AS17: Kapitel 9 - Das Programm R
Jürgen Hedderich
2020-04-29
- Aktuelle R-Umgebung zu den Beispielen
- 9.1 Befehle im Konsolfenster
- 9.2 Hilfestellung in R
- 9.3 Objekte in R
- 9.4 Fehlende Angaben (not assigned NA)
- 9.5 Auswahl und Sortierung von Daten
- 9.6 Ablaufsteuerung: logische Bedingungen und Funktionen
- 9.7 Mathematische und statistische Funktionen
- 9.8 Graphikfunktionen
Hinweis: Die Gliederung zu den Befehlen Und Ergebnissen in R orientiert sich an dem Inhaltsverzeichnis der 17. Auflage der ‘Angewandten Statistik’. Nähere Hinweise zu den verwendeten Formeln sowie Erklärungen zu den Beispielen sind in dem Buch (Ebook) nachzulesen!
Hinweis: Die thematische Gliederung zu den aufgeführten Befehlen und Beispielen orientiert sich an dem Inhaltsverzeichnis der 17. Auflage der ‘Angewandten Statistik’. Nähere Hinweise zu den verwendeten Formeln sowie Erklärungen zu den Beispielen sind in dem Buch (Ebook) nachzulesen!
Aktuelle R-Umgebung zu den Beispielen
sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18363)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=German_Germany.1252 LC_CTYPE=German_Germany.1252
## [3] LC_MONETARY=German_Germany.1252 LC_NUMERIC=C
## [5] LC_TIME=German_Germany.1252
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## loaded via a namespace (and not attached):
## [1] compiler_3.6.3 magrittr_1.5 tools_3.6.3 htmltools_0.4.0
## [5] yaml_2.2.1 Rcpp_1.0.4 stringi_1.4.6 rmarkdown_2.1
## [9] knitr_1.28 stringr_1.4.0 xfun_0.12 digest_0.6.25
## [13] rlang_0.4.5 evaluate_0.14Download von Datensätzen, die in den folgenden Beispielen verwendet werden:
Infarkt-Daten: infarkt
9.1 Befehle im Konsolfenster
mean(c(4,6,8,9)) # Mittelwertberechnung
## [1] 6.75
sqrt(5) # Wurzelfunktion
## [1] 2.236068
round(5.23454, digits=3) # Rundung auf 3 Dezimalziffern
## [1] 5.2359.2 Hilfestellung in R
# help()
# help(sqrt) # Quadratwurzel
# ?srt
# ?mean
example(mean) # arithmetischer Mittelwert
##
## mean> x <- c(0:10, 50)
##
## mean> xm <- mean(x)
##
## mean> c(xm, mean(x, trim = 0.10))
## [1] 8.75 5.509.3 Objekte in R
x <- 1:10 # numerisch
length(x)
## [1] 10
mode(x)
## [1] "numeric"name <- c("Statistik","Mathematik") # Zeichenketten
length(name)
## [1] 2
mode(name)
## [1] "character"logic <- c(TRUE, FALSE) # logisch
mode(logic)
