Statystyki opisowe
Katarzyna Smoter
05 06 2020
Katarzyna Smoter
kierunek: geoinformacja
wydział: Geodecji Górniczej i Inżynierii Środowiska
1. Dodanie odpowiednich bibliotek
Do dalszej pracy na danych w R dodałam odpowiednie biblioteki.
library(ggplot2)
library(tidyverse)
library(Hmisc)
library(pastecs)
library(psych)
library(doBy)
library(sm)
library(ggpubr)2. Podstawowe operacje na danych
Do przeprowadzenia dalszych analiz wybrałam dane “diamonds” z pakietu ggplot. W następnym kroku postanowiłam sprawdzić jakie kolumny zawiera moja tabela “diamonds”. Następnie wybrałam kolumny zawierające wartości tekstowe, i sprawdziłam co zawierają i w jakich ilociach. Ustawiłam także kolumne “cut” jako kolumne główną.
## tibble [53,940 x 10] (S3: tbl_df/tbl/data.frame)
## $ carat : num [1:53940] 0.23 0.21 0.23 0.29 0.31 0.24 0.24 0.26 0.22 0.23 ...
## $ cut : Ord.factor w/ 5 levels "Fair"<"Good"<..: 5 4 2 4 2 3 3 3 1 3 ...
## $ color : Ord.factor w/ 7 levels "D"<"E"<"F"<"G"<..: 2 2 2 6 7 7 6 5 2 5 ...
## $ clarity: Ord.factor w/ 8 levels "I1"<"SI2"<"SI1"<..: 2 3 5 4 2 6 7 3 4 5 ...
## $ depth : num [1:53940] 61.5 59.8 56.9 62.4 63.3 62.8 62.3 61.9 65.1 59.4 ...
## $ table : num [1:53940] 55 61 65 58 58 57 57 55 61 61 ...
## $ price : int [1:53940] 326 326 327 334 335 336 336 337 337 338 ...
## $ x : num [1:53940] 3.95 3.89 4.05 4.2 4.34 3.94 3.95 4.07 3.87 4 ...
## $ y : num [1:53940] 3.98 3.84 4.07 4.23 4.35 3.96 3.98 4.11 3.78 4.05 ...
## $ z : num [1:53940] 2.43 2.31 2.31 2.63 2.75 2.48 2.47 2.53 2.49 2.39 ...## [1] "carat" "cut" "color" "clarity" "depth" "table" "price"
## [8] "x" "y" "z"## [1] Ideal Premium Good Very Good Fair
## Levels: Fair < Good < Very Good < Premium < Ideal##
## Fair Good Very Good Premium Ideal
## 1610 4906 12082 13791 21551## # A tibble: 2 x 10
## carat cut color clarity depth table price x y z
## <dbl> <ord> <ord> <ord> <dbl> <dbl> <int> <dbl> <dbl> <dbl>
## 1 0.23 Ideal E SI2 61.5 55 326 3.95 3.98 2.43
## 2 0.21 Premium E SI1 59.8 61 326 3.89 3.84 2.31## [1] E I J H F G D
## Levels: D < E < F < G < H < I < J##
## D E F G H I J
## 6775 9797 9542 11292 8304 5422 2808## [1] SI2 SI1 VS1 VS2 VVS2 VVS1 I1 IF
## Levels: I1 < SI2 < SI1 < VS2 < VS1 < VVS2 < VVS1 < IF##
## I1 SI2 SI1 VS2 VS1 VVS2 VVS1 IF
## 741 9194 13065 12258 8171 5066 3655 17903. Dodawanie kolumny
Następnie dodałam nową kolumne zawierającą wartości “kod1”, “kod2” na przemian, zmieniłam także typ kolumny na factor.
4. Podstawowe statystyki
Zrobiłam także podstawowe statystyki opisowe.
