#EXPLORATORY FACTOR ANALYSIS - Ad Engagement Scale
library(mice)
##
## Attaching package: 'mice'
## The following objects are masked from 'package:base':
##
## cbind, rbind
library(haven)
library(lavaan)
## This is lavaan 0.6-6
## lavaan is BETA software! Please report any bugs.
library(semPlot)
## Registered S3 methods overwritten by 'huge':
## method from
## plot.sim BDgraph
## print.sim BDgraph
library(foreign)
HalukSPSSData <- read.spss("haluk.sav",
to.data.frame=TRUE,
use.value.labels=FALSE)
halukvectorclean <- HalukSPSSData[,c(1:63)]
##accuracy
summary(halukvectorclean)
## M1 M2 M3 M4 M5
## Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:3.750 1st Qu.:3.00 1st Qu.:3.000 1st Qu.:3.00 1st Qu.:3.000
## Median :4.000 Median :4.00 Median :4.000 Median :4.00 Median :4.000
## Mean :3.825 Mean :3.75 Mean :3.813 Mean :3.47 Mean :3.545
## 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:4.000
## Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.00 Max. :5.000
## M6 M7 M8 M9 M10
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:3.00
## Median :4.000 Median :3.000 Median :4.000 Median :3.000 Median :4.00
## Mean :3.295 Mean :3.209 Mean :3.455 Mean :2.985 Mean :3.53
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.00
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.00
## M11 M12 M13 M14 M15
## Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.00 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.000
## Median :3.00 Median :3.000 Median :2.000 Median :2.000 Median :4.000
## Mean :2.91 Mean :2.974 Mean :2.541 Mean :2.795 Mean :3.761
## 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## M16 M17 M18 M19 M20
## Min. :1.000 Min. :1.00 Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:2.00 1st Qu.:3.00 1st Qu.:2.000 1st Qu.:3.000
## Median :4.000 Median :2.00 Median :4.00 Median :3.000 Median :4.000
## Mean :3.806 Mean :2.72 Mean :3.56 Mean :3.168 Mean :3.802
## 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.00 Max. :5.00 Max. :5.000 Max. :5.000
## M21 M22 M23 M24 M25
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.00 1st Qu.:2.000
## Median :4.000 Median :2.000 Median :3.000 Median :3.00 Median :2.000
## Mean :3.392 Mean :2.362 Mean :3.246 Mean :3.09 Mean :2.433
## 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:3.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.00 Max. :5.000
## M26 M27 M28 M29 M30
## Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.00 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000
## Median :3.000 Median :4.00 Median :3.000 Median :2.000 Median :3.000
## Mean :2.944 Mean :3.31 Mean :3.078 Mean :2.265 Mean :2.735
## 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000
## M31 M32 M33 M34
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:3.000 1st Qu.:2.000
## Median :4.000 Median :4.000 Median :4.000 Median :2.000
## Mean :3.668 Mean :3.358 Mean :3.571 Mean :2.646
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:3.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## M35 M36 M37 M38
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000
## Median :3.000 Median :3.000 Median :4.000 Median :2.000
## Mean :3.284 Mean :2.862 Mean :3.254 Mean :2.638
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## M39 M40 M41 M42 M43
## Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.00 1st Qu.:3.000 1st Qu.:3.750 1st Qu.:3.000
## Median :3.000 Median :2.00 Median :4.000 Median :4.000 Median :4.000
## Mean :2.948 Mean :2.09 Mean :3.381 Mean :3.795 Mean :3.481
## 3rd Qu.:4.000 3rd Qu.:2.00 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000
## M44 M45 M46 M47 M48
## Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.00 1st Qu.:2.000 1st Qu.:1.000
## Median :2.000 Median :3.000 Median :2.00 Median :3.000 Median :2.000
## Mean :2.698 Mean :2.925 Mean :2.56 Mean :3.235 Mean :2.131
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:3.00 3rd Qu.:4.000 3rd Qu.:3.000
## Max. :5.000 Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.000
## M49 M50 M51 M52
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:4.000 1st Qu.:2.000
## Median :3.000 Median :3.000 Median :4.000 Median :3.000
## Mean :2.873 Mean :2.944 Mean :3.907 Mean :2.981
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## M53 M54 M55 M56 M57
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.00 1st Qu.:2.000
## Median :2.000 Median :3.000 Median :2.000 Median :3.00 Median :4.000
## Mean :2.716 Mean :3.209 Mean :2.146 Mean :2.78 Mean :3.291
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:2.250 3rd Qu.:4.00 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.00 Max. :5.000
## M58 M59 M60 M61
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.000
## Median :2.000 Median :3.000 Median :3.000 Median :4.000
## Mean :2.045 Mean :2.802 Mean :2.728 Mean :3.784
## 3rd Qu.:2.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## M62 M63
## Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000
## Median :2.000 Median :3.000
## Mean :2.347 Mean :3.037
## 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000
##Reverse scored items (Kontrol etmek icin M22 ye baktim)
table(halukvectorclean$M22)
##
## 1 2 3 4 5
## 56 121 40 40 11
##Recode (Reverse scored items)
halukvectorclean[ , c(22,29,30,38,40,48,49,55,58)] = 6 - halukvectorclean[ , c(22,29,30,38,40,48,49,55,58) ]
##Reverse scored items (Ters cevirdi mi diye kontrol etmek icin M22 ye baktim)
table(halukvectorclean$M22)
##
## 1 2 3 4 5
## 11 40 40 121 56
##Replace missing data (Results 0 = no missing data in this file;, but still keep the formula here for future use)
#For the rest of the code to deal with missing data : https://www.youtube.com/watch?v=C5RJvMaHJNo (34:40 - 37:00)
percentmissing = function (x){ sum(is.na(x))/length(x) * 100}
missing = apply(halukvectorclean, 1, percentmissing)
table(missing)
## missing
## 0
## 268
#outliers (We check for weird patterns and scores)
cutoff = qchisq(1-.001, ncol(halukvectorclean))
mahal = mahalanobis(halukvectorclean,
colMeans(halukvectorclean),
cov(halukvectorclean))
cutoff ##cutoff score
## [1] 103.4424
ncol(halukvectorclean) ##df (degrees of freedom)
## [1] 63
summary(mahal < cutoff) ##This shows number of people (FALSE Column) whose score exceed thre cutoff score
## Mode FALSE TRUE
## logical 18 250
##Exclude those people (outliers)
haluknoutliers = subset(halukvectorclean, mahal < cutoff)
##additivity (We want the questions to be correleated but we want to be sure that nothing is correleated at 1 other than the diagonal in our symbol chart. Basicallay the rules is r < .999)
correl = cor(haluknoutliers, use = "pairwise.complete.obs")
symnum(correl)
