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Aktueller Ordner: duesseldorfer-schuelerinventar-spss-R
β¬… Übergeordnet
πŸ““ Jupyter Notebook - Kernel: R
🧩 Code Zelle #1
πŸ“ Markdown Zelle #2
Histogramm:
πŸ“ Markdown Zelle #3
Ein erster Hinweis auf die GΓΌte der Items ist sicherlich eine grobe AnnΓ€herung der Rohdaten an eine Normalverteilung
🧩 Code Zelle #4
🧩 Code Zelle #5 [In [5]]
fallprozeile <- read.csv2 ("https://paul-koop.org/fallprozeilenurdaten.csv", header=FALSE, dec=",");

for (i in 1:36){
  hist(fallprozeile[,i],
       freq=FALSE,
       main=paste("Histogram item",i),
       xlab=paste("item",i)
       )
  x <- seq(1,4,0.01)
  curve(dnorm(x,mean=mean(fallprozeile[,i]),sd=sd(fallprozeile[,i])),add=TRUE)
}


Output:
Plot with title β€œHistogram item 1”
Plot with title β€œHistogram item 2”
Plot with title β€œHistogram item 3”
Plot with title β€œHistogram item 4”
Plot with title β€œHistogram item 5”
Plot with title β€œHistogram item 6”
Plot with title β€œHistogram item 7”
Plot with title β€œHistogram item 8”
Plot with title β€œHistogram item 9”
Plot with title β€œHistogram item 10”
Plot with title β€œHistogram item 11”
Plot with title β€œHistogram item 12”
Plot with title β€œHistogram item 13”
Plot with title β€œHistogram item 14”
Plot with title β€œHistogram item 15”
Plot with title β€œHistogram item 16”
Plot with title β€œHistogram item 17”
Plot with title β€œHistogram item 18”
Plot with title β€œHistogram item 19”
Plot with title β€œHistogram item 20”
Plot with title β€œHistogram item 21”
Plot with title β€œHistogram item 22”
Plot with title β€œHistogram item 23”
Plot with title β€œHistogram item 24”
Plot with title β€œHistogram item 25”
Plot with title β€œHistogram item 26”
Plot with title β€œHistogram item 27”
Plot with title β€œHistogram item 28”
Plot with title β€œHistogram item 29”
Plot with title β€œHistogram item 30”
Plot with title β€œHistogram item 31”
Plot with title β€œHistogram item 32”
Plot with title β€œHistogram item 33”
Plot with title β€œHistogram item 34”
Plot with title β€œHistogram item 35”
Plot with title β€œHistogram item 36”
🧩 Code Zelle #6
πŸ“ Markdown Zelle #7