## carat cut color clarity depth
## Min. :0.2000 Fair : 1610 D: 6775 SI1 :13065 Min. :43.00
## 1st Qu.:0.4000 Good : 4906 E: 9797 VS2 :12258 1st Qu.:61.00
## Median :0.7000 Very Good:12082 F: 9542 SI2 : 9194 Median :61.80
## Mean :0.7979 Premium :13791 G:11292 VS1 : 8171 Mean :61.75
## 3rd Qu.:1.0400 Ideal :21551 H: 8304 VVS2 : 5066 3rd Qu.:62.50
## Max. :5.0100 I: 5422 VVS1 : 3655 Max. :79.00
## J: 2808 (Other): 2531
## table price x y
## Min. :43.00 Min. : 326 Min. : 0.000 Min. : 0.000
## 1st Qu.:56.00 1st Qu.: 950 1st Qu.: 4.710 1st Qu.: 4.720
## Median :57.00 Median : 2401 Median : 5.700 Median : 5.710
## Mean :57.46 Mean : 3933 Mean : 5.731 Mean : 5.735
## 3rd Qu.:59.00 3rd Qu.: 5324 3rd Qu.: 6.540 3rd Qu.: 6.540
## Max. :95.00 Max. :18823 Max. :10.740 Max. :58.900
##
## z kod
## Min. : 0.000 kod1:26970
## 1st Qu.: 2.910 kod2:26970
## Median : 3.530
## Mean : 3.539
## 3rd Qu.: 4.040
## Max. :31.800
## 5. Tworzenie wykresów
Utworzyłam także wykresy od wszystkich kolumn.
## [1] 11nazwa=names(diamonds)
par(mfrow=c(4,3))
for(i in 1:length(diamonds)){
plot(diamonds[,i],ylab=nazwa[i])
}
par(mfrow=c(1,1))
6. Sapply i describe
Utworzyłam statystyki za pomocą sapply i describe.
## carat cut color clarity depth table
## 0.7979397 NA NA NA 61.7494049 57.4571839
## price x y z kod
## 3932.7997219 5.7311572 5.7345260 3.5387338 NA## vars n mean sd median trimmed mad min max
## carat 1 53940 0.80 0.47 0.70 0.73 0.47 0.2 5.01
## cut* 2 53940 3.90 1.12 4.00 4.04 1.48 1.0 5.00
## color* 3 53940 3.59 1.70 4.00 3.55 1.48 1.0 7.00
## clarity* 4 53940 4.05 1.65 4.00 3.91 1.48 1.0 8.00
## depth 5 53940 61.75 1.43 61.80 61.78 1.04 43.0 79.00
## table 6 53940 57.46 2.23 57.00 57.32 1.48 43.0 95.00
## price 7 53940 3932.80 3989.44 2401.00 3158.99 2475.94 326.0 18823.00
## x 8 53940 5.73 1.12 5.70 5.66 1.38 0.0 10.74
## y 9 53940 5.73 1.14 5.71 5.66 1.36 0.0 58.90
## z 10 53940 3.54 0.71 3.53 3.49 0.85 0.0 31.80
## kod* 11 53940 1.50 0.50 1.50 1.50 0.74 1.0 2.00
## range skew kurtosis se
## carat 4.81 1.12 1.26 0.00
## cut* 4.00 -0.72 -0.40 0.00
## color* 6.00 0.19 -0.87 0.01
## clarity* 7.00 0.55 -0.39 0.01
## depth 36.00 -0.08 5.74 0.01
## table 52.00 0.80 2.80 0.01
## price 18497.00 1.62 2.18 17.18
## x 10.74 0.38 -0.62 0.00
## y 58.90 2.43 91.20 0.00
## z 31.80 1.52 47.08 0.00
## kod* 1.00 0.00 -2.00 0.00## carat cut color clarity depth table
## nbr.val 5.394000e+04 NA NA NA 5.394000e+04 5.394000e+04
## nbr.null 0.000000e+00 NA NA NA 0.000000e+00 0.000000e+00
## nbr.na 0.000000e+00 NA NA NA 0.000000e+00 0.000000e+00
## min 2.000000e-01 NA NA NA 4.300000e+01 