
## 3rd Qu.:7.131 3rd Qu.:240.9 3rd Qu.:212.0
## Max. :9.986 Max. :369.5 Max. :309.5
## NA's :168 NA's :300 NA's :180Minimum and Maximum
DE0 <- c("DE0",min(f$DE.0),max(f$DE.0))
DE1 <- c("DE1",min(f$DE.1),max(f$DE.1))
DE7 <- c("DE7",min(f$DE7),max(f$DE7))
DE14 <- c("DE14",min(f$DE14),max(f$DE14))
TP0 <- c("TP0",min(f$TP.0[complete.cases(f$TP.0)]),max(f$TP.0[complete.cases(f$TP.0)]))
TP14 <- c("TP15",min(f$TP.14[complete.cases(f$TP.14)]),max(f$TP.14[complete.cases(f$TP.14)]))
VHN0 <- c("VHN0",min(f$VHN.0[complete.cases(f$VHN.0)]),max(f$VHN.0[complete.cases(f$VHN.0)]))
VHN14 <- c("VHN14",min(f$VHN.14[complete.cases(f$VHN.14)]),max(f$VHN.14[complete.cases(f$VHN.14)]))
df <- data.frame(rbind(DE0,DE1,DE7,DE14,TP0,TP14,VHN0,VHN14))
colnames(df) <- c("Variable","Min Value", "Max Value")
kable(df,caption = "Minimum and Maximum value of each variable")| Variable | Min Value | Max Value | |
|---|---|---|---|
| DE0 | DE0 | 0.03 | 1.84 |
| DE1 | DE1 | 0.38 | 3.97 |
| DE7 | DE7 | 0.55 | 4.99 |
| DE14 | DE14 | 0.66 | 6.61 |
| TP0 | TP0 | 2.92710909397343 | 10.2050177739622 |
| TP14 | TP15 | 3.09417792201952 | 9.98570391778946 |
| VHN0 | VHN0 | 78.8 | 369.5 |
| VHN14 | VHN14 | 72.1 | 309.5 |
Range of each variable
DE0 <- c("DE0",max(f$DE.0)-min(f$DE.0))
DE1 <- c("DE1",max(f$DE.1)-min(f$DE.1))
DE7 <- c("DE7",max(f$DE7)-min(f$DE7))
DE14 <- c("DE14",max(f$DE14)-min(f$DE14))
TP0 <- c("TP0",max(f$TP.0[complete.cases(f$TP.0)])-min(f$TP.0[complete.cases(f$TP.0)]))
TP14 <- c("TP15",max(f$TP.14[complete.cases(f$TP.14)])-min(f$TP.14[complete.cases(f$TP.14)]))
VHN0 <- c("VHN0",max(f$VHN.0[complete.cases(f$VHN.0)])-min(f$VHN.0[complete.cases(f$VHN.0)]))
VHN14 <- c("VHN14",max(f$VHN.14[complete.cases(f$VHN.14)])-min(f$VHN.14[complete.cases(f$VHN.14)]))
df <- data.frame(rbind(DE0,DE1,DE7,DE14,TP0,TP14,VHN0,VHN14))
colnames(df) <- c("Variable","Range")
kable(df,caption = "Range of each variable")| Variable | Range | |
|---|---|---|
| DE0 | DE0 | 1.81 |
| DE1 | DE1 | 3.59 |
| DE7 | DE7 | 4.44 |
| DE14 | DE14 | 5.95 |
| TP0 | TP0 | 7.2779086799888 |
| TP14 | TP15 | 6.89152599576994 |
| VHN0 | VHN0 | 290.7 |
| VHN14 | VHN14 | 237.4 |
Summary of Data by each group
by(f, f$Groups, summary)## f$Groups: Control
## Groups Groups.1 Material Material.1 DE.0
## Control :120 1:120 CS :30 1:30 Min. :0.030
## Regular dentifrice : 0 2: 0 GB :30 2:30 1st Qu.:0.470
## Whitening dentifrice: 0 3: 0 RC :30 3:30 Median :0.825
## RC : 0 4:30 Mean :0.820
## VE :30 3rd Qu.:1.170
## Max. :1.840
##
## DE.1 DE7 DE14 TP.0
## Min. :0.3800 Min. :0.550 Min. :0.660 Min. : 2.927
## 1st Qu.:0.8275 1st Qu.:1.090 1st Qu.:1.410 1st Qu.: 6.671
## Median :1.0000 Median :1.345 Median :1.730 Median : 6.879
## Mean :1.0422 Mean :1.413 Mean :1.966 Mean : 7.016
## 3rd Qu.:1.1750 3rd Qu.:1.692 3rd Qu.:2.527 3rd Qu.: 7.502
## Max. :1.9200 Max. :2.830 Max. :4.510 Max. :10.205
## NA's :56
## TP.14 VHN.0 VHN.14
## Min. :3.986 Min. : 78.8 Min. : 72.4
## 1st Qu.:6.351 1st Qu.:146.4 1st Qu.:128.9
## Median :6.866 Median :187.8 Median :155.8
## Mean :6.837 Mean :204.3 Mean :170.5
## 3rd Qu.:7.381 3rd Qu.:240.9 3rd Qu.:193.6
## Max. :8.996 Max. :369.5 Max. :304.2
## NA's :56 NA's :60 NA's :60
## ------------------------------------------------------------
## f$Groups: Regular dentifrice
## Groups Groups.1 Material Material.1 DE.0
## Control : 0 1: 0 CS :30 1:30 Min. :0.030
## Regular dentifrice :120 2:120 GB :30 2:30 1st Qu.:0.470
## Whitening dentifrice: 0 3: 0 RC :30 3:30 Median :0.825
## RC : 0 4:30 Mean :0.820
## VE :30 3rd Qu.:1.170
## Max. :1.840
##
## DE.1 DE7 DE14 TP.0 TP.14
## Min. :0.380 Min. :0.810 Min. :1.210 Min. : NA Min. :4.342
## 1st Qu.:1.012 1st Qu.:1.512 1st Qu.:2.163 1st Qu.: NA 1st Qu.:5.222
## Median :1.885 Median :2.815 Median :3.910 Median : NA Median :5.774
## Mean :1.954 Mean :2.699 Mean :3.566 Mean :NaN Mean :6.077
## 3rd Qu.:2.860 3rd Qu.:3.873 3rd Qu.:4.605 3rd Qu.: NA 3rd Qu.:6.640
## Max. :3.970 Max. :4.990 Max. :6.610 Max. : NA Max. :9.986
## NA's :120 NA's :56
## VHN.0 VHN.14
## Min. : NA Min. : 72.1
## 1st Qu.: NA 1st Qu.:128.3
## Median : NA Median :169.2
## Mean :NaN Mean :174.5
## 3rd Qu.: NA 3rd Qu.:212.9
## Max. : NA Max. :288.0
## NA's :120 NA's :60
## ------------------------------------------------------------
## f$Groups: Whitening dentifrice
## Groups Groups.1 Material Material.1 DE.0
## Control : 0 1: 0 CS :30 1:30 Min. :0.030
## Regular dentifrice : 0 2: 0 GB :30 2:30 1st Qu.:0.470
## Whitening dentifrice:120 3:120 RC : 0 3:30 Median :0.825
## RC :30 4:30 Mean :0.820
## VE :30 3rd Qu.:1.170
## Max. :1.840
##
## DE.1 DE7 DE14 TP.0 TP.14
## Min. :0.990 Min. :1.040 Min. :1.860 Min. : NA Min. :3.094
## 1st Qu.:1.475 1st Qu.:2.188 1st Qu.:3.265 1st Qu.: NA 1st Qu.:5.140
## Median :1.950 Median :3.015 Median :3.965 Median : NA Median :5.679
## Mean :2.050 Mean :2.884 Mean :3.951 Mean :NaN Mean :5.924
## 3rd Qu.:2.550 3rd Qu.:3.453 3rd Qu.:4.758 3rd Qu.: NA 3rd Qu.:6.768
## Max. :3.690 Max. :4.910 Max. :6.000 Max. : NA Max. :8.716
## NA's :120 NA's :56
## VHN.0 VHN.14
## Min. : NA Min. : 75.1
## 1st Qu.: NA 1st Qu.:150.8
## Median : NA Median :176.8
## Mean :NaN Mean :184.4
## 3rd Qu.: NA 3rd Qu.:215.8
## Max. : NA Max. :309.5
## NA's :120 NA's :60Summary of Data by each Material
by(f, f$Material, summary)## f$Material: CS