## M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17 M18 M19 M20 M21
## M1 1
## M2 , 1
## M3 . , 1
## M4 . , , 1
## M5 . , , , 1
## M6 . . , , , 1
## M7 . . . . . . 1
## M8 . , , , , , . 1
## M9 . , , , , , . , 1
## M10 . , , , , , . , , 1
## M11 . . . , , , . , , , 1
## M12 . . . , . , . . , , , 1
## M13 . . . , . , . , , , , , 1
## M14 . . . . . , . . , . , , , 1
## M15 . , , , , , . , , , , , . . 1
## M16 . , , , , , . , , , , , . . , 1
## M17 . . . , , , . . , , , , , , . . 1
## M18 . , , , , , . , , , , , , , , , , 1
## M19 . , , , , , . , , , , . , , , , , , 1
## M20 . , , , , , . , . , . . . . + , . , , 1
## M21 . , , , , , . , , , , , , , , , , , , , 1
## M22 . . . . . . . . . . . . . . . . . . .
## M23 . , , , , , . , , , , , , , , , , + , , ,
## M24 . , , , , , . , , , , , , , , , , , , . ,
## M25 . . . . . . . , . . . , . . . , . . . .
## M26 . , . , . , . . , . , + , + . . , , . . ,
## M27 . , , , , , . , , , , , , , , , , + , , ,
## M28 . , , , , , . , , , , , , , , , , , , . ,
## M29 . . . . . . . . . . . . . . . . . . . . .
## M30 . . . . . . . . . . . . . . . . . , . . .
## M31 . , , , , , . , , , , , , , + , , + , , ,
## M32 . . , , . , . , , , , , , . , , , , , , ,
## M33 . , , , , , . , , , , , . . , , , , , , ,
## M34 . . . . . . . . . . . . . . . . . . . .
## M35 . , . , , , . , , , , , , . , , , , , . ,
## M36 . . . , . , . , , . , , , , . . + , , . ,
## M37 . , . , , , . , , , , , , , , , , , , , ,
## M38 . . . . . . . . . . . . . . . . . . . . .
## M39 . . . . . . . . . . .
## M40 . . . . . . . . . . . . . . . . . . .
## M41 . , . , . , . , , , , , , , , , , , , , ,
## M42 . . . . . . . . . . . . . . , . . . . , .
## M43 . . . . , , . . . . . . . . , , . , . , ,
## M44 . . . . . , . . , . , . , . . . , . , . .
## M45 . . . . . , . . , . , , , . . , , , , . ,
## M46 . . . . . , . . , . , . , . . . , . , . .
## M47 . , , , , , . , , , , , , , , , , , , , ,
## M48 . . . . . . . . . . . . . . . .
## M49 . . . . . . . . . . . . . . . . . . . .
## M50 . . . , , , . . , , , , , , . , , , , . ,
## M51 . . . . . . . . . . . . . . , . . . . , .
## M52 . . . , , , . , , , , , , , . , , , , , ,
## M53 . . . . . . . . , . , . . . . . , . . . .
## M54 . , , , , , . , , , , , , , , , , , , , ,
## M55 . . . . . . . . . . . . . . . . . . .
## M56 . . . , , , . . , , , , , , . . , , , . ,
## M57 . . , , . , . , , , . , . . , , , , , , ,
## M58 . . . . . . . . . . . . . . . . . . .
## M59 . . . . . . . . . , . . . . . , , , . ,
## M60 . . . . . , . . , . , , , . . . , , , . ,
## M61 . . . . . . . . . . . . . . , . . . . , .
## M62 . . . . . . . . . . . , . . . , . . . .
## M63 . . . , , , . . , , , , . , . , , , , . ,
## M22 M23 M24 M25 M26 M27 M28 M29 M30 M31 M32 M33 M34 M35 M36 M37 M38 M39 M40
## M1
## M2
## M3
## M4
## M5
## M6
## M7
## M8
## M9
## M10
## M11
## M12
## M13
## M14
## M15
## M16
## M17
## M18
## M19
## M20
## M21
## M22 1
## M23 . 1
## M24 . , 1
## M25 , . 1
## M26 . , , , 1
## M27 . , , . , 1
## M28 . , , , , + 1
## M29 , . . . . . 1
## M30 , . . . . . , , 1
## M31 . , , . , , , , . 1
## M32 . , , . , , , . . , 1
## M33 . , , . , , , . . , , 1
## M34 . . . . . . . . . 1
## M35 . , , . , , , . . , , , . 1
## M36 . , , , , , , . . , , , . , 1
## M37 . , , . , , , . . , , , . , , 1
## M38 . . . . . . . , , . , . . , . 1
## M39 . . . . . 1
## M40 , . . . . . , , . . . . . . , 1
## M41 . , , . , , , . . , , , . , , , . .
## M42 . . . . . . . . . . . . . . .