Ein erstes objektives Merkmal der ValiditΓ€t eines Tests ist die TrennschΓ€rfe der Items. Valide ist ein Test dann, wenn er auch tatsΓ€chlich die Variable misst, die er auch vorgibt zu messen. Unter der TrennschΓ€rfe eines Items versteht man die Korrelation des Items mit dem Gesamtergebnis der jeweils gemessenen Dimension eines Tests.
πŸ“ Markdown Zelle #8
🧩 Code Zelle #9
Fachkompetenz:
🧩 Code Zelle #10
🧩 Code Zelle #11 [In [3]]
fachkompetenz <- read.csv2 ("https://paul-koop.org/SV.csv", header=TRUE, dec=",");
fachkompetenz$ts <- rowSums(fachkompetenz[,-1])
round(cor(fachkompetenz[,-1]),2)
Output:
    X21  X22  X23  X24  X25  X26  X27  X28  ts  
X21 1.00 0.61 0.47 0.49 0.48 0.39 0.46 0.42 0.75
X22 0.61 1.00 0.45 0.50 0.47 0.50 0.47 0.36 0.75
X23 0.47 0.45 1.00 0.42 0.56 0.42 0.44 0.41 0.72
X24 0.49 0.50 0.42 1.00 0.54 0.28 0.46 0.27 0.68
X25 0.48 0.47 0.56 0.54 1.00 0.45 0.43 0.40 0.75
X26 0.39 0.50 0.42 0.28 0.45 1.00 0.52 0.46 0.70
X27 0.46 0.47 0.44 0.46 0.43 0.52 1.00 0.56 0.76
X28 0.42 0.36 0.41 0.27 0.40 0.46 0.56 1.00 0.68
ts  0.75 0.75 0.72 0.68 0.75 0.70 0.76 0.68 1.00
🧩 Code Zelle #12
Arbeitsverhalten:
🧩 Code Zelle #13
🧩 Code Zelle #14 [In [1]]
arbeitsverhalten <- read.csv2 ("https://paul-koop.org/AV.csv", header=TRUE, dec=",");
arbeitsverhalten$ts <- rowSums(arbeitsverhalten[,-1])
round(cor(arbeitsverhalten[,-1]),2)
Output:
    X1   X2   X3   X4   X5   X6   X7   X8   X9   X10  ts  
X1  1.00 0.41 0.45 0.40 0.41 0.43 0.55 0.40 0.39 0.43 0.69
X2  0.41 1.00 0.44 0.56 0.36 0.35 0.35 0.49 0.51 0.35 0.69
X3  0.45 0.44 1.00 0.60 0.42 0.35 0.34 0.54 0.56 0.41 0.75
X4  0.40 0.56 0.60 1.00 0.43 0.31 0.36 0.61 0.46 0.49 0.76
X5  0.41 0.36 0.42 0.43 1.00 0.29 0.45 0.53 0.43 0.43 0.68
X6  0.43 0.35 0.35 0.31 0.29 1.00 0.64 0.27 0.31 0.26 0.59
X7  0.55 0.35 0.34 0.36 0.45 0.64 1.00 0.33 0.28 0.43 0.66
X8  0.40 0.49 0.54 0.61 0.53 0.27 0.33 1.00 0.55 0.52 0.76
X9  0.39 0.51 0.56 0.46 0.43 0.31 0.28 0.55 1.00 0.37 0.72
X10 0.43 0.35 0.41 0.49 0.43 0.26 0.43 0.52 0.37 1.00 0.67
ts  0.69 0.69 0.75 0.76 0.68 0.59 0.66 0.76 0.72 0.67 1.00
🧩 Code Zelle #15
Sozialverhalten:
🧩 Code Zelle #16
🧩 Code Zelle #17 [In [7]]
sozialverhalten <- read.csv2 ("https://paul-koop.org/SV.csv", header=TRUE, dec=",");
sozialverhalten$ts <- rowSums(sozialverhalten[,-1])
round(cor(sozialverhalten[,-1]),2)
Output:
    X21  X22  X23  X24  X25  X26  X27  X28  ts  
X21 1.00 0.61 0.47 0.49 0.48 0.39 0.46 0.42 0.75
X22 0.61 1.00 0.45 0.50 0.47 0.50 0.47 0.36 0.75
X23 0.47 0.45 1.00 0.42 0.56 0.42 0.44 0.41 0.72
X24 0.49 0.50 0.42 1.00 0.54 0.28 0.46 0.27 0.68
X25 0.48 0.47 0.56 0.54 1.00 0.45 0.43 0.40 0.75
X26 0.39 0.50 0.42 0.28 0.45 1.00 0.52 0.46 0.70
X27 0.46 0.47 0.44 0.46 0.43 0.52 1.00 0.56 0.76
X28 0.42 0.36 0.41 0.27 0.40 0.46 0.56 1.00 0.68
ts  0.75 0.75 0.72 0.68 0.75 0.70 0.76 0.68 1.00
🧩 Code Zelle #18
Lernverhalten:
🧩 Code Zelle #19
🧩 Code Zelle #20 [In [6]]
lernverhalten <- read.csv2 ("https://paul-koop.org/LV.csv", header=TRUE, dec=",");
lernverhalten$ts <- rowSums(lernverhalten[,-1])
round(cor(lernverhalten[,-1]),2)
Output:
    X11  X12  X13  X14  X15  X16  X17  X18  X19  X20  ts  
X11 1.00 0.54 0.52 0.47 0.55 0.47 0.53 0.50 0.46 0.46 0.77
X12 0.54 1.00 0.53 0.48 0.50 0.49 0.45 0.29 0.53 0.42 0.73
X13 0.52 0.53 1.00 0.35 0.51 0.45 0.48 0.44 0.48 0.46 0.74
X14 0.47 0.48 0.35 1.00 0.50 0.38 0.43 0.28 0.52 0.48 0.68
X15 0.55 0.50 0.51 0.50 1.00 0.39 0.34 0.34 0.44 0.44 0.71
X16 0.47 0.49 0.45 0.38 0.39 1.00 0.49 0.33 0.52 0.42 0.69
X17 0.53 0.45 0.48 0.43 0.34 0.49 1.00 0.45 0.48 0.42 0.71
X18 0.50 0.29 0.44 0.28 0.34 0.33 0.45 1.00 0.46 0.45 0.64
X19 0.46 0.53 0.48 0.52 0.44 0.52 0.48 0.46 1.00 0.55 0.76
X20 0.46 0.42 0.46 0.48 0.44 0.42 0.42 0.45 0.55 1.00 0.71
ts  0.77 0.73 0.74 0.68 0.71 0.69 0.71 0.64 0.76 0.71 1.00
🧩 Code Zelle #21
πŸ“ Markdown Zelle #22
Interkorrelation:
πŸ“ Markdown Zelle #23
Einen weiteren ersten qualitativen Hinweis auf die GΓΌte der Items bieten ihre Interkorrelationen innerhalb der Dimensionen, denen die Items zugeordnet sind. Denn wenn die Items eine gemeinsame Dimension messen, mΓΌssen sie positiv miteinander korreliert sein.
🧩 Code Zelle #24
🧩 Code Zelle #25 [In [3]]
install.packages("psych", repos='http://cran.us.r-project.org')
library(psych)
options(max.print = 9999)
interkorrelation <- read.csv2 ("https://paul-koop.org/rohdaten.csv", header=TRUE, dec=",");
round(cor(interkorrelation[,-1]),2)
Output:
Installing package into β€˜/srv/rlibs’
(as β€˜lib’ is unspecified)