## Groups Groups.1 Material Material.1 DE.0
## Control :30 1:30 CS :90 1:90 Min. :0.0300
## Regular dentifrice :30 2:30 GB : 0 2: 0 1st Qu.:0.2400
## Whitening dentifrice:30 3:30 RC : 0 3: 0 Median :0.8500
## RC : 0 4: 0 Mean :0.7623
## VE : 0 3rd Qu.:1.1700
## Max. :1.7700
##
## DE.1 DE7 DE14 TP.0
## Min. :0.380 Min. :0.810 Min. :1.210 Min. :2.927
## 1st Qu.:0.620 1st Qu.:1.150 1st Qu.:1.390 1st Qu.:5.600
## Median :0.850 Median :1.460 Median :1.550 Median :6.296
## Mean :0.989 Mean :1.775 Mean :2.196 Mean :6.054
## 3rd Qu.:1.240 3rd Qu.:2.328 3rd Qu.:2.795 3rd Qu.:6.872
## Max. :2.470 Max. :3.960 Max. :5.300 Max. :7.048
## NA's :74
## TP.14 VHN.0 VHN.14
## Min. :3.094 Min. :78.80 Min. :72.10
## 1st Qu.:5.247 1st Qu.:81.20 1st Qu.:74.60
## Median :5.670 Median :82.90 Median :76.20
## Mean :5.905 Mean :82.41 Mean :76.73
## 3rd Qu.:6.364 3rd Qu.:83.60 3rd Qu.:78.30
## Max. :8.996 Max. :86.10 Max. :83.50
## NA's :42 NA's :75 NA's :45
## ------------------------------------------------------------
## f$Material: GB
## Groups Groups.1 Material Material.1 DE.0
## Control :30 1:30 CS : 0 1: 0 Min. :0.4700
## Regular dentifrice :30 2:30 GB :90 2:90 1st Qu.:0.5600
## Whitening dentifrice:30 3:30 RC : 0 3: 0 Median :0.7400
## RC : 0 4: 0 Mean :0.8207
## VE : 0 3rd Qu.:0.9800
## Max. :1.8300
##
## DE.1 DE7 DE14 TP.0
## Min. :0.810 Min. :0.550 Min. :0.660 Min. : 6.131
## 1st Qu.:1.090 1st Qu.:1.050 1st Qu.:1.853 1st Qu.: 6.785
## Median :1.310 Median :1.560 Median :2.575 Median : 6.919
## Mean :1.351 Mean :1.489 Mean :2.654 Mean : 7.269
## 3rd Qu.:1.490 3rd Qu.:1.772 3rd Qu.:3.460 3rd Qu.: 7.284
## Max. :2.600 Max. :2.860 Max. :5.090 Max. :10.205
## NA's :74
## TP.14 VHN.0 VHN.14
## Min. :6.066 Min. :166.5 Min. :143.2
## 1st Qu.:6.900 1st Qu.:171.3 1st Qu.:155.0
## Median :7.447 Median :176.2 Median :163.4
## Mean :7.484 Mean :176.8 Mean :163.5
## 3rd Qu.:7.914 3rd Qu.:181.1 3rd Qu.:173.8
## Max. :9.986 Max. :190.4 Max. :176.2
## NA's :42 NA's :75 NA's :45
## ------------------------------------------------------------
## f$Material: RC
## Groups Groups.1 Material Material.1 DE.0
## Control :30 1:30 CS : 0 1: 0 Min. :0.2300
## Regular dentifrice :30 2:30 GB : 0 2: 0 1st Qu.:0.4500
## Whitening dentifrice: 0 3: 0 RC :60 3: 0 Median :0.6000
## RC : 0 4:60 Mean :0.6503
## VE : 0 3rd Qu.:0.9200
## Max. :1.2600
##
## DE.1 DE7 DE14 TP.0
## Min. :0.700 Min. :1.060 Min. :1.190 Min. :7.210
## 1st Qu.:1.067 1st Qu.:1.370 1st Qu.:1.657 1st Qu.:7.540
## Median :2.135 Median :2.890 Median :3.165 Median :7.968
## Mean :2.004 Mean :2.784 Mean :3.263 Mean :8.089
## 3rd Qu.:2.860 3rd Qu.:4.005 3rd Qu.:4.830 