## [1] "logical"wurzel.12 <- sqrt(12) # Variablen
wurzel.12 # Wurzel aus 12
## [1] 3.464102data(Titanic) # Datenrahmen (Tabellenstruktur)
str(Titanic) #
## 'table' num [1:4, 1:2, 1:2, 1:2] 0 0 35 0 0 0 17 0 118 154 ...
## - attr(*, "dimnames")=List of 4
## ..$ Class : chr [1:4] "1st" "2nd" "3rd" "Crew"
## ..$ Sex : chr [1:2] "Male" "Female"
## ..$ Age : chr [1:2] "Child" "Adult"
## ..$ Survived: chr [1:2] "No" "Yes"mat <- matrix(c("a","b","c","d"),
nrow=2) # Matrix
mat
## [,1] [,2]
## [1,] "a" "c"
## [2,] "b" "d"
is.matrix(mat)
## [1] TRUE
is.numeric(mat)
## [1] FALSElibrary(date) # Datumsangaben
dat <- as.date(c("15jul2008","10mar1980"))
dat
## [1] 15Jul2008 10Mar80
(dat[1] - dat[2])/360
## [1] 28.76111
dat1 <- mdy.date(7, 15, 2008)
dat2 <- mdy.date(3, 10, 1980)
str(dat1); str(dat2)
## 'date' int 17728
## 'date' int 7374
(dat1 - dat2)/360
## [1] 28.76111ls() # Objekte im 'Arbeitsspeicher'
## [1] "colorize" "dat" "dat1" "dat2" "logic" "mat"
## [7] "name" "opar" "Titanic" "wurzel.12" "x" "xm"
rm(list = ls()) # Löschen aller Objekte im Arbeitspeicher9.3.2 Erzeugen von Vektoren und Dateneingabe
1:10
## [1] 1 2 3 4 5 6 7 8 9 10
20:15
## [1] 20 19 18 17 16 15
seq(1, 5, by=0.5)
## [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
seq(1, 5, length=11)
## [1] 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8 4.2 4.6 5.0
rep(5, 20)
## [1] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
c(1, 7:9)
## [1] 1 7 8 9
c(1:5, 10.5, "next")
## [1] "1" "2" "3" "4" "5" "10.5" "next"9.3.3 Faktoren in R - Klasseneinteilungen
m <- rep(1, 15); w <- rep(2, 20)
sex <- c(m, w)
faktor <- factor(sex, levels=1:2, labels=c("männlich", "weiblich"))
summary(faktor)
## männlich weiblich
## 15 20alter <- rnorm(50, mean=40, sd=10)
summary(alter)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 11.96 33.63 38.70 40.49 48.10 63.15
alter.k <- cut(alter, breaks=c(10, 20, 30, 40, 50, 60, 70))
summary(alter.k)
## (10,20] (20,30] (30,40] (40,50] (50,60] (60,70]
## 2 6 21 13 5 39.3.4 Matrizen und Tabellen
mat <- matrix(1:9, ncol=3, byrow=T); mat
## [,1] [,2] [,3]
## [1,] 1 2 3
## [2,] 4 5 6
## [3,] 7 8 9
mat[1,] # Zeilen
## [1] 1 2 3
mat[,2] # Spalten
## [1] 2 5 8
mat[2,2] # Zellen
## [1] 5
margin.table(mat, 1) # Zeilensummen
## [1] 6 15 24
margin.table(mat, 2) # Spaltensummen
## [1] 12 15 18mat <- rbind(mat, c(10, 11, 12)); mat # Zeilen ergänzen (Verbinden)
## [,1] [,2] [,3]
## [1,] 1 2 3
## [2,] 4 5 6
## [3,] 7 8 9
## [4,] 10 11 12
mat <- cbind(mat, c(13, 14, 15, 16)); mat # Spalten ergänzen (verbinden)
## [,1] [,2] [,3] [,4]
## [1,] 1 2 3 13
## [2,] 4 5 6 14
## [3,] 7 8 9 15
## [4,] 10 11 12 16count <- matrix(c(12, 6, 5, 10), # Zeilen- / Spaltenbezeichnungen
ncol=2, byrow=T,
dimnames=list(c("Zeile 1", "Zeile 2"), c("Spalte 1", "Spalte 2")))
count
## Spalte 1 Spalte 2
## Zeile 1 12 6
## Zeile 2 5 109.3.5 Rechnen mit Matrizen
n <- 10
data <- matrix(c(11, 6,11, 9, 8, 6, 2, 7, 4, 9,10, 4,