    X1    X2   X3    X4   X5   X6   X7   X8   X9   X10  β‹― X27   X28   X29  X30 
X1   1.00 0.41  0.45 0.40 0.41 0.43 0.55 0.40 0.39 0.43 β‹―  0.28  0.22 0.12 0.32
X2   0.41 1.00  0.44 0.56 0.36 0.35 0.35 0.49 0.51 0.35 β‹―  0.18  0.33 0.12 0.36
X3   0.45 0.44  1.00 0.60 0.42 0.35 0.34 0.54 0.56 0.41 β‹―  0.24  0.30 0.08 0.43
X4   0.40 0.56  0.60 1.00 0.43 0.31 0.36 0.61 0.46 0.49 β‹―  0.30  0.31 0.06 0.43
X5   0.41 0.36  0.42 0.43 1.00 0.29 0.45 0.53 0.43 0.43 β‹―  0.08  0.10 0.12 0.27
X6   0.43 0.35  0.35 0.31 0.29 1.00 0.64 0.27 0.31 0.26 β‹―  0.32  0.21 0.31 0.29
X7   0.55 0.35  0.34 0.36 0.45 0.64 1.00 0.33 0.28 0.43 β‹―  0.21  0.18 0.30 0.31
X8   0.40 0.49  0.54 0.61 0.53 0.27 0.33 1.00 0.55 0.52 β‹―  0.21  0.18 0.06 0.44
X9   0.39 0.51  0.56 0.46 0.43 0.31 0.28 0.55 1.00 0.37 β‹―  0.20  0.30 0.15 0.38
X10  0.43 0.35  0.41 0.49 0.43 0.26 0.43 0.52 0.37 1.00 β‹―  0.30  0.27 0.08 0.36
X11  0.44 0.56  0.48 0.49 0.41 0.33 0.34 0.52 0.48 0.49 β‹―  0.27  0.23 0.04 0.42
X12  0.47 0.49  0.43 0.38 0.45 0.34 0.43 0.45 0.54 0.36 β‹―  0.26  0.36 0.08 0.25
X13  0.55 0.42  0.44 0.38 0.49 0.42 0.43 0.42 0.48 0.49 β‹―  0.29  0.37 0.09 0.34
X14  0.33 0.39  0.45 0.51 0.37 0.33 0.36 0.46 0.37 0.45 β‹―  0.38  0.32 0.13 0.37
X15  0.48 0.44  0.54 0.49 0.44 0.38 0.36 0.52 0.40 0.46 β‹―  0.27  0.28 0.07 0.27
X16  0.46 0.44  0.44 0.53 0.38 0.38 0.44 0.38 0.42 0.38 β‹―  0.24  0.31 0.06 0.31
X17  0.41 0.54  0.42 0.46 0.43 0.39 0.41 0.47 0.53 0.47 β‹―  0.23  0.30 0.15 0.44
X18  0.30 0.39  0.32 0.39 0.33 0.32 0.36 0.41 0.46 0.50 β‹―  0.29  0.25 0.13 0.44
X19  0.44 0.49  0.45 0.54 0.46 0.41 0.50 0.47 0.48 0.45 β‹―  0.33  0.35 0.15 0.39
X20  0.37 0.40  0.41 0.43 0.43 0.42 0.48 0.46 0.37 0.48 β‹―  0.33  0.21 0.19 0.42
X21  0.43 0.37  0.37 0.38 0.29 0.34 0.43 0.29 0.24 0.24 β‹―  0.46  0.42 0.27 0.34
X22  0.30 0.29  0.30 0.34 0.18 0.37 0.37 0.27 0.19 0.24 β‹―  0.47  0.36 0.19 0.33
X23  0.21 0.26  0.30 0.38 0.26 0.25 0.26 0.36 0.27 0.29 β‹―  0.44  0.41 0.14 0.34
X24  0.41 0.21  0.22 0.25 0.22 0.40 0.40 0.30 0.21 0.19 β‹―  0.46  0.27 0.20 0.25
X25  0.40 0.27  0.32 0.32 0.23 0.32 0.33 0.31 0.18 0.31 β‹―  0.43  0.40 0.11 0.38
X26  0.31 0.25  0.30 0.39 0.07 0.15 0.15 0.23 0.19 0.29 β‹―  0.52  0.46 0.09 0.31
X27  0.28 0.18  0.24 0.30 0.08 0.32 0.21 0.21 0.20 0.30 β‹―  1.00  0.56 0.19 0.24
X28  0.22 0.33  0.30 0.31 0.10 0.21 0.18 0.18 0.30 0.27 β‹―  0.56  1.00 0.07 0.28
X29  0.12 0.12  0.08 0.06 0.12 0.31 0.30 0.06 0.15 0.08 β‹―  0.19  0.07 1.00 0.28
X30  0.32 0.36  0.43 0.43 0.27 0.29 0.31 0.44 0.38 0.36 β‹―  0.24  0.28 0.28 1.00
X31  0.02 0.15 -0.07 0.03 0.13 0.06 0.16 0.06 0.06 0.11 β‹― -0.13 -0.07 0.12 0.17
X32  0.10 0.06  0.14 0.23 0.10 0.22 0.24 0.11 0.08 0.20 β‹―  0.11  0.07 0.12 0.28