3rd Qu.:8.532
## Max. :3.970 Max. :4.990 Max. :6.610 Max. :9.417
## NA's :44
## TP.14 VHN.0 VHN.14
## Min. :3.986 Min. :179.5 Min. :146.3
## 1st Qu.:5.009 1st Qu.:194.0 1st Qu.:151.6
## Median :5.828 Median :197.0 Median :167.4
## Mean :6.006 Mean :196.0 Mean :168.5
## 3rd Qu.:7.103 3rd Qu.:199.6 3rd Qu.:186.1
## Max. :8.472 Max. :203.2 Max. :191.9
## NA's :28 NA's :45 NA's :30
## ------------------------------------------------------------
## f$Material: RC
## Groups Groups.1 Material Material.1 DE.0
## Control : 0 1: 0 CS : 0 1: 0 Min. :0.2300
## Regular dentifrice : 0 2: 0 GB : 0 2: 0 1st Qu.:0.4525
## Whitening dentifrice:30 3:30 RC : 0 3: 0 Median :0.6000
## RC :30 4:30 Mean :0.6503
## VE : 0 3rd Qu.:0.8875
## Max. :1.2600
##
## DE.1 DE7 DE14 TP.0 TP.14
## Min. :1.240 Min. :2.020 Min. :2.740 Min. : NA Min. :3.620
## 1st Qu.:1.833 1st Qu.:2.652 1st Qu.:4.213 1st Qu.: NA 1st Qu.:4.847
## Median :2.130 Median :3.185 Median :4.705 Median : NA Median :5.390
## Mean :2.126 Mean :3.400 Mean :4.643 Mean :NaN Mean :5.527
## 3rd Qu.:2.428 3rd Qu.:4.202 3rd Qu.:5.045 3rd Qu.: NA 3rd Qu.:6.232
## Max. :3.060 Max. :4.820 Max. :5.610 Max. : NA Max. :8.163
## NA's :30 NA's :14
## VHN.0 VHN.14
## Min. : NA Min. :177.3
## 1st Qu.: NA 1st Qu.:179.9
## Median : NA Median :183.8
## Mean :NaN Mean :183.3
## 3rd Qu.: NA 3rd Qu.:185.5
## Max. : NA Max. :189.4
## NA's :30 NA's :15
## ------------------------------------------------------------
## f$Material: VE
## Groups Groups.1 Material Material.1 DE.0
## Control :30 1:30 CS : 0 1: 0 Min. :0.120
## Regular dentifrice :30 2:30 GB : 0 2: 0 1st Qu.:0.990
## Whitening dentifrice:30 3:30 RC : 0 3:90 Median :1.210
## RC : 0 4: 0 Mean :1.047
## VE :90 3rd Qu.:1.380
## Max. :1.840
##
## DE.1 DE7 DE14 TP.0
## Min. :0.990 Min. :1.420 Min. :2.440 Min. :6.149
## 1st Qu.:1.540 1st Qu.:2.072 1st Qu.:3.365 1st Qu.:6.534
## Median :2.485 Median :3.280 Median :4.030 Median :6.688
## Mean :2.343 Mean :3.074 Mean :4.071 Mean :6.653
## 3rd Qu.:3.005 3rd Qu.:3.632 3rd Qu.:4.800 3rd Qu.:6.774
## Max. :3.750 Max. :4.910 Max. :6.000 Max. :7.186
## NA's :74
## TP.14 VHN.0 VHN.14
## Min. :4.342 Min. :354.2 Min. :272.3
## 1st Qu.:5.316 1st Qu.:359.0 1st Qu.:284.7
## Median :5.939 Median :360.5 Median :295.3
## Mean :5.882 Mean :362.0 Mean :292.1
## 3rd Qu.:6.430 3rd Qu.:366.6 3rd Qu.:299.2
## Max. :7.856 Max. :369.5 Max. :309.5
## NA's :42 NA's :75 NA's :45Mean of each variable
DE0 <- c("DE0",mean(f$DE.0))
DE1 <- c("DE1",mean(f$DE.1))
DE7 <- c("DE7",mean(f$DE7))
DE14 <- c("DE14",mean(f$DE14))
TP0 <- c("TP0",mean(f$TP.0[complete.cases(f$TP.0)]))
TP14 <- c("TP15",mean(f$TP.14[complete.cases(f$TP.14)]))