6, 4, 9, 6, 5, 4, 1, 2, 10,10, 6, 9,
6, 8, 2, 1, 2, 2, 8, 4, 8, 2, 4,10,
9, 7, 6, 9), nrow=n, byrow=T,
dimnames = list(
c("S1","S2","S3","S4","S5","S6","S7","S8","S9","S10"),
c("V.1", "V.2", "V.3","V.4"))); data
## V.1 V.2 V.3 V.4
## S1 11 6 11 9
## S2 8 6 2 7
## S3 4 9 10 4
## S4 6 4 9 6
## S5 5 4 1 2
## S6 10 10 6 9
## S7 6 8 2 1
## S8 2 2 8 4
## S9 8 2 4 10
## S10 9 7 6 9
one <- rep(1,10); one # Vektor mit Einsen "1"
## [1] 1 1 1 1 1 1 1 1 1 1
summe <- one %*% data; summe # Summen über "inner product" mit Einsen
## V.1 V.2 V.3 V.4
## [1,] 69 58 59 61
mittel <- summe / n; mittel # Mittelwerte
## V.1 V.2 V.3 V.4
## [1,] 6.9 5.8 5.9 6.1
# Abweichungen vom Mittelwert
deviat <- data - one %*% mittel; round(deviat,2)
## V.1 V.2 V.3 V.4
## S1 4.1 0.2 5.1 2.9
## S2 1.1 0.2 -3.9 0.9
## S3 -2.9 3.2 4.1 -2.1
## S4 -0.9 -1.8 3.1 -0.1
## S5 -1.9 -1.8 -4.9 -4.1
## S6 3.1 4.2 0.1 2.9
## S7 -0.9 2.2 -3.9 -5.1
## S8 -4.9 -3.8 2.1 -2.1
## S9 1.1 -3.8 -1.9 3.9
## S10 2.1 1.2 0.1 2.9
# Kovarianzmatrix
covar <- t(deviat) %*% deviat/(n - 1); round(covar,2)
## V.1 V.2 V.3 V.4
## V.1 7.88 2.76 0.32 6.79
## V.2 2.76 7.73 0.87 -0.09
## V.3 0.32 0.87 12.77 3.46
## V.4 6.79 -0.09 3.46 10.32
# Varianzen aus der Diagonalen
varia <- diag(covar); round(varia,2)
## V.1 V.2 V.3 V.4
## 7.88 7.73 12.77 10.32
# Korrelationskoeffizienten
sdi <- diag(1/sqrt(diag(covar)))
correl <- sdi %*% covar %*% sdi; round(correl,2)
## [,1] [,2] [,3] [,4]
## [1,] 1.00 0.35 0.03 0.75
## [2,] 0.35 1.00 0.09 -0.01
## [3,] 0.03 0.09 1.00 0.30
## [4,] 0.75 -0.01 0.30 1.009.3.6 Daten im Rahmen (Tabellen)
alter <- c(19, 22, 24)
geschlecht <- c("maennlich","weiblich","maennlich")
groesse <- c(170, 165, 181)
studenten <- data.frame(alter, geschlecht, groesse)
studentenstudenten[2,] # Auswahl 2. Zeile (fallweise)studenten[geschlecht=="maennlich",] # Auswahl nach dem GeschlechtEinlesen von Daten aus externe Datei (CSv-Format)
infarkt <- read.csv2("infarkt.csv")
infarkt[1:10, 1:9]
str(infarkt) # Datenstruktur
## 'data.frame': 80 obs. of 14 variables:
## $ Nummer : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Gruppe : Factor w/ 2 levels "Infarkt","Kontrolle": 1 1 1 1 1 1 1 1 1 1 ...
## $ Geschlecht: Factor w/ 2 levels "m","w": 1 1 1 1 1 1 1 1 1 1 ...
## $ Alter : int 39 43 45 50 51 52 53 53 56 56 ...
## $ RelGew : int 128 106 94 98 132 108 165 116 138 140 ...
## $ RRsyst : int 155 145 160 200 190 195 220 140 180 175 ...
## $ RRdias : int 95 95 90 110 110 110 105 85 100 95 ...
## $ Blutz : int 100 140 95 80 90 90 70 85 200 90 ...
## $ Diabet : logi FALSE TRUE FALSE FALSE FALSE FALSE ...
## $ Chol : int 195 205 245 190 260 190 340 195 285 380 ...
## $ Trigl : int 146 138 200 101 202 164 150 93 135 127 ...
## $ Hbdh : int 410 380 260 165 300 290 605 170 277 523 ...
## $ Got : num 28.3 19 15.4 23.2 20.6 18.7 33.1 20.2 18.2 29.7 ...
## $ Zigarr : int 30 0 15 15 5 20 0 5 20 10 ...
attach(infarkt) # vereinfachter Zugriff über Namen (cave!!!)