X33  0.00 0.07  0.10 0.10 0.02 0.14 0.20 0.05 0.08 0.25 β‹―  0.01  0.01 0.20 0.27
X34  0.07 0.05  0.18 0.11 0.16 0.31 0.31 0.13 0.08 0.18 β‹―  0.09  0.03 0.33 0.35
X35 -0.01 0.11  0.12 0.11 0.25 0.08 0.27 0.15 0.00 0.15 β‹― -0.18 -0.09 0.08 0.27
X36  0.19 0.09  0.11 0.21 0.16 0.22 0.30 0.21 0.00 0.22 β‹―  0.05 -0.05 0.12 0.28
    X31   X32  X33   X34   X35   X36  
X1   0.02 0.10  0.00  0.07 -0.01  0.19
X2   0.15 0.06  0.07  0.05  0.11  0.09
X3  -0.07 0.14  0.10  0.18  0.12  0.11
X4   0.03 0.23  0.10  0.11  0.11  0.21
X5   0.13 0.10  0.02  0.16  0.25  0.16
X6   0.06 0.22  0.14  0.31  0.08  0.22
X7   0.16 0.24  0.20  0.31  0.27  0.30
X8   0.06 0.11  0.05  0.13  0.15  0.21
X9   0.06 0.08  0.08  0.08  0.00  0.00
X10  0.11 0.20  0.25  0.18  0.15  0.22
X11  0.08 0.06  0.05  0.16  0.00  0.17
X12  0.10 0.15 -0.13  0.14  0.09  0.08
X13 -0.02 0.09  0.01  0.11  0.01  0.09
X14  0.03 0.16  0.08  0.27  0.18  0.19
X15  0.03 0.05 -0.05  0.20  0.10  0.19
X16 -0.08 0.23 -0.07 -0.01  0.01  0.01
X17  0.10 0.15  0.12  0.12  0.07  0.18
X18  0.23 0.12  0.22  0.18  0.09  0.25
X19 -0.03 0.22  0.02  0.13  0.05  0.11
X20  0.07 0.21  0.19  0.30  0.23  0.23
X21  0.01 0.04  0.10  0.25  0.09  0.15
X22  0.04 0.20  0.03  0.30  0.16  0.14
X23 -0.12 0.06  0.08  0.10 -0.06  0.08
X24 -0.16 0.11  0.08  0.13 -0.06  0.08
X25 -0.03 0.14  0.14  0.16  0.08  0.15
X26  0.04 0.17  0.00  0.15 -0.04  0.11
X27 -0.13 0.11  0.01  0.09 -0.18  0.05
X28 -0.07 0.07  0.01  0.03 -0.09 -0.05
X29  0.12 0.12  0.20  0.33  0.08  0.12
X30  0.17 0.28  0.27  0.35  0.27  0.28
X31  1.00 0.26  0.24  0.26  0.47  0.36
X32  0.26 1.00  0.14  0.37  0.46  0.37
X33  0.24 0.14  1.00  0.44  0.31  0.30
X34  0.26 0.37  0.44  1.00  0.49  0.49
X35  0.47 0.46  0.31  0.49  1.00  0.42
X36  0.36 0.37  0.30  0.49  0.42  1.00
🧩 Code Zelle #26
πŸ“ Markdown Zelle #27
Cronbachs Alpha:
πŸ“ Markdown Zelle #28
Ein Test muss eine Variable aber auch mâglichst genau messen. Ein Maß für die Genauigkeit der Messung ist die ReliabilitÀt. Wenn es nicht mâglich ist, an derselben Testgruppe einen Wiederholungstest zu machen oder die Testergebnisse mit anderen bereits als valide und reliabel eingestuften Tests zu korrelieren, wird hÀufig der Split-Half Test und die Konsistenzanalyse nach Cronbach durchgeführt. Bei der Split-Half Analyse wird der Test über alle Dimensionen in zwei HÀlften aufgeteilt und diese beiden HÀlften werden miteinander korreliert. 
πŸ“ Markdown Zelle #29
🧩 Code Zelle #30 [In [1]]
install.packages("psych", repos='http://cran.us.r-project.org')
library(psych)
cronalpha <- read.csv2 ("https://paul-koop.org/rohdaten.csv", header=TRUE, dec=",");
alpha(cronalpha[,-1])#paket psych