## M43 . , . . . , . . . , . . . . , . .
## M44 . , , . . , . . . , . . . , . .
## M45 . , , . , , , . . , , , . , , , . .
## M46 . , , , . , . . . , , . , , . .
## M47 . , , . , , , . . , , , . , , , , .
## M48 . . . . . , . . . . . . . ,
## M49 . . . . . . . , , . , . . . , . , .
## M50 . , , , , , , . . , , , . , , , . .
## M51 . . . . . . . . , . . . . . . .
## M52 , , . , , , . . , , , . , , , . .
## M53 . , . . . , . . . , . . . , . . .
## M54 . , , . , , , . . , , , . , , , , .
## M55 . . . . . . , , . . . . . . . ,
## M56 . , , , , , , . . , , , . , , , . .
## M57 . , , . , , , . . , + , . , , , . .
## M58 . . . . . . , , . . . . . . , ,
## M59 . , . . . , . . . , , . , , , . .
## M60 . , , . , , , . . . , , . , + , . .
## M61 . . . . . . . . . . . . . . . . .
## M62 . . . . . . . . . . . . , . .
## M63 . , , . , , , . . , , , . , , , . .
## M41 M42 M43 M44 M45 M46 M47 M48 M49 M50 M51 M52 M53 M54 M55 M56 M57 M58 M59
## M1
## M2
## M3
## M4
## M5
## M6
## M7
## M8
## M9
## M10
## M11
## M12
## M13
## M14
## M15
## M16
## M17
## M18
## M19
## M20
## M21
## M22
## M23
## M24
## M25
## M26
## M27
## M28
## M29
## M30
## M31
## M32
## M33
## M34
## M35
## M36
## M37
## M38
## M39
## M40
## M41 1
## M42 . 1
## M43 . , 1
## M44 , . . 1
## M45 , . . + 1
## M46 , . . * , 1
## M47 + . . , , , 1
## M48 . . . 1
## M49 . . . , . , . 1
## M50 , . . , , , , . 1
## M51 . . , . . . . . . . 1
## M52 , . . , , , , . . , . 1
## M53 , . . + , + , . , . , 1
## M54 , . . , , , + . , , . , , 1
## M55 . . . . , . . . . . 1
## M56 , . , , , , , . . , . , , , . 1
## M57 , . . , , , , . . , . , , , . , 1
## M58 . . . . . , . . . . . , . . 1
## M59 , . . , , , , . , . , , , , , . 1
## M60 , . . + + + , . , . , + , , , . ,
## M61 . , , . . . . . . . . . . . . . . . .
## M62 . . . , , , . . , . , , . , . ,
## M63 , . . , , , , . . , . , , , . , + . ,
## M60 M61 M62 M63
## M1
## M2
## M3
## M4
## M5
## M6
## M7
## M8
## M9
## M10
## M11
## M12
## M13
## M14
## M15
## M16
## M17
## M18
## M19
## M20
## M21
## M22
## M23
## M24
## M25
## M26
## M27
## M28
## M29
## M30
## M31
## M32
## M33
## M34
## M35
## M36
## M37
## M38
## M39
## M40
## M41
## M42
## M43
## M44
## M45
## M46
## M47
## M48
## M49
## M50
## M51
## M52
## M53
## M54
## M55
## M56
## M57
## M58
## M59
## M60 1
## M61 . 1
## M62 , . 1
## M63 + . , 1
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1
correl
## M1 M2 M3 M4 M5 M6 M7
## M1 1.0000000 0.6321523 0.5795418 0.4317280 0.5216483 0.4548816 0.3779043
## M2 0.6321523 1.0000000 0.7655722 0.6906350 0.6744217 0.5853255 0.4568489
## M3 0.5795418 0.7655722 1.0000000 0.6751008 0.6992313 0.6114384 0.4680335
## M4 0.4317280 0.6906350 0.6751008 1.0000000 0.7465273 0.6731425 0.4737944
## M5 0.5216483 0.6744217 0.6992313 0.7465273 1.0000000 0.7153987 0.5364444
## M6 0.4548816 0.5853255 0.6114384 0.6731425 0.7153987 1.0000000 0.5202606
## M7 0.3779043 0.4568489 0.4680335 0.4737944 0.5364444 0.5202606 1.0000000
## M8 0.5424643 0.7265811 0.7668668 0.6530401 0.6844235 0.6165880 0.5743154
## M9 0.4910246 0.6613296 0.6547015 0.7381613 0.6879359 0.6836640 0.5710996
## M10 0.5131836 0.6823433 0.7158665 0.6651990 0.7469557 0.6579725 0.4797385
## M11 0.4369026 0.5937089 0.5800273 0.6371852 0.6385396 0.6546240 0.4826837
## M12 0.4157482 0.5669997 0.5392246 0.6537988 0.5867596 0.6505204 0.5199397
## M13 0.3705668 0.5732277 0.5208453 0.6233333 0.5826167 0.6061546 0.5353663
## M14 0.3618388 0.5582460 0.5203061 0.5900534 0.5791358 