# edit(infarkt) # Änderungen in der Tabelleattach(infarkt)
Chol
## [1] 195 205 245 190 260 190 340 195 285 380 220 240 235 215 190 275 205 290 200
## [20] 210 220 265 235 200 350 220 800 230 185 295 380 200 485 210 185 210 395 290
## [39] 190 210 220 200 185 220 215 135 220 180 220 135 150 165 150 195 160 190 85
## [58] 180 160 200 205 230 125 195 100 185 180 205 160 195 190 175 140 145 170 150
## [77] 180 190 175 200
mean(Chol)
## [1] 219.75Berechnungen / Transformationen / Rekodierungen:
infarkt <- transform(infarkt, lnHbdh=log(Hbdh))
infarkt$lnHbdh
## [1] 6.016157 5.940171 5.560682 5.105945 5.703782 5.669881 6.405228 5.135798
## [9] 5.624018 6.259581 6.595781 5.433722 5.880533 5.652489 5.517453 5.783825
## [17] 5.379897 5.666427 4.955827 5.463832 4.934474 6.602588 6.434547 6.495266
## [25] 5.252273 5.541264 6.198479 5.631212 6.200509 5.918894 6.107023 5.560682
## [33] 4.859812 5.609472 5.572154 5.743003 6.177944 6.077642 6.175867 5.799093
## [41] 4.276666 5.247024 4.584967 5.003946 4.532599 4.204693 4.356709 4.007333
## [49] 4.510860 4.882802 4.330733 4.955827 3.713572 4.553877 4.234107 4.615121
## [57] 5.036953 5.111988 4.672829 5.327876 4.700480 4.644391 3.850148 4.682131
## [65] 4.465908 4.905275 4.941642 5.267858 5.575949 4.488636 4.077537 5.017280
## [73] 4.007333 5.043425 4.969813 5.081404 4.890349 4.812184 4.605170 4.605170replace(1:10, list=c(2, 4, 6), values=c(20, 40, 60)) #Funktion replace()
## [1] 1 20 3 40 5 60 7 8 9 10re.code <- function(var, alt, neu) { # Umkodieren einzelner Faktorstufen
x <- as.vector(var)
i <- which(x == alt); ni <- length(i)
x <- replace(x, list=i, values=rep(neu, ni))
if (is.factor(x)) factor(x) else x }
re.code(as.factor(c("A", "A", "A", "B", "B", "C", "C")), "B", "X")
## [1] "A" "A" "A" "X" "X" "C" "C"
infarkt <- transform(infarkt, Gruppe=re.code(Gruppe, "Infarkt", "1"))
infarkt <- transform(infarkt, Gruppe=re.code(Gruppe, "Kontrolle", "0"))
infarkt$Gruppe
## [1] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
## [20] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
## [39] "1" "1" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0"
## [58] "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "0"
## [77] "0" "0" "0" "0"Funktion recode() in library(car)
library(car)
farben <- c("red", "purple", "blue", "blue", "orange", "red", "orange")
farben
## [1] "red" "purple" "blue" "blue" "orange" "red" "orange"
recode(farben, "'red'='rot'; 'blue'='blau'; 'purple'='violett'")
## [1] "rot" "violett" "blau" "blau" "orange" "rot" "orange"Stutzen der Verteilung (Nachweisgrenze)
daten <- c(5, 9, 11, 8, 9, 3, 1, 13, 9, 12, 5, 12, 6, 3, 17, 5, 8, 7)
cutoff <- 10