cronalpha <- cronalpha[,-1]

erste_haelfte <- cronalpha[,1:18]
zweite_haelfte <- cronalpha[,19:36]

cor(rowSums(erste_haelfte),rowSums(zweite_haelfte))
Output:
Installing package into β€˜/srv/rlibs’
(as β€˜lib’ is unspecified)


Reliability analysis   
Call: alpha(x = cronalpha[, -1])

  raw_alpha std.alpha G6(smc) average_r S/N    ase mean   sd median_r
      0.94      0.94    0.96      0.29  15 0.0057  2.8 0.43     0.31

    95% confidence boundaries 
         lower alpha upper
Feldt     0.92  0.94  0.95
Duhachek  0.93  0.94  0.95

 Reliability if an item is dropped:
    raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
X1       0.93      0.93    0.96      0.29  14   0.0059 0.025  0.30
X2       0.93      0.93    0.96      0.29  14   0.0060 0.025  0.30
X3       0.93      0.93    0.96      0.29  14   0.0060 0.025  0.30
X4       0.93      0.93    0.96      0.28  14   0.0060 0.025  0.30
X5       0.93      0.93    0.96      0.29  14   0.0059 0.026  0.31
X6       0.93      0.93    0.96      0.29  14   0.0059 0.026  0.30
X7       0.93      0.93    0.96      0.29  14   0.0060 0.026  0.30
X8       0.93      0.93    0.96      0.29  14   0.0060 0.025  0.31
X9       0.93      0.93    0.96      0.29  14   0.0059 0.025  0.31
X10      0.93      0.93    0.96      0.29  14   0.0060 0.026  0.31
X11      0.93      0.93    0.96      0.28  14   0.0060 0.025  0.30
X12      0.93      0.93    0.96      0.29  14   0.0060 0.025  0.31
X13      0.93      0.93    0.96      0.29  14   0.0060 0.025  0.30
X14      0.93      0.93    0.96      0.29  14   0.0060 0.026  0.30
X15      0.93      0.93    0.96      0.29  14   0.0060 0.025  0.30
X16      0.93      0.93    0.96      0.29  14   0.0059 0.025  0.30
X17      0.93      0.93    0.96      0.29  14   0.0060 0.026  0.30
X18      0.93      0.93    0.96      0.29  14   0.0059 0.026  0.31
X19      0.93      0.93    0.96      0.28  14   0.0060 0.025  0.30
X20      0.93      0.93    0.96      0.28  14   0.0060 0.026  0.30
X21      0.93      0.93    0.96      0.29  14   0.0059 0.026  0.30
X22      0.93      0.93    0.96      0.29  14   0.0059 0.026  0.31
X23      0.93      0.93    0.96      0.29  14   0.0059 0.026  0.31
X24      0.94      0.93    0.96      0.29  14   0.0059 0.026  0.31
X25      0.93      0.93    0.96      0.29  14   0.0059 0.026  0.30
X26      0.94      0.93    0.96      0.29  14   0.0058 0.026  0.31
X27      0.94      0.93    0.96      0.29  14   0.0058 0.025  0.31
X28      0.94      0.94    0.96      0.29  14   0.0058 0.025  0.31
X29      0.94      0.94    0.96      0.30  15   0.0057 0.025  0.32
X30      0.93      0.93    0.96      0.29  14   0.0059 0.026  0.30
X31      0.94      0.94    0.96      0.30  15   0.0056 0.023  0.32
X32      0.94      0.94    0.96      0.30  15   0.0057 0.025  0.32
X33      0.94      0.94    0.96      0.30  15   0.0056 0.024  0.32
X34      0.94      0.94    0.96      0.29  15   0.0057 0.025  0.31
X35      0.94      0.94    0.96      0.30  15   0.0056 0.024  0.32
X36      0.94      0.94    0.96      0.30  15   0.0057 0.025  0.32