0.6498232 0.4853923
## M15 0.4867034 0.6438350 0.6649510 0.6358677 0.6739252 0.6121998 0.5181396
## M16 0.5885688 0.7096790 0.7611271 0.6648424 0.7204487 0.6588858 0.5150699
## M17 0.4020923 0.5447092 0.5450069 0.6297363 0.6022583 0.6475735 0.4830283
## M18 0.4901415 0.6612701 0.7108030 0.7255092 0.7253987 0.6782678 0.5156280
## M19 0.4909787 0.6598523 0.6912659 0.6927596 0.7289461 0.6669013 0.5664422
## M20 0.4856511 0.6126779 0.6977935 0.6035320 0.6437605 0.6128525 0.5090548
## M21 0.4130215 0.6205777 0.6161453 0.6267899 0.6376531 0.7422742 0.4988461
## M22 0.4189056 0.3746733 0.3909715 0.3527703 0.3703703 0.3725927 0.1913121
## M23 0.4585483 0.6277258 0.6533532 0.6771221 0.6408321 0.6640316 0.4931404
## M24 0.4570523 0.6450875 0.6210639 0.6482070 0.6216841 0.6592808 0.4842513
## M25 0.2962229 0.4858321 0.4906179 0.5808742 0.5110873 0.5070925 0.4296117
## M26 0.4116060 0.6103101 0.5378916 0.6322722 0.5700752 0.6419726 0.4589025
## M27 0.4608002 0.6483211 0.6646605 0.6944840 0.6692769 0.6853387 0.4470609
## M28 0.4491591 0.6450875 0.6658678 0.7455521 0.6792981 0.6524582 0.5015252
## M29 0.4178225 0.4669634 0.5055613 0.4446808 0.5242113 0.4316458 0.3650334
## M30 0.3826603 0.5055339 0.4982545 0.5807407 0.5404429 0.5288117 0.3186184
## M31 0.5101444 0.6818617 0.7460880 0.6939652 0.7041842 0.6639134 0.4871885
## M32 0.4491311 0.5937515 0.6421308 0.6474061 0.5962912 0.6663733 0.4189599
## M33 0.4643834 0.6613732 0.6644876 0.6643074 0.6770374 0.6093925 0.4910528
## M34 0.2992731 0.3830585 0.3619056 0.3958279 0.3700924 0.3653330 0.3693312
## M35 0.4350556 0.6051265 0.5603202 0.6117605 0.6786661 0.6693292 0.5110175
## M36 0.3864130 0.5881541 0.5643923 0.6446825 0.5712593 0.6740804 0.4773295
## M37 0.4072344 0.6050421 0.5974517 0.6531507 0.6531559 0.6984232 0.5183772
## M38 0.3730494 0.4331078 0.4592547 0.5138264 0.4613842 0.5138920 0.3147916
## M39 0.2698974 0.3191019 0.3611779 0.3295367 0.3491661 0.3037925 0.2922731
## M40 0.3715737 0.4127864 0.4573541 0.3806399 0.4350868 0.4068644 0.2765414
## M41 0.4858458 0.6193167 0.5961205 0.6325387 0.5919097 0.6242997 0.4912837
## M42 0.3682592 0.4853848 0.5092397 0.4716771 0.5011734 0.4239969 0.4145879
## M43 0.4035903 0.5400041 0.5750424 0.5732013 0.6133471 0.6806723 0.4561533
## M44 0.3499932 0.5390487 0.5171287 0.5962100 0.5532469 0.6117503 0.4356509
## M45 0.4045192 0.5663508 0.5420711 0.5956580 0.5575695 0.6529462 0.4635993
## M46 0.3255800 0.5372544 0.5152131 0.5763453 0.5097800 0.6035093 0.4827717
## M47 0.4864959 0.6470131 0.6518542 0.6591348 0.6219662 0.6324232 0.4252873
## M48 0.3140135 0.3650953 0.3636870 0.3281918 0.3051202 0.3393295 0.1914439
## M49 0.3354886 0.4642639 0.4487445 0.5089530 0.4396331 0.4805999 0.2899469
## M50 0.3848525 0.5657894 0.5510407 0.6138263 0.6049772 0.6356114 0.4445485
## M51 0.4224918 0.5482469 0.5486998 0.4901552 0.5585907 0.5053274 0.4257945
## M52 0.3847002 0.5809179 0.5957132 0.6158578 0.6241632 0.6103746 0.4493199
## M53 0.3295401 0.4991292 0.5039808 0.5835413 0.4868968 0.5746755 0.4230984
## M54 0.4895777 0.6530094 0.6590389 0.6262675 0.6199928 0.6223598 0.4321229
## M55 0.3832656 0.4190462 0.4272173 0.3875857 0.3824845 0.3567347 0.2647031
## M56 0.3790819 0.5611048 0.5817650 0.6272108 0.6565332 0.6952175 0.5139863
## M57 0.4144613 0.5771374 0.6232211 0.6175142 0.5974404 0.6479697 0.4191692
## M58 0.4056651 0.4010706 0.4326304 0.3826051 0.4027125 0.3922343 0.2806483
## M59 0.2880050 0.4970002 0.4696283 0.5710317 