VHN0 <- c("VHN0",mean(f$VHN.0[complete.cases(f$VHN.0)]))
VHN14 <- c("VHN14",mean(f$VHN.14[complete.cases(f$VHN.14)]))
df <- data.frame(rbind(DE0,DE1,DE7,DE14,TP0,TP14,VHN0,VHN14))
colnames(df) <- c("Variable","Mean Value")
kable(df,caption = "Mean of each variable")| Variable | Mean Value | |
|---|---|---|
| DE0 | DE0 | 0.82 |
| DE1 | DE1 | 1.68205555555556 |
| DE7 | DE7 | 2.33172222222222 |
| DE14 | DE14 | 3.16105555555556 |
| TP0 | TP0 | 7.01637932999703 |
| TP14 | TP15 | 6.27924091906769 |
| VHN0 | VHN0 | 204.318333333333 |
| VHN14 | VHN14 | 176.439444444444 |
Median of each variable
DE0 <- c("DE0",median(f$DE.0))
DE1 <- c("DE1",median(f$DE.1))
DE7 <- c("DE7",median(f$DE7))
DE14 <- c("DE14",median(f$DE14))
TP0 <- c("TP0",median(f$TP.0[complete.cases(f$TP.0)]))
TP14 <- c("TP15",median(f$TP.14[complete.cases(f$TP.14)]))
VHN0 <- c("VHN0",median(f$VHN.0[complete.cases(f$VHN.0)]))
VHN14 <- c("VHN14",median(f$VHN.14[complete.cases(f$VHN.14)]))
df <- data.frame(rbind(DE0,DE1,DE7,DE14,TP0,TP14,VHN0,VHN14))
colnames(df) <- c("Variable","Median Value")
kable(df,caption = "Median of each variable")| Variable | Median Value | |
|---|---|---|
| DE0 | DE0 | 0.825 |
| DE1 | DE1 | 1.44 |
| DE7 | DE7 | 1.995 |
| DE14 | DE14 | 3.17 |
| TP0 | TP0 | 6.87938232456182 |
| TP14 | TP15 | 6.1371069648664 |
| VHN0 | VHN0 | 187.75 |
| VHN14 | VHN14 | 170.45 |
Standard Deviation of each variable
DE0 <- c("DE0",sd(f$DE.0))
DE1 <- c("DE1",sd(f$DE.1))
DE7 <- c("DE7",sd(f$DE7))
DE14 <- c("DE14",sd(f$DE14))
TP0 <- c("TP0",sd(f$TP.0[complete.cases(f$TP.0)]))
TP14 <- c("TP15",sd(f$TP.14[complete.cases(f$TP.14)]))
VHN0 <- c("VHN0",sd(f$VHN.0[complete.cases(f$VHN.0)]))
VHN14 <- c("VHN14",sd(f$VHN.14[complete.cases(f$VHN.14)]))
df <- data.frame(rbind(DE0,DE1,DE7,DE14,TP0,TP14,VHN0,VHN14))
colnames(df) <- c("Variable","Standard Deviation")
kable(df,caption = "Standard Deviation of each variable")| Variable | Standard Deviation | |
|---|---|---|
| DE0 | DE0 | 0.442472793177106 |
| DE1 | DE1 | 0.857843508088838 |
| DE7 | DE7 | 1.16178823386211 |
| DE14 | DE14 | 1.42081207789534 |
| TP0 | TP0 | 1.09812749949824 |
| TP14 | TP15 | 1.21552974031525 |
| VHN0 | VHN0 | 101.678830507861 |
| VHN14 | VHN14 | 77.5675755109012 |
Variance of each variable
DE0 <- c("DE0",var(f$DE.0))
DE1 <- c("DE1",var(f$DE.1))
DE7 <- c("DE7",var(f$DE7))
DE14 <- c("DE14",var(f$DE14))
TP0 <- c("TP0",var(f$TP.0[complete.cases(f$TP.0)]))
TP14 <- c("TP15",var(f$TP.14[complete.cases(f$TP.14)]))
VHN0 <- c("VHN0",var(f$VHN.0[complete.cases(f$VHN.0)]))
VHN14 <- c("VHN14",var(f$VHN.14[complete.cases(f$VHN.14)]))