4.300000e+01
## max 5.010000e+00 NA NA NA 7.900000e+01 9.500000e+01
## range 4.810000e+00 NA NA NA 3.600000e+01 5.200000e+01
## sum 4.304087e+04 NA NA NA 3.330763e+06 3.099241e+06
## median 7.000000e-01 NA NA NA 6.180000e+01 5.700000e+01
## mean 7.979397e-01 NA NA NA 6.174940e+01 5.745718e+01
## SE.mean 2.040954e-03 NA NA NA 6.168448e-03 9.621063e-03
## CI.mean.0.95 4.000286e-03 NA NA NA 1.209021e-02 1.885736e-02
## var 2.246867e-01 NA NA NA 2.052404e+00 4.992948e+00
## std.dev 4.740112e-01 NA NA NA 1.432621e+00 2.234491e+00
## coef.var 5.940439e-01 NA NA NA 2.320057e-02 3.888966e-02
## price x y z kod
## nbr.val 5.394000e+04 5.394000e+04 5.394000e+04 5.394000e+04 NA
## nbr.null 0.000000e+00 8.000000e+00 7.000000e+00 2.000000e+01 NA
## nbr.na 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 NA
## min 3.260000e+02 0.000000e+00 0.000000e+00 0.000000e+00 NA
## max 1.882300e+04 1.074000e+01 5.890000e+01 3.180000e+01 NA
## range 1.849700e+04 1.074000e+01 5.890000e+01 3.180000e+01 NA
## sum 2.121352e+08 3.091386e+05 3.093203e+05 1.908793e+05 NA
## median 2.401000e+03 5.700000e+00 5.710000e+00 3.530000e+00 NA
## mean 3.932800e+03 5.731157e+00 5.734526e+00 3.538734e+00 NA
## SE.mean 1.717736e+01 4.829974e-03 4.917698e-03 3.038533e-03 NA
## CI.mean.0.95 3.366776e+01 9.466787e-03 9.638727e-03 5.955549e-03 NA
## var 1.591563e+07 1.258347e+00 1.304472e+00 4.980109e-01 NA
## std.dev 3.989440e+03 1.121761e+00 1.142135e+00 7.056988e-01 NA
## coef.var 1.014402e+00 1.957302e-01 1.991681e-01 1.994213e-01 NA## vars n mean sd median trimmed mad min max
## carat 1 53940 0.80 0.47 0.70 0.73 0.47 0.2 5.01
## cut* 2 53940 3.90 1.12 4.00 4.04 1.48 1.0 5.00
## color* 3 53940 3.59 1.70 4.00 3.55 1.48 1.0 7.00
## clarity* 4 53940 4.05 1.65 4.00 3.91 1.48 1.0 8.00
## depth 5 53940 61.75 1.43 61.80 61.78 1.04 43.0 79.00
## table 6 53940 57.46 2.23 57.00 57.32 1.48 43.0 95.00
## price 7 53940 3932.80 3989.44 2401.00 3158.99 2475.94 326.0 18823.00
## x 8 53940 5.73 1.12 5.70 5.66 1.38 0.0 10.74
## y 9 53940 5.73 1.14 5.71 5.66 1.36 0.0 58.90
## z 10 53940 3.54 0.71 3.53 3.49 0.85 0.0 31.80
## kod* 11 53940 1.50 0.50 1.50 1.50 0.74 1.0 2.00
## range skew kurtosis se
## carat 4.81 1.12 1.26 0.00
## cut* 4.00 -0.72 -0.40 0.00
## color* 6.00 0.19 -0.87 0.01
## clarity* 7.00 0.55 -0.39 0.01
## depth 36.00 -0.08 5.74 0.01
## table 52.00 0.80 2.80 0.01
## price 18497.00 1.62 2.18 17.18
## x 10.74 0.38 -0.62 0.00
## y 58.90 2.43 91.20 0.00
## z 31.80 1.52 47.08 0.00
## kod* 1.00 0.00 -2.00 0.00##
## Descriptive statistics by group
## group: kod1
## vars n mean sd median trimmed