0.5403731 0.5708515 0.4267509
## M60 0.3432942 0.5183160 0.5305361 0.5832719 0.5386269 0.6458525 0.4380789
## M61 0.3698628 0.4883801 0.5273762 0.4890578 0.5327361 0.4664917 0.3570427
## M62 0.2234211 0.4147514 0.4037703 0.4869849 0.4500102 0.5308664 0.4214689
## M63 0.3738716 0.5632419 0.5708411 0.6396421 0.6039417 0.6636587 0.4476430
## M8 M9 M10 M11 M12 M13 M14
## M1 0.5424643 0.4910246 0.5131836 0.4369026 0.4157482 0.3705668 0.3618388
## M2 0.7265811 0.6613296 0.6823433 0.5937089 0.5669997 0.5732277 0.5582460
## M3 0.7668668 0.6547015 0.7158665 0.5800273 0.5392246 0.5208453 0.5203061
## M4 0.6530401 0.7381613 0.6651990 0.6371852 0.6537988 0.6233333 0.5900534
## M5 0.6844235 0.6879359 0.7469557 0.6385396 0.5867596 0.5826167 0.5791358
## M6 0.6165880 0.6836640 0.6579725 0.6546240 0.6505204 0.6061546 0.6498232
## M7 0.5743154 0.5710996 0.4797385 0.4826837 0.5199397 0.5353663 0.4853923
## M8 1.0000000 0.7257017 0.7316584 0.6479352 0.5837358 0.6027326 0.5626522
## M9 0.7257017 1.0000000 0.6827080 0.6902069 0.7158793 0.7266039 0.6559704
## M10 0.7316584 0.6827080 1.0000000 0.6576479 0.6167345 0.6002691 0.5975896
## M11 0.6479352 0.6902069 0.6576479 1.0000000 0.6865104 0.6716035 0.6198329
## M12 0.5837358 0.7158793 0.6167345 0.6865104 1.0000000 0.7450761 0.7639932
## M13 0.6027326 0.7266039 0.6002691 0.6716035 0.7450761 1.0000000 0.7471690
## M14 0.5626522 0.6559704 0.5975896 0.6198329 0.7639932 0.7471690 1.0000000
## M15 0.6698322 0.6131103 0.7128879 0.6048074 0.6000115 0.5749387 0.5769775
## M16 0.7359108 0.6591614 0.7704290 0.6426291 0.6071548 0.5654842 0.5629857
## M17 0.5742985 0.7058158 0.6100741 0.7270236 0.7169220 0.6871390 0.6252221
## M18 0.7403417 0.6958319 0.7464067 0.6570255 0.6744937 0.6137592 0.6371066
## M19 0.7500789 0.7098137 0.7076354 0.6542936 0.5991298 0.6498768 0.6258826
## M20 0.6812009 0.5920469 0.6733781 0.5707480 0.5651716 0.4997291 0.5092601
## M21 0.6459354 0.6607701 0.6546792 0.6198579 0.6350962 0.6046777 0.6193537
## M22 0.3673319 0.3452476 0.4137193 0.3160229 0.3069308 0.2523609 0.3103868
## M23 0.6550142 0.6936775 0.6986966 0.6389647 0.6686875 0.6439611 0.6277915
## M24 0.6829713 0.7088935 0.6923548 0.7089912 0.6917082 0.6323422 0.6108524
## M25 0.5245157 0.6043457 0.5427529 0.5532411 0.5735054 0.6915342 0.5934824
## M26 0.5956344 0.7203675 0.5933721 0.6327072 0.8202898 0.7144694 0.8010517
## M27 0.6778633 0.7146645 0.6800312 0.6381283 0.7071061 0.6363602 0.7052043
## M28 0.7186051 0.7792256 0.6992902 0.6897147 0.7343027 0.7180370 0.6856130
## M29 0.5175670 0.4655609 0.5042525 0.4254940 0.4283498 0.3454983 0.3461469
## M30 0.5731563 0.5594014 0.5620848 0.4775611 0.4956239 0.4890821 0.4899169
## M31 0.7270608 0.6741831 0.7706722 0.6493449 0.6446088 0.6037950 0.6125982
## M32 0.6252472 0.6654321 0.6557783 0.6551173 0.6280865 0.6061130 0.5591574
## M33 0.6837936 0.6734176 0.6923130 0.6289594 0.6200568 0.5999901 0.5746950
## M34 0.4583846 0.4767703 0.4082927 0.5143166 0.4149687 0.4778058 0.4194263
## M35 0.6198552 0.6634017 0.6420570 0.6688372 0.6656885 0.6630043 0.5917499
## M36 0.6388161 0.7302718 0.5950718 0.7300000 0.6954439 0.6779232 0.6148917
## M37 0.6493976 0.6486655 0.6767648 0.6586810 0.6692258 0.6547742 0.6412764
## M38 0.4804774 0.5319439 0.5048936 0.5015999 0.5098747 0.4561097 0.4049860
## M39 0.3505303 0.2962663 0.3300978 0.2791581 0.2529800 0.2954479 0.2291170
## M40 0.4487257 0.3845874 0.4599047 0.3655036 0.3754697 0.2985257 0.3602075
## M41 0.6454668 