 Item statistics 
      n raw.r std.r r.cor r.drop mean   sd
X1  240  0.62  0.63  0.62   0.60  3.2 0.72
X2  240  0.64  0.63  0.62   0.60  2.9 0.77
X3  240  0.66  0.65  0.64   0.63  2.7 0.85
X4  240  0.70  0.69  0.69   0.67  2.8 0.89
X5  240  0.59  0.58  0.57   0.55  3.0 0.80
X6  240  0.59  0.60  0.59   0.56  3.1 0.74
X7  240  0.65  0.66  0.66   0.63  3.3 0.67
X8  240  0.66  0.66  0.65   0.64  2.7 0.76
X9  240  0.61  0.60  0.59   0.57  2.6 0.95
X10 240  0.65  0.64  0.64   0.62  2.7 0.75
X11 240  0.69  0.68  0.68   0.66  2.8 0.83
X12 240  0.64  0.64  0.63   0.61  2.9 0.76
X13 240  0.66  0.65  0.64   0.62  2.8 0.83
X14 240  0.67  0.67  0.66   0.64  2.9 0.76
X15 240  0.65  0.64  0.63   0.61  2.8 0.87
X16 240  0.62  0.61  0.60   0.58  3.0 0.80
X17 240  0.66  0.66  0.65   0.63  2.7 0.74
X18 240  0.61  0.61  0.60   0.58  2.7 0.79
X19 240  0.71  0.71  0.70   0.68  3.0 0.79
X20 240  0.70  0.70  0.69   0.67  2.9 0.74
X21 240  0.61  0.62  0.61   0.58  3.3 0.75
X22 240  0.60  0.61  0.60   0.57  3.3 0.69
X23 240  0.54  0.55  0.53   0.51  3.0 0.75
X24 240  0.52  0.53  0.51   0.48  3.3 0.68
X25 240  0.59  0.59  0.58   0.55  3.1 0.70
X26 240  0.51  0.51  0.50   0.47  2.9 0.74
X27 240  0.49  0.49  0.48   0.45  2.8 0.80
X28 240  0.48  0.48  0.46   0.44  3.0 0.74
X29 240  0.29  0.30  0.27   0.25  2.2 0.75
X30 240  0.63  0.63  0.62   0.60  2.6 0.77
X31 240  0.18  0.18  0.16   0.13  2.4 0.71
X32 240  0.33  0.34  0.32   0.29  2.3 0.78
X33 240  0.23  0.24  0.22   0.19  2.3 0.75
X34 240  0.40  0.41  0.39   0.35  2.4 0.72
X35 240  0.27  0.27  0.26   0.22  2.5 0.79
X36 240  0.35  0.36  0.34   0.31  2.3 0.61