ifelse(daten <= cutoff, daten, cutoff)
## [1] 5 9 10 8 9 3 1 10 9 10 5 10 6 3 10 5 8 7Klasseneinteilung (kategoriell)
infarkt <- read.csv2("infarkt.csv")
infarkt$Alter
## [1] 39 43 45 50 51 52 53 53 56 56 57 57 59 59 61 61 62 62 67 68 68 71 72 74 75
## [26] 76 79 81 57 58 61 63 66 67 69 69 70 72 79 81 28 40 42 46 51 51 52 53 53 54
## [51] 55 55 57 58 59 60 61 61 62 62 62 64 64 65 65 36 42 42 45 48 49 49 51 52 55
## [76] 56 59 61 63 72
Klassen <- cut(infarkt$Alter, breaks=c(0, 50, 70, Inf),
labels=c("-50", ">50-70", ">70"))
Klassen
## [1] -50 -50 -50 -50 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70
## [11] >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70
## [21] >50-70 >70 >70 >70 >70 >70 >70 >70 >50-70 >50-70
## [31] >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >70 >70 >70
## [41] -50 -50 -50 -50 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70
## [51] >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70
## [61] >50-70 >50-70 >50-70 >50-70 >50-70 -50 -50 -50 -50 -50
## [71] -50 -50 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >50-70 >70
## Levels: -50 >50-70 >70Wiederholte Beobachtungen:
c1 <- c(1,2,3,4)
c2 <- c(2,5,6,7)
c3 <- c(3,8,9,10)
df <- as.data.frame(rbind(c1,c2,c3))
names(df) <- c("Fall","t1","t2","t3"); df # weites Format von Daten
reshape(df, timevar="Zeit", idvar="Fall", varying=list(2:4),
v.names="Wert", direction="long") # langes Format 9.4 Fehlende Angaben (not assigned NA)
x <- c(1, 2, NA, 4); x
## [1] 1 2 NA 4
y <- x + 1; y
## [1] 2 3 NA 5
is.na(x)
## [1] FALSE FALSE TRUE FALSE
which(is.na(x)) # Auffinden fehlender Angaben
## [1] 3Fehlende Anbgaben in Funktionsaufrufen!
x <- c(1, 2, NA, 4); x
## [1] 1 2 NA 4
mean(x)
## [1] NA
mean(x, na.rm=TRUE)
## [1] 2.333333Fehlende Angaben in Datentabellen!
any.missing.value <- function(dfr=NA) { any(is.na(dfr)) }
alter <- c(19, 22, 24, 30, NA, 25)
geschlecht <- c("maennlich","weiblich","maennlich",NA,"weiblich","maennlich")
groesse <- c(170, NA, 181, 177, 182, 196)
studenten <- data.frame(alter, geschlecht, groesse)
studenten
y <- studenten[,c("alter","geschlecht","groesse")]
y.na <- !apply(y, 1, any.missing.value); y[y.na,]colSums(is.na(studenten))
## alter geschlecht groesse
## 1 1 1
na.omit(studenten)
studenten[complete.cases(studenten),]9.5 Auswahl und Sortierung von Daten
Zahl1bis20 <- 1:20
Zahl1bis20[6:10]
## [1] 6 7 8 9 10
Zahl1bis20[Zahl1bis20 > 13]
## [1] 14 15 16 17 18 19 20
blut <- c("A","B","AB","0")
blut[3]
## [1] "AB"infarkt <- read.csv2("infarkt.csv")
attach(infarkt)
infarkt[, 10]