mad min max
## carat 1 26970 0.80 0.48 0.70 0.74 0.47 0.2 4.50
## cut* 2 26970 3.90 1.12 4.00 4.04 1.48 1.0 5.00
## color* 3 26970 3.58 1.70 4.00 3.54 1.48 1.0 7.00
## clarity* 4 26970 4.04 1.65 4.00 3.91 1.48 1.0 8.00
## depth 5 26970 61.75 1.43 61.80 61.79 1.04 43.0 79.00
## table 6 26970 57.45 2.23 57.00 57.31 1.48 43.0 95.00
## price 7 26970 3932.63 3989.23 2401.00 3158.89 2475.94 326.0 18818.00
## x 8 26970 5.73 1.12 5.70 5.66 1.36 0.0 10.23
## y 9 26970 5.73 1.11 5.71 5.66 1.36 0.0 10.16
## z 10 26970 3.54 0.72 3.53 3.50 0.85 0.0 31.80
## kod* 11 26970 1.00 0.00 1.00 1.00 0.00 1.0 1.00
## range skew kurtosis se
## carat 4.30 1.13 1.34 0.00
## cut* 4.00 -0.71 -0.40 0.01
## color* 6.00 0.19 -0.87 0.01
## clarity* 7.00 0.55 -0.39 0.01
## depth 36.00 0.05 5.54 0.01
## table 52.00 0.86 4.12 0.01
## price 18492.00 1.62 2.18 24.29
## x 10.23 0.39 -0.62 0.01
## y 10.16 0.39 -0.65 0.01
## z 31.80 2.61 89.38 0.00
## kod* 0.00 NaN NaN 0.00
## ------------------------------------------------------------
## group: kod2
## vars n mean sd median trimmed mad min max
## carat 1 26970 0.80 0.47 0.70 0.73 0.47 0.2 5.01
## cut* 2 26970 3.91 1.12 4.00 4.04 1.48 1.0 5.00
## color* 3 26970 3.60 1.70 4.00 3.56 1.48 1.0 7.00
## clarity* 4 26970 4.06 1.65 4.00 3.92 1.48 1.0 8.00
## depth 5 26970 61.74 1.43 61.80 61.78 1.04 43.0 79.00
## table 6 26970 57.46 2.23 57.00 57.32 1.48 44.0 79.00
## price 7 26970 3932.97 3989.72 2401.00 3159.10 2475.94 326.0 18823.00
## x 8 26970 5.73 1.12 5.69 5.66 1.36 0.0 10.74
## y 9 26970 5.73 1.17 5.71 5.66 1.36 0.0 58.90
## z 10 26970 3.54 0.70 3.52 3.49 0.85 0.0 8.06
## kod* 11 26970 2.00 0.00 2.00 2.00 0.00 2.0 2.00
## range skew kurtosis se
## carat 4.81 1.10 1.17 0.00
## cut* 4.00 -0.72 -0.39 0.01
## color* 6.00 0.19 -0.87 0.01
## clarity* 7.00 0.55 -0.40 0.01
## depth 36.00 -0.21 5.93 0.01
## table 35.00 0.73 1.49 0.01
## price 18497.00 1.62 2.18 24.29
## x 10.74 0.37 -0.62 0.01
## y 58.90 4.20 166.19 0.01
## z 8.06 0.33 -0.38 0.00
## kod* 0.00 NaN NaN 0.00## item group1 vars n mean sd median trimmed
## carat1 1 kod1 1 26970 0.7984854 0.4751665 0.70 0.7351863
## carat2 2 kod2 1 26970 0.7973941 0.4728613 0.70 0.7347446
## cut*1 3 kod1 2 26970 3.9030033 1.1165241 4.00 4.0410178
## cut*2 4 kod2 2 26970 3.9051910 1.1166954 4.00 4.0438450
## color*1 5 kod1 3 26970 3.5845384 1.7024558 4.00 3.5409251
## color*2 6 kod2 3 26970 3.6038561 1.6997294 4.00 3.5644234
## clarity*1 7 kod1 4 26970 4.0446793 1.6461309 4.00 3.9078142
## clarity*2 8 kod2 4 26970 4.0573600 1.6481468 4.00 3.9217649
## depth1 9 kod1 5 26970 61.7541861 1.4316223 