0.6675664 0.6297138 0.7109185 0.6993372 0.6224969 0.6263188
## M42 0.4679101 0.5023382 0.4964774 0.3911294 0.4296611 0.4296355 0.3598198
## M43 0.5666176 0.5747446 0.5673990 0.5824232 0.5108464 0.5221566 0.4897790
## M44 0.5480657 0.6777309 0.5442984 0.6357979 0.5840255 0.6044987 0.5627781
## M45 0.5928143 0.6383920 0.5966822 0.6465732 0.6181649 0.6372439 0.5982440
## M46 0.5774322 0.6687278 0.5232889 0.6286322 0.5928864 0.6425985 0.5683830
## M47 0.6964761 0.6967317 0.6868430 0.6785125 0.6845984 0.6565836 0.6261321
## M48 0.3519678 0.2820582 0.3424081 0.2408525 0.3048145 0.2134459 0.3150946
## M49 0.4859888 0.5170626 0.4840569 0.5216855 0.4988868 0.4508515 0.4682391
## M50 0.5894689 0.6494861 0.6374303 0.7734545 0.6784800 0.6638044 0.6152783
## M51 0.5415973 0.5434770 0.5793035 0.5236575 0.4797999 0.5019403 0.4616136
## M52 0.6208911 0.6440399 0.6314268 0.6332663 0.6172263 0.6188626 0.6276389
## M53 0.5468885 0.6442651 0.4873944 0.6035463 0.5866033 0.5910017 0.5500225
## M54 0.7068281 0.7066693 0.6749338 0.6657378 0.6388169 0.6545025 0.6077477
## M55 0.4180057 0.3580252 0.4321386 0.3240005 0.3605596 0.2549917 0.3352358
## M56 0.5998247 0.6857617 0.6063300 0.6467481 0.6244020 0.6859288 0.6269180
## M57 0.6354736 0.6474076 0.6409329 0.5909837 0.6133397 0.5576389 0.5453173
## M58 0.4563957 0.3671418 0.4696652 0.3928956 0.3900784 0.2756863 0.3139797
## M59 0.5220011 0.5959968 0.4799934 0.6145506 0.5288328 0.5974590 0.5377333
## M60 0.5623527 0.6930458 0.5447904 0.6912711 0.6397456 0.6452051 0.5845962
## M61 0.4979879 0.5009237 0.4948258 0.3911245 0.4420496 0.4140903 0.4032669
## M62 0.4275457 0.5746850 0.4266049 0.5736499 0.5494893 0.6146896 0.5426786
## M63 0.5739886 0.6669951 0.6059574 0.6517208 0.6562481 0.5995649 0.6028620
## M15 M16 M17 M18 M19 M20 M21
## M1 0.4867034 0.5885688 0.4020923 0.4901415 0.4909787 0.4856511 0.4130215
## M2 0.6438350 0.7096790 0.5447092 0.6612701 0.6598523 0.6126779 0.6205777
## M3 0.6649510 0.7611271 0.5450069 0.7108030 0.6912659 0.6977935 0.6161453
## M4 0.6358677 0.6648424 0.6297363 0.7255092 0.6927596 0.6035320 0.6267899
## M5 0.6739252 0.7204487 0.6022583 0.7253987 0.7289461 0.6437605 0.6376531
## M6 0.6121998 0.6588858 0.6475735 0.6782678 0.6669013 0.6128525 0.7422742
## M7 0.5181396 0.5150699 0.4830283 0.5156280 0.5664422 0.5090548 0.4988461
## M8 0.6698322 0.7359108 0.5742985 0.7403417 0.7500789 0.6812009 0.6459354
## M9 0.6131103 0.6591614 0.7058158 0.6958319 0.7098137 0.5920469 0.6607701
## M10 0.7128879 0.7704290 0.6100741 0.7464067 0.7076354 0.6733781 0.6546792
## M11 0.6048074 0.6426291 0.7270236 0.6570255 0.6542936 0.5707480 0.6198579
## M12 0.6000115 0.6071548 0.7169220 0.6744937 0.5991298 0.5651716 0.6350962
## M13 0.5749387 0.5654842 0.6871390 0.6137592 0.6498768 0.4997291 0.6046777
## M14 0.5769775 0.5629857 0.6252221 0.6371066 0.6258826 0.5092601 0.6193537
## M15 1.0000000 0.7772481 0.5506741 0.7848155 0.6229657 0.8046204 0.6548188
## M16 0.7772481 1.0000000 0.5866535 0.7416004 0.7057396 0.7210891 0.6773408
## M17 0.5506741 0.5866535 1.0000000 0.6947641 0.6736143 0.5542134 0.6424386
## M18 0.7848155 0.7416004 0.6947641 1.0000000 0.7540421 0.7601753 0.7430112
## M19 0.6229657 0.7057396 0.6736143 0.7540421 1.0000000 0.6429599 0.6826267
## M20 0.8046204 0.7210891 0.5542134 0.7601753 0.6429599 1.0000000 0.7331573
## M21 0.6548188 0.6773408 0.6424386 0.7430112 0.6826267 0.7331573 1.0000000
## M22 0.4241762 0.4092903 0.3169794 0.4468327 0.3497437 0.3964406 