Non missing response frequency for each item
       1    2    3    4 miss
X1  0.00 0.19 0.46 0.35    0
X2  0.02 0.32 0.45 0.22    0
X3  0.05 0.37 0.37 0.20    0
X4  0.06 0.34 0.35 0.25    0
X5  0.02 0.29 0.40 0.29    0
X6  0.01 0.19 0.46 0.34    0
X7  0.00 0.12 0.48 0.40    0
X8  0.03 0.38 0.43 0.15    0
X9  0.12 0.38 0.30 0.21    0
X10 0.03 0.35 0.46 0.16    0
X11 0.04 0.38 0.38 0.21    0
X12 0.02 0.29 0.48 0.21    0
X13 0.04 0.34 0.39 0.23    0
X14 0.03 0.27 0.50 0.20    0
X15 0.06 0.34 0.38 0.23    0
X16 0.03 0.25 0.44 0.29    0
X17 0.02 0.39 0.44 0.16    0
X18 0.05 0.36 0.44 0.16    0
X19 0.03 0.25 0.45 0.27    0
X20 0.01 0.30 0.47 0.22    0
X21 0.01 0.15 0.39 0.45    0
X22 0.01 0.11 0.46 0.42    0
X23 0.01 0.22 0.47 0.30    0
X24 0.00 0.11 0.45 0.43    0
X25 0.00 0.19 0.51 0.30    0
X26 0.02 0.27 0.50 0.21    0
X27 0.04 0.30 0.45 0.21    0
X28 0.02 0.25 0.50 0.23    0
X29 0.11 0.69 0.10 0.10    0
X30 0.06 0.38 0.44 0.12    0
X31 0.03 0.67 0.20 0.10    0
X32 0.05 0.69 0.12 0.14    0
X33 0.07 0.70 0.11 0.11    0
X34 0.03 0.67 0.19 0.11    0
X35 0.02 0.60 0.21 0.17    0
X36 0.03 0.69 0.23 0.05    0
[1] 0.674236
🧩 Code Zelle #31
πŸ“ Markdown Zelle #32
Hauptkomponentenanalyse PCA
πŸ“ Markdown Zelle #33
Die Hauptkomponentenanalyse (abgekürzt: PCA) ist eine Methode der multivariaten Statistik und strukturiert DatensÀtze durch Approximation einer großen Anzahl statistischer Variablen mit einer kleineren Anzahl korrelierter linearer Hauptkomponenten.
🧩 Code Zelle #34
🧩 Code Zelle #35 [In [5]]
install.packages("stats", repos='http://cran.us.r-project.org')
library(psych)
tabellePCAMVS <- read.csv2 ("https://paul-koop.org/PCAMVS.csv", header=TRUE, dec=","); 
PCAbeobachtung <- tabellePCAMVS;

PCAMVSnr  <- PCAbeobachtung[,1]; PCAbeobachtung <- PCAbeobachtung[,-1];
PCAMVSart <- PCAbeobachtung[,1];PCAbeobachtung <- PCAbeobachtung[,-1];


MVS <-cmdscale(dist(PCAbeobachtung));
plot (MVS, type = "p", col = 1);
text(MVS[,1],
     MVS[,2],
     PCAMVSart,
     col=1)

PCA<-prcomp(scale(PCAbeobachtung))
biplot(PCA,choices=c(1,2))
Output:
Installing package into β€˜/srv/rlibs’
(as β€˜lib’ is unspecified)

Warning message:
β€œpackage β€˜stats’ is a base package, and should not be updated”

plot without title
plot without title
🧩 Code Zelle #36
πŸ“ Markdown Zelle #37
Faktorenanalyse:
πŸ“ Markdown Zelle #38
Mithilfe der Faktorenanalyse wird ΓΌberprΓΌft, ob sich die Items in mehrere Subskalen unterteilen lassen.
🧩 Code Zelle #39
🧩 Code Zelle #40 [In [4]]
install.packages("psych", repos='http://cran.us.r-project.org')
library(psych)
rohdaten <- read.csv2 ("http://paul-koop.org/rohdaten.csv", header=TRUE, dec=",");
rohdaten <- rohdaten[,-1]
KMO(rohdaten)
scree(rohdaten)
print(factanal(rohdaten, factors=4, rotation="varimax", scores="Bartlett"), digits=2, cutoff=.3)
print(factanal(rohdaten, factors=6, rotation="varimax", scores="Bartlett"), digits=2, cutoff=.3)
Output:
Installing package into β€˜/srv/rlibs’
(as β€˜lib’ is unspecified)


Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = rohdaten)
Overall MSA =  0.9
MSA for each item = 
  X1   X2   X3   X4   X5   X6   X7   X8   X9  X10  X11  X12  X13  X14  X15  X16 
0.91 0.92 0.94 0.93 0.93 0.88 0.89 0.93 0.91 0.91 0.92 0.91 0.95 0.95 0.94 0.94 
 X17  X18  X19  X20  X21  X22  X23  X24  X25  X26  X27  X28  X29  X30  X31  X32 
0.96 0.90 0.94 0.95 0.90 0.90 0.92 0.87 0.90 0.85 0.89 0.85 0.76 0.93 0.68 0.70 
 X33  X34  X35  X36 
0.68 0.82 0.68 0.85 
Call:
factanal(x = rohdaten, factors = 4, scores = "Bartlett", rotation = "varimax")