61.80 61.7865406
## depth2 10 kod2 5 26970 61.7446237 1.4336302 61.80 61.7826752
## table1 11 kod1 6 26970 57.4534557 2.2340739 57.00 57.3145532
## table2 12 kod2 6 26970 57.4609121 2.2349424 57.00 57.3221496
## price1 13 kod1 7 26970 3932.6286244 3989.2349561 2401.00 3158.8863089
## price2 14 kod2 7 26970 3932.9708194 3989.7184613 2401.00 3159.0983964
## x1 15 kod1 8 26970 5.7324138 1.1224196 5.70 5.6608282
## x2 16 kod2 8 26970 5.7299006 1.1211209 5.69 5.6593252
## y1 17 kod1 9 26970 5.7343367 1.1136608 5.71 5.6633060
## y2 18 kod2 9 26970 5.7347152 1.1699364 5.71 5.6621825
## z1 19 kod1 10 26970 3.5403089 0.7155786 3.53 3.4955223
## z2 20 kod2 10 26970 3.5371587 0.6956885 3.52 3.4942445
## kod*1 21 kod1 11 26970 1.0000000 0.0000000 1.00 1.0000000
## kod*2 22 kod2 11 26970 2.0000000 0.0000000 2.00 2.0000000
## mad min max range skew kurtosis
## carat1 0.474432 0.2 4.50 4.30 1.13331065 1.3448172
## carat2 0.474432 0.2 5.01 4.81 1.09949928 1.1651945
## cut*1 1.482600 1.0 5.00 4.00 -0.71355322 -0.4033855
## cut*2 1.482600 1.0 5.00 4.00 -0.72068935 -0.3930713
## color*1 1.482600 1.0 7.00 6.00 0.19356737 -0.8673174
## color*2 1.482600 1.0 7.00 6.00 0.18518525 -0.8664942
## clarity*1 1.482600 1.0 8.00 7.00 0.54995798 -0.3887358
## clarity*2 1.482600 1.0 8.00 7.00 0.55281547 -0.4014077
## depth1 1.037820 43.0 79.00 36.00 0.04580134 5.5376313
## depth2 1.037820 43.0 79.00 36.00 -0.20981285 5.9343078
## table1 1.482600 43.0 95.00 52.00 0.86153647 4.1178222
## table2 1.482600 44.0 79.00 35.00 0.73220034 1.4872204
## price1 2475.942000 326.0 18818.00 18492.00 1.61820156 2.1767756
## price2 2475.942000 326.0 18823.00 18497.00 1.61831892 2.1772216
## x1 1.363992 0.0 10.23 10.23 0.38772844 -0.6217964
## x2 1.363992 0.0 10.74 10.74 0.36952271 -0.6150674
## y1 1.363992 0.0 10.16 10.16 0.38702787 -0.6525155
## y2 1.363992 0.0 58.90 58.90 4.19533118 166.1948031
## z1 0.845082 0.0 31.80 31.80 2.61212158 89.3848321
## z2 0.845082 0.0 8.06 8.06 0.33497846 -0.3836541
## kod*1 0.000000 1.0 1.00 0.00 NaN NaN
## kod*2 0.000000 2.0 2.00 0.00 NaN NaN
## se
## carat1 0.002893379
## carat2 0.002879342
## cut*1 0.006798727
## cut*2 0.006799770
## color*1 0.010366577
## color*2 0.010349975
## clarity*1 0.010023604
## clarity*2 0.010035879
## depth1 0.008717420
## depth2 0.008729647
## table1 0.013603700
## table2 0.013608989
## price1 24.291209674
## price2 24.294153830
## x1 0.006834626
## x2 0.006826718
## y1 0.006781292
## y2 0.007123965
## z1 0.004357294
## z2 0.004236179
## kod*1 0.000000000
## kod*2 0.0000000007. Summary
Utworzyłam statystyki za pomocą summary.