0.3206274
## M23 0.6840215 0.6876774 0.6543821 0.8036646 0.7093017 0.6548881 0.7397641
## M24 0.6077687 0.6689508 0.7448723 0.7114231 0.6977605 0.5821650 0.6925941
## M25 0.4636040 0.4673953 0.6003112 0.5554750 0.5890015 0.4458467 0.5016105
## M26 0.5897425 0.5843129 0.6661021 0.6493944 0.5915994 0.5181713 0.6495444
## M27 0.6819679 0.6852451 0.6538563 0.8022745 0.6675790 0.6626301 0.6995754
## M28 0.6422557 0.6727365 0.7132284 0.7599604 0.7045107 0.5983318 0.6588420
## M29 0.5371283 0.5388412 0.4347466 0.5438497 0.5132409 0.5512428 0.4420975
## M30 0.4974189 0.4884291 0.5170065 0.6009382 0.5259709 0.4709997 0.5177127
## M31 0.8086787 0.7987842 0.6122296 0.8186980 0.7268862 0.7869735 0.7312913
## M32 0.6111966 0.6591955 0.7298153 0.7151911 0.7013440 0.6328264 0.6811099
## M33 0.7048444 0.7110186 0.6536918 0.7355010 0.6979137 0.6840921 0.6691762
## M34 0.3524835 0.4066623 0.4340188 0.4030416 0.4770943 0.3721765 0.3964798
## M35 0.6537474 0.6721024 0.6334996 0.7012471 0.6225167 0.5976378 0.6533055
## M36 0.5555003 0.5669813 0.8519033 0.6872386 0.6804249 0.5467926 0.6472245
## M37 0.6613086 0.6583048 0.6574280 0.7241316 0.6795389 0.6327602 0.7295526
## M38 0.4339486 0.4937871 0.5809730 0.5246530 0.4997932 0.4366254 0.4743686
## M39 0.3410359 0.3650483 0.2295227 0.3372350 0.3382734 0.2645099 0.2775461
## M40 0.5157209 0.4619756 0.3231428 0.5184057 0.4005200 0.5024606 0.3989103
## M41 0.6266186 0.6673294 0.7567621 0.7269017 0.6782729 0.6292417 0.6447393
## M42 0.6347479 0.5576191 0.3767726 0.5521470 0.4000761 0.6067985 0.4926507
## M43 0.6283987 0.6220023 0.4909755 0.6010605 0.5631593 0.6536049 0.6995459
## M44 0.4861803 0.5417883 0.7471870 0.5731481 0.6261531 0.4894444 0.5704794
## M45 0.5809731 0.6203218 0.7326862 0.6722386 0.6620596 0.5761714 0.6373409
## M46 0.4818276 0.5206538 0.7568419 0.5715789 0.6161680 0.5036936 0.5926976
## M47 0.6369472 0.6675506 0.7492154 0.7699705 0.7092568 0.6401267 0.6470103
## M48 0.3954636 0.3855666 0.2390395 0.3995668 0.3540150 0.4242314 0.3575683
## M49 0.4292078 0.4761028 0.5940397 0.5239970 0.5331044 0.4518340 0.5043173
## M50 0.5811727 0.6233713 0.7556777 0.6545252 0.6345158 0.5767442 0.6427554
## M51 0.6318621 0.5968018 0.4503668 0.5905126 0.5325953 0.6099318 0.5437737
## M52 0.5900750 0.6090815 0.6786994 0.6579927 0.6562050 0.6581081 0.6385444
## M53 0.4595392 0.5024381 0.7401517 0.5540361 0.5807998 0.4950355 0.5479895
## M54 0.6421872 0.6956316 0.7037757 0.7119339 0.7005216 0.6013549 0.6419172
## M55 0.4720392 0.4470531 0.3365239 0.4794802 0.3721734 0.4311482 0.3988639
## M56 0.5700893 0.5937027 0.7061729 0.6714342 0.6936701 0.5889040 0.6974267
## M57 0.6141441 0.6466834 0.6972638 0.7059466 0.6925341 0.6242115 0.6575278
## M58 0.5147877 0.4830692 0.3303844 0.5146595 0.4056789 0.5154438 0.4385299
## M59 0.4419483 0.5136099 0.6767602 0.6085219 0.6255496 0.4896203 0.6064084
## M60 0.5073639 0.5207059 0.7859641 0.6237941 0.6100774 0.5175627 0.6081248
## M61 0.6144400 0.5454978 0.3787609 0.5550687 0.4368657 0.6126459 0.4977011
## M62 0.4413277 0.4481349 0.6446261 0.4822119 0.5253699 0.4523872 0.5208965
## M63 0.5910301 0.6056741 0.7390437 0.6873391 0.6585640 0.5674291 0.6073881
## M22 M23 M24 M25 M26 M27 M28
## M1 0.41890556 0.4585483 0.4570523 0.2962229 0.4116060 0.4608002 0.4491591
## M2 0.37467333 0.6277258 0.6450875 0.4858321 0.6103101 0.6483211 0.6450875
## M3 0.39097153 0.6533532 0.6210639 0.4906179 0.5378916 0.6646605 0.6658678
## M4 0.35277033 0.6771221 