df <- data.frame(rbind(DE0,DE1,DE7,DE14,TP0,TP14,VHN0,VHN14))
colnames(df) <- c("Variable","Variance")
kable(df,caption = "Variance of each variable")| Variable | Variance | |
|---|---|---|
| DE0 | DE0 | 0.19578217270195 |
| DE1 | DE1 | 0.735895484370164 |
| DE7 | DE7 | 1.34975190034045 |
| DE14 | DE14 | 2.01870696069328 |
| TP0 | TP0 | 1.20588400515426 |
| TP14 | TP15 | 1.47751254959086 |
| VHN0 | VHN0 | 10338.5845734463 |
| VHN14 | VHN14 | 6016.72877063935 |
Detailed Stats about each variable
stat.desc(f,basic = T,norm = T)## Groups Groups.1 Material Material.1 DE.0 DE.1
## nbr.val NA NA NA NA 3.600000e+02 3.600000e+02
## nbr.null NA NA NA NA 0.000000e+00 0.000000e+00
## nbr.na NA NA NA NA 0.000000e+00 0.000000e+00
## min NA NA NA NA 3.000000e-02 3.800000e-01
## max NA NA NA NA 1.840000e+00 3.970000e+00
## range NA NA NA NA 1.810000e+00 3.590000e+00
## sum NA NA NA NA 2.952000e+02 6.055400e+02
## median NA NA NA NA 8.250000e-01 1.440000e+00
## mean NA NA NA NA 8.200000e-01 1.682056e+00
## SE.mean NA NA NA NA 2.332036e-02 4.521232e-02
## CI.mean NA NA NA NA 4.586169e-02 8.891428e-02
## var NA NA NA NA 1.957822e-01 7.358955e-01
## std.dev NA NA NA NA 4.424728e-01 8.578435e-01
## coef.var NA NA NA NA 5.396010e-01 5.099971e-01
## skewness NA NA NA NA 1.859398e-01 6.281323e-01
## skew.2SE NA NA NA NA 7.231307e-01 2.442842e+00
## kurtosis NA NA NA NA -8.592988e-01 -6.722446e-01
## kurt.2SE NA NA NA NA -1.675476e+00 -1.310755e+00
## normtest.W NA NA NA NA 9.715510e-01 9.323120e-01
## normtest.p NA NA NA NA 1.656365e-06 1.022359e-11
## DE7 DE14 TP.0 TP.14 VHN.0
## nbr.val 3.600000e+02 3.600000e+02 64.000000000 192.0000000 6.000000e+01
## nbr.null 0.000000e+00 0.000000e+00 0.000000000 0.0000000 0.000000e+00
## nbr.na 0.000000e+00 0.000000e+00 296.000000000 168.0000000 3.000000e+02
## min 5.500000e-01 6.600000e-01 2.927109094 3.0941779 7.880000e+01
## max 4.990000e+00 6.610000e+00 10.205017774 9.9857039 3.695000e+02
## range 4.440000e+00 5.950000e+00 7.277908680 6.8915260 2.907000e+02
## sum 8.394200e+02 1.137980e+03 449.048277120 1205.6142565 1.225910e+04
## median 1.995000e+00 3.170000e+00 6.879382325 6.1371070 1.877500e+02
## mean 2.331722e+00 3.161056e+00 7.016379330 6.2792409 2.043183e+02
## SE.mean 6.123162e-02 7.488337e-02 0.137265937 0.0877233 1.312668e+01
## CI.mean 1.204177e-01 1.472652e-01 0.274304088 0.1730309 2.626643e+01
## var 1.349752e+00 2.018707e+00 1.205884005 1.4775125 1.033858e+04
## std.dev 1.161788e+00 1.420812e+00 1.098127499 1.2155297 1.016788e+02
## coef.var 4.982533e-01 4.494739e-01 0.156509141 0.1935791 4.976491e-01
## skewness 5.606173e-01 1.561504e-01 -0.204526323 0.2707034 4.975577e-01
## skew.2SE 