## [1] 195 205 245 190 260 190 340 195 285 380 220 240 235 215 190 275 205 290 200
## [20] 210 220 265 235 200 350 220 800 230 185 295 380 200 485 210 185 210 395 290
## [39] 190 210 220 200 185 220 215 135 220 180 220 135 150 165 150 195 160 190 85
## [58] 180 160 200 205 230 125 195 100 185 180 205 160 195 190 175 140 145 170 150
## [77] 180 190 175 200
Chol[5]
## [1] 260
set <- infarkt[Gruppe=="Infarkt" & Blutz>100, ]
set[, 1:9]
subset(infarkt, Geschlecht=="w" & Alter<45, select = c(Chol, Trigl))alter <- c(19, 22, 24, 30, NA, 25)
geschlecht <- c("maennlich","weiblich","maennlich",NA,"weiblich","maennlich")
groesse <- c(170, NA, 181, 177, 182, 196)
studenten <- data.frame(alter, geschlecht, groesse)
studenten
studenten[geschlecht=="maennlich",]Sortieren / Rangzahlen
a <- c(3, 7, 2, 8, 5, 10, 4); a
## [1] 3 7 2 8 5 10 4
sort(a)
## [1] 2 3 4 5 7 8 10
sort(a, decreasing=TRUE)
## [1] 10 8 7 5 4 3 2
a <- c(3, 7, 2, 8, 5, 10, 4)
rank(a)
## [1] 2 5 1 6 4 7 3
b <- c(3, 5, 7, 3, 6, 5)
rank(b)
## [1] 1.5 3.5 6.0 1.5 5.0 3.5
rank(b, ties.method = "min")
## [1] 1 3 6 1 5 3
o <- order(a)
a
## [1] 3 7 2 8 5 10 4
o
## [1] 3 1 7 5 2 4 6
a[o]
## [1] 2 3 4 5 7 8 10Sortieren in Matrizen und Datentabellen
SortMat <- function(Mat, Sort) {
m <- do.call("order", as.data.frame(Mat[, Sort]))
Mat[m, ] }alter <- c(19, 22, 24, 30, NA, 25)
geschlecht <- c("maennlich","weiblich","maennlich",NA,"weiblich","maennlich")
groesse <- c(170, NA, 181, 177, 182, 196)
studenten <- data.frame(alter, geschlecht, groesse)
studenten
SortMat(studenten, 3)
studenten[order(studenten[,3]),]
m <- matrix(c(2,5,4, 5,2,3, 2,6,7), byrow=T, nrow=3); m
## [,1] [,2] [,3]
## [1,] 2 5 4
## [2,] 5 2 3
## [3,] 2 6 7
SortMat(m, 2)
## [,1] [,2] [,3]
## [1,] 5 2 3
## [2,] 2 5 4
## [3,] 2 6 79.6 Ablaufsteuerung: logische Bedingungen und Funktionen
for (…) und if (…)
a <- rep(NA, 10) # for (...) if (...)
a
## [1] NA NA NA NA NA NA NA NA NA NA
for (i in 1:10) if (i<6) a[i]<-"unten" else a[i]<-"oben"
a
## [1] "unten" "unten" "unten" "unten" "unten" "oben" "oben" "oben" "oben"
## [10] "oben"ifelse()
zaehler <- c(2, 4,NA, 8, 7, 5, 3, 1) # ifelse()
nenner <- c(4, 3, 2, 1, 0, 3, 2, 0)
quot <- round(ifelse(nenner != 0, zaehler/nenner, NA), 3)
round(quot, 2)
## [1] 0.50 1.33 NA 8.00 NA 1.67 1.50 NAwhile (…)
i <- 0; summe <- 0 # while()
while (i < 10) {i <- i+1; summe <- summe + i }
summe
## [1] 55
sum(1:10)
## [1] 55function()
stdabw <- function(x) { # function()
anzahl <- length(x)
summe <- sum(x)
mittel <- summe / anzahl
saq <- sum((x-mittel)^2)
return(sqrt(saq/(anzahl-1)))
}
x <- c (2,3,4,5,6,7)
stdabw(x)
## [1] 1.870829apply()
# apply functions
X <- matrix(sample(1:20, 20, replace=T), ncol=4, byrow=T)
X