Uniquenesses:
  X1   X2   X3   X4   X5   X6   X7   X8   X9  X10  X11  X12  X13  X14  X15  X16 
0.50 0.53 0.51 0.45 0.53 0.48 0.24 0.44 0.48 0.56 0.45 0.52 0.50 0.53 0.55 0.53 
 X17  X18  X19  X20  X21  X22  X23  X24  X25  X26  X27  X28  X29  X30  X31  X32 
0.52 0.63 0.46 0.52 0.49 0.45 0.56 0.51 0.52 0.48 0.45 0.59 0.83 0.57 0.69 0.73 
 X33  X34  X35  X36 
0.75 0.46 0.42 0.60 

Loadings:
    Factor1 Factor2 Factor3 Factor4
X1   0.53                    0.43  
X2   0.66                          
X3   0.66                          
X4   0.67                          
X5   0.62                          
X6   0.33                    0.58  
X7   0.40                    0.70  
X8   0.72                          
X9   0.71                          
X10  0.60                          
X11  0.69                          
X12  0.63                          
X13  0.62                          
X14  0.51    0.40                  
X15  0.62                          
X16  0.57                          
X17  0.65                          
X18  0.53                          
X19  0.61    0.30                  
X20  0.51                          
X21          0.58            0.31  
X22          0.65                  
X23          0.59                  
X24          0.52            0.43  
X25          0.60                  
X26          0.67                  
X27          0.71                  
X28          0.57                  
X29                                
X30  0.44    0.30    0.38          
X31                  0.53          
X32                  0.49          
X33                  0.50          
X34                  0.70          
X35                  0.75          
X36                  0.62          

               Factor1 Factor2 Factor3 Factor4
SS loadings       7.88    4.19    2.89    2.01
Proportion Var    0.22    0.12    0.08    0.06
Cumulative Var    0.22    0.34    0.42    0.47

Test of the hypothesis that 4 factors are sufficient.
The chi square statistic is 1022.46 on 492 degrees of freedom.
The p-value is 2.15e-39 

Call:
factanal(x = rohdaten, factors = 6, scores = "Bartlett", rotation = "varimax")

Uniquenesses:
  X1   X2   X3   X4   X5   X6   X7   X8   X9  X10  X11  X12  X13  X14  X15  X16 
0.50 0.52 0.47 0.39 0.51 0.47 0.26 0.37 0.46 0.52 0.44 0.31 0.47 0.48 0.51 0.53 
 X17  X18  X19  X20  X21  X22  X23  X24  X25  X26  X27  X28  X29  X30  X31  X32 
0.49 0.41 0.46 0.51 0.47 0.37 0.53 0.48 0.51 0.46 0.43 0.55 0.81 0.53 0.53 0.72 
 X33  X34  X35  X36 
0.59 0.49 0.30 0.61 

Loadings:
    Factor1 Factor2 Factor3 Factor4 Factor5 Factor6
X1   0.53                    0.42                  
X2   0.65                                          
X3   0.66                                          
X4   0.68                                          
X5   0.63                                          
X6   0.33                    0.60                  
X7   0.40                    0.69                  
X8   0.74                                          
X9   0.71                                          
X10  0.59                                          
X11  0.68                                          
X12  0.65                           -0.34          
X13  0.61                                          
X14  0.52    0.42                                  
X15  0.62                                          
X16  0.58                                          
X17  0.63                                          
X18  0.51                            0.45          
X19  0.61    0.30                                  
X20  0.51                                          
X21          0.57            0.32                  
X22          0.67                                  
X23          0.57                                  
X24          0.49            0.46                  
X25          0.58                                  
X26          0.69                                  
X27          0.71                                  
X28          0.58                                  
X29                          0.32                  
X30  0.42            0.35                          
X31                  0.57                    0.34  
X32                  0.50                          
X33                  0.45            0.44          
X34                  0.67                          
X35                  0.81                          
X36                  0.58                          

               Factor1 Factor2 Factor3 Factor4 Factor5 Factor6
SS loadings       7.83    4.17    2.87    2.14    0.91    0.60
Proportion Var    0.22    0.12    0.08    0.06    0.03    0.02
Cumulative Var    0.22    0.33    0.41    0.47    0.50    0.51

Test of the hypothesis that 6 factors are sufficient.
The chi square statistic is 810.71 on 429 degrees of freedom.
The p-value is 7.64e-26 

Plot with title β€œScree plot”