2.180273e+00 6.072778e-01 -0.341643571 0.7716025 8.059079e-01
## kurtosis -8.750807e-01 -1.162157e+00 2.481283044 -0.1610153 -1.026537e+00
## kurt.2SE -1.706248e+00 -2.265995e+00 2.101032952 -0.2306246 -8.435094e-01
## normtest.W 9.249549e-01 9.498039e-01 0.931966013 0.9905939 8.282249e-01
## normtest.p 1.864326e-12 1.018096e-09 0.001632336 0.2430921 7.347752e-07
## VHN.14
## nbr.val 1.800000e+02
## nbr.null 0.000000e+00
## nbr.na 1.800000e+02
## min 7.210000e+01
## max 3.095000e+02
## range 2.374000e+02
## sum 3.175910e+04
## median 1.704500e+02
## mean 1.764394e+02
## SE.mean 5.781546e+00
## CI.mean 1.140876e+01
## var 6.016729e+03
## std.dev 7.756758e+01
## coef.var 4.396272e-01
## skewness 3.083468e-01
## skew.2SE 8.514241e-01
## kurtosis -1.024336e+00
## kurt.2SE -1.421758e+00
## normtest.W 8.768612e-01
## normtest.p 5.517536e-11Histograms of each variable
par(mfrow=c(2,2))
hist(f$DE.0,xlab = "Values",main = "DE0", col = "red")
hist(f$DE.1,xlab = "Values",main = "DE1", col = "green")
hist(f$DE7,xlab = "Values",main = "DE7", col = "blue")
hist(f$DE14,xlab = "Values",main = "DE14",col = "pink")
par(mfrow=c(1,2))
hist(f$TP.0,xlab = "Values",main = "TP0",col = "red")
hist(f$TP.14,xlab = "Values",main = "TP14",col = "green")
par(mfrow=c(1,2))
hist(f$VHN.0,xlab = "Values",main = "VHN0",col = "red")
hist(f$VHN.14,xlab = "Values",main = "VHN14",col = "blue")
Plots about each group
ggplot(f) +
aes(x = Groups, y = DE.0, colour = Groups) +
geom_point() +
scale_color_hue()
ggplot(f) +
aes(x = Groups, y = DE.1, colour = Groups) +
geom_point() +
scale_color_hue()
ggplot(f) +
aes(x = Groups, y = DE7, colour = Groups) +
geom_point() +
scale_color_hue()
ggplot(f) +
aes(x = Groups, y = DE14, colour = Groups) +
geom_point() +
scale_color_hue()
ggplot(f) +
aes(x = Groups, y = TP.0, colour = Groups) +
geom_point() +
scale_color_hue()
ggplot(f) +
aes(x = Groups, y = TP.14, colour = Groups) +
geom_point() +
scale_color_hue()
ggplot(f) +
aes(x = Groups, y = VHN.0, colour = Groups) +
geom_point() +
scale_color_hue()
ggplot(f) +
aes(x = Groups, y = VHN.14, colour = Groups) +
geom_point() +
scale_color_hue()
Correlation
dat <- f[, 5:8]
round(cor(dat), 2)## DE.0 DE.1 DE7 DE14
## DE.0 1.00 0.05 0.07 0.09
## DE.1 0.05 1.00 0.78 0.75
## DE7 0.07 0.78 1.00 0.83
## DE14 0.09 0.75 0.83 1.00Normality Test
Density plot and Q-Q plot can be used to check normality visually.
ggdensity(f$DE.0,
main = "Density plot of DE0",
xlab = "DE0")
ggdensity(f$DE.1,
main = "Density plot of DE0",
xlab = "DE1")
ggdensity(f$DE7,
main = "Density plot of DE0",
xlab = "DE7")
ggdensity(f$DE14,
main = "Density plot of DE0",
xlab = "DE14")