## [,1] [,2] [,3] [,4]
## [1,] 3 17 12 12
## [2,] 5 20 7 5
## [3,] 7 20 5 20
## [4,] 18 10 3 19
## [5,] 19 17 20 17
apply(X, 1, sum) # Zeilensummen
## [1] 44 37 52 50 73
apply(X, 2, sum) # Spaltensummen
## [1] 52 84 47 73
apply(X, 2, which.max) # Pos. max. Wert je Spalte
## [1] 5 2 5 3
apply(X, 1, function(x) {max(x) - min(x)}) # Spannweite je Zeile
## [1] 14 15 15 16 3
apply(X, 1:2, function(x) sqrt(x)) # Quadratwurzel elementweise
## [,1] [,2] [,3] [,4]
## [1,] 1.732051 4.123106 3.464102 3.464102
## [2,] 2.236068 4.472136 2.645751 2.236068
## [3,] 2.645751 4.472136 2.236068 4.472136
## [4,] 4.242641 3.162278 1.732051 4.358899
## [5,] 4.358899 4.123106 4.472136 4.123106by()
# by functions
infarkt <- read.csv2("infarkt.csv")
by(infarkt[, 10:12], infarkt$Gruppe, summary)
## infarkt$Gruppe: Infarkt
## Chol Trigl Hbdh
## Min. :185.0 Min. : 70.00 Min. :129.0
## 1st Qu.:200.0 1st Qu.: 99.75 1st Qu.:253.5
## Median :220.0 Median :125.00 Median :295.0
## Mean :263.0 Mean :127.53 Mean :352.5
## 3rd Qu.:286.2 3rd Qu.:141.50 3rd Qu.:457.0
## Max. :800.0 Max. :203.00 Max. :737.0
## ------------------------------------------------------------
## infarkt$Gruppe: Kontrolle
## Chol Trigl Hbdh
## Min. : 85.0 Min. : 65.0 Min. : 41.00
## 1st Qu.:157.5 1st Qu.: 99.5 1st Qu.: 84.75
## Median :180.0 Median :123.5 Median :105.50
## Mean :176.5 Mean :130.1 Mean :116.03
## 3rd Qu.:200.0 3rd Qu.:158.8 3rd Qu.:145.25
## Max. :230.0 Max. :239.0 Max. :264.00tapply()
# tapply functions
x <- 1:12
g <- factor(sample(1:3, 12, replace=T))
rbind(x,g)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
## x 1 2 3 4 5 6 7 8 9 10 11 12
## g 3 1 1 3 3 2 2 3 2 1 1 3
round(tapply(x, g, mean), 2)
## 1 2 3
## 6.50 7.33 6.00infarkt <- read.csv2("Infarkt.csv")
tapply(infarkt$Chol, infarkt$Gruppe, mean)
## Infarkt Kontrolle
## 263.0 176.5sapply()
# sapply functions
l <- list(groesse=c(160,170,177,182), gewicht=c(70,75,80,90,65,78))
sapply(l, mean)
## groesse gewicht
## 172.25000 76.33333replicate()
normal <- replicate(8, rnorm(5))
round(normal, 3)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1.097 -0.549 -0.245 -0.036 -0.511 0.471 0.346 -1.291
## [2,] 0.478 1.005 0.804 -0.038 -1.394 -0.386 0.273 -0.782
## [3,] -0.281 -0.315 0.294 -0.905 -0.675 1.887 0.007 -0.479
## [4,] 1.124 0.030 -0.310 -1.434 -0.045 -1.433 0.042 -1.373
## [5,] 0.578 -0.299 -0.883 1.690 0.625 -0.164 0.585 1.4069.7 Mathematische und statistische Funktionen
vect <- c(1.42, 4.84, -2.55, - 1.24)
vect
## [1] 1.42 4.84 -2.55 -1.24
abs(vect)
## [1] 1.42 4.84 2.55 1.24
round(vect, digits=1)
## [1] 1.4 4.8 -2.5 -1.2
ceiling(vect)
## [1] 2 5 -2 -1
floor(vect)
## [1] 1 4 -3 -2
trunc(vect)
## [1] 1 4 -2 -1
round(vect, digits=1)