## # A tibble: 5 x 3
## cut depth.m depth.s
## <ord> <dbl> <dbl>
## 1 Fair 64.0 3.64
## 2 Good 62.4 2.17
## 3 Very Good 61.8 1.38
## 4 Premium 61.3 1.16
## 5 Ideal 61.7 0.719## # A tibble: 10 x 4
## cut kod depth.m depth.s
## <ord> <fct> <dbl> <dbl>
## 1 Fair kod1 64.2 3.54
## 2 Fair kod2 63.9 3.74
## 3 Good kod1 62.4 2.16
## 4 Good kod2 62.4 2.18
## 5 Very Good kod1 61.8 1.39
## 6 Very Good kod2 61.8 1.37
## 7 Premium kod1 61.3 1.16
## 8 Premium kod2 61.3 1.16
## 9 Ideal kod1 61.7 0.708
## 10 Ideal kod2 61.7 0.729## # A tibble: 10 x 6
## cut kod depth.m depth.s table.m table.s
## <ord> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 Fair kod1 64.2 3.54 58.9 4.04
## 2 Fair kod2 63.9 3.74 59.2 3.85
## 3 Good kod1 62.4 2.16 58.6 2.85
## 4 Good kod2 62.4 2.18 58.8 2.85
## 5 Very Good kod1 61.8 1.39 58.0 2.14
## 6 Very Good kod2 61.8 1.37 57.9 2.10
## 7 Premium kod1 61.3 1.16 58.7 1.48
## 8 Premium kod2 61.3 1.16 58.7 1.48
## 9 Ideal kod1 61.7 0.708 56.0 1.25
## 10 Ideal kod2 61.7 0.729 55.9 1.24## # A tibble: 10 x 16
## cut kod carat.m carat.s depth.m depth.s table.m table.s price.m price.s
## <ord> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Fair kod1 1.06 0.519 64.2 3.54 58.9 4.04 4450. 3626.
## 2 Fair kod2 1.04 0.514 63.9 3.74 59.2 3.85 4268. 3494.
## 3 Good kod1 0.845 0.454 62.4 2.16 58.6 2.85 3927. 3717.
## 4 Good kod2 0.853 0.454 62.4 2.18 58.8 2.85 3931. 3646.
## 5 Very~ kod1 0.802 0.458 61.8 1.39 58.0 2.14 3946. 3903.
## 6 Very~ kod2 0.810 0.461 61.8 1.37 57.9 2.10 4018. 3969.
## 7 Prem~ kod1 0.893 0.515 61.3 1.16 58.7 1.48 4570. 4323.
## 8 Prem~ kod2 0.891 0.516 61.3 1.16 58.7 1.48 4599. 4375.
## 9 Ideal kod1 0.706 0.437 61.7 0.708 56.0 1.25 3481. 3838.
## 10 Ideal kod2 0.699 0.428 61.7 0.729 55.9 1.24 3434. 3778.
## # ... with 6 more variables: x.m <dbl>, x.s <dbl>, y.m <dbl>, y.s <dbl>,
## # z.m <dbl>, z.s <dbl>8. Histogramy
Utworzyłam także histogramy.
x=diamonds$carat
h=hist(x,breaks=seq(0,5.5,0.1))
xfit <- seq(min(x), max(x), length=150)
yfit <- dnorm(xfit, mean=mean(x), sd=sd(x))
yfit <- yfit*diff(h$mids[1:2])*length(x)
lines(xfit, yfit, col="blue", lwd=2)
9. Estymator jądrowy gęstości (ang. Kernel Density Plot)
Utworzyłam estymator jądrowy gęstości.
library(sm)
sm.density.compare(diamonds$carat, diamonds$cut, xlab="carat")
cyl.f <-diamonds$cut
title(main="karat po rodzaju ciecia")
colfill <- c(2:(2+length(levels(cyl.f))))
legend(4,1.5, levels(cyl.f), fill=colfill)
11. GGboxplot
Utworzyłam boxploty.
12. Gghistogram
Utworzyłam histogramy.
gghistogram(diamonds, x = "carat", add ="mean", rug=T, color = "cut",
palette = c("#00AFBB", "#E7B800","red", "pink", "purple"))
gghistogram(diamonds, x = "carat", add = "mean",rug=T,color = "cut",
fill="cut", palette = c("#00AFBB", "#E7B800","red", "pink", "purple"))
gghistogram(diamonds, x = "carat", add = "mean",rug=T,color = "cut",
fill="cut", palette = c("#00AFBB", "#E7B800","red", "pink", "purple"),add_density = TRUE)