## [1] 1.4 4.8 -2.5 -1.2
max(vect)
## [1] 4.84
min(vect)
## [1] -2.55
exp(5)
## [1] 148.4132
round(sin(seq(0, 2*pi, by=(pi/4))), digits=3)
## [1] 0.000 0.707 1.000 0.707 0.000 -0.707 -1.000 -0.707 0.000
sqrt(7)
## [1] 2.645751Kontingenztafeln
infarkt <- read.csv2("infarkt.csv")
table(infarkt$Gruppe, infarkt$Geschlecht)
##
## m w
## Infarkt 28 12
## Kontrolle 25 15
tab <- as.data.frame(table(infarkt$Gruppe, infarkt$Geschlecht))
names(tab) <- c("Gruppe","Geschlecht","H?ufigkeit")
tabStatistische Maßzahlen:
infarkt <- read.csv2("infarkt.CSV")
attach(infarkt)
mean(Alter)
## [1] 58.4875
sd(Alter)
## [1] 10.70549
max(Blutz)
## [1] 350
quantile(RRsyst, prob=c(0.10,0.25,0.50,0.75,0.90))
## 10% 25% 50% 75% 90%
## 140.00 148.75 160.00 175.00 190.00
summary(Chol)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 85.0 180.0 200.0 219.8 222.5 800.0aggregate()
infarkt <- read.csv2("infarkt.csv")
attach(infarkt)
stat <- aggregate(Chol, by=data.frame(Geschlecht), summary, na.rm=T)
print(stat)
## Geschlecht x.Min. x.1st Qu. x.Median x.Mean x.3rd Qu. x.Max.
## 1 m 85.0000 190.0000 205.0000 220.8491 230.0000 800.0000
## 2 w 140.0000 177.5000 190.0000 217.5926 210.0000 485.0000
stat[[2]][,3] # Teilergebnisse: Medianwerte
## [1] 205 1909.8 Graphikfunktionen
infarkt <- read.csv2("infarkt.CSV")
attach(infarkt)
par(mfrow=c(1,3), ps=14, font=2, font.axis=2, font.lab=2,
font.main=2, font.sub=2, lwd=2)
hist(Chol, main="Histogramm", col="grey")
boxplot(Blutz[Gruppe=="Infarkt"], Blutz[Gruppe=="Kontrolle"],
xlab="Gruppe", main="Box-Whisker Plot")
plot(RRsyst, RRdias, main="Punktwolke")
par(mfrow=c(1,2), lwd=2, font.axis=2, bty="l", ps=12)
Pex <- 2.0
ipch <- 1:20
k <- floor(sqrt(20))
dd <- c(-1, 1)/2
rx <- dd + range(ix <- (ipch - 1)%/%k)
ry <- dd + range(iy <- 3 + (k - 1) - (ipch - 1)%%k)
pch <- as.list(ipch)
plot(rx, ry, type = "n", axes = FALSE, xlab = "", ylab = "",
main = "Symbole (pch)")
for (i in 1:20) {
pc <- pch[[i]]
points(ix[i], iy[i], pch = pc, col = "black",
bg = "yellow", cex = Pex)
text(ix[i] - 0.5, iy[i], pc, col = "black", font=3, cex = 1.0)
}
Pex <- 3
ity <- 7
dd <- c(-1, 1)/2
rx <- dd + range(ix <- rep(c(1,2), 7))
ry <- dd + range(iy <- seq(1, 7, by=1))
plot(rx, ry, type = "n", axes = FALSE, xlab = "", ylab = "",
main = "Linien (lty)")
for (i in 1:7) {
pc <- i
lines(c(ix[i], ix[i+1]), c(iy[i], iy[i]), lty=i, lwd=2, cex = Pex)
text(1 - 0.2, iy[i], pc, col = "black", font=3, cex = 1.0)
}
par(mfrow=c(1,1),ps=14, font=2, font.axis=2, font.lab=2,
font.main=2, font.sub=2, lwd=2)
x <- seq(-4, +4, by=0.2)
y <- x^2
plot(x, y, type="l")
abline(v=0)
polygon(x[10:30], y[10:30], density=10)
text(2.5,1, "Segment")
title("Parabel")