0.6482070 0.5808742 0.6322722 0.6944840 0.7455521
## M5 0.37037032 0.6408321 0.6216841 0.5110873 0.5700752 0.6692769 0.6792981
## M6 0.37259271 0.6640316 0.6592808 0.5070925 0.6419726 0.6853387 0.6524582
## M7 0.19131210 0.4931404 0.4842513 0.4296117 0.4589025 0.4470609 0.5015252
## M8 0.36733185 0.6550142 0.6829713 0.5245157 0.5956344 0.6778633 0.7186051
## M9 0.34524762 0.6936775 0.7088935 0.6043457 0.7203675 0.7146645 0.7792256
## M10 0.41371927 0.6986966 0.6923548 0.5427529 0.5933721 0.6800312 0.6992902
## M11 0.31602295 0.6389647 0.7089912 0.5532411 0.6327072 0.6381283 0.6897147
## M12 0.30693078 0.6686875 0.6917082 0.5735054 0.8202898 0.7071061 0.7343027
## M13 0.25236092 0.6439611 0.6323422 0.6915342 0.7144694 0.6363602 0.7180370
## M14 0.31038676 0.6277915 0.6108524 0.5934824 0.8010517 0.7052043 0.6856130
## M15 0.42417622 0.6840215 0.6077687 0.4636040 0.5897425 0.6819679 0.6422557
## M16 0.40929026 0.6876774 0.6689508 0.4673953 0.5843129 0.6852451 0.6727365
## M17 0.31697945 0.6543821 0.7448723 0.6003112 0.6661021 0.6538563 0.7132284
## M18 0.44683274 0.8036646 0.7114231 0.5554750 0.6493944 0.8022745 0.7599604
## M19 0.34974372 0.7093017 0.6977605 0.5890015 0.5915994 0.6675790 0.7045107
## M20 0.39644062 0.6548881 0.5821650 0.4458467 0.5181713 0.6626301 0.5983318
## M21 0.32062745 0.7397641 0.6925941 0.5016105 0.6495444 0.6995754 0.6588420
## M22 1.00000000 0.3924842 0.3424138 0.1665203 0.3473095 0.4131849 0.3424138
## M23 0.39248422 1.0000000 0.7251840 0.6539168 0.6909281 0.7837509 0.7746457
## M24 0.34241378 0.7251840 1.0000000 0.5925975 0.6821971 0.7285850 0.7191642
## M25 0.16652029 0.6539168 0.5925975 1.0000000 0.6048198 0.5823829 0.7020298
## M26 0.34730951 0.6909281 0.6821971 0.6048198 1.0000000 0.7647429 0.7018020
## M27 0.41318488 0.7837509 0.7285850 0.5823829 0.7647429 1.0000000 0.8063407
## M28 0.34241378 0.7746457 0.7191642 0.7020298 0.7018020 0.8063407 1.0000000
## M29 0.60130575 0.4548511 0.4222960 0.2915302 0.3985023 0.4707307 0.4989311
## M30 0.60789701 0.5859859 0.5361215 0.4823795 0.5309867 0.5982012 0.6477256
## M31 0.45865359 0.7659949 0.6809044 0.5459138 0.6472983 0.7494609 0.7193354
## M32 0.37638075 0.6870505 0.7131327 0.5414077 0.6057425 0.6881784 0.6935677
## M33 0.41600942 0.6982989 0.6557396 0.5906335 0.6470017 0.6962419 0.6986920
## M34 0.10871224 0.4225784 0.4358801 0.4995428 0.4065747 0.3736270 0.4537160
## M35 0.39172241 0.6973493 0.6804859 0.5543159 0.6662757 0.7111562 0.6839432
## M36 0.31992846 0.6799672 0.7734864 0.6176030 0.6881620 0.6717349 0.7085218
## M37 0.36959702 0.7347880 0.6872682 0.5894992 0.6693518 0.7616197 0.7173846
## M38 0.55332716 0.4915009 0.5314707 0.3694524 0.4727357 0.4993087 0.5248650
## M39 0.06794328 0.2775077 0.2799213 0.2561371 0.2829544 0.3003206 0.3077520
## M40 0.62762438 0.4108995 0.3823364 0.2175506 0.3209083 0.4584907 0.4039755
## M41 0.37278372 0.7168162 0.7475057 0.5596755 0.6681295 0.7167492 0.7256181
## M42 0.25015657 0.5052378 0.3639925 0.3029725 0.4063433 0.5138724 0.4752663
## M43 0.31423509 0.6095350 0.5405112 0.4007808 0.5199778 0.6008874 0.5699942
## M44 0.22115588 0.5950274 0.6996579 0.6039262 0.5866241 0.5837408 0.6314790
## M45 0.36809852 0.6774040 0.7505532 0.5752226 0.6299708 0.6999370 0.6700669
## M46 0.20880876 0.5964134 0.6796113 0.6321379 0.6313291 0.5711902 0.6382368
## M47 0.42399010 0.7115047 0.7495860 0.5868824 0.6506367 0.7262369 0.7299606
## M48 0.50119054 0.3548789 0.3230307 0.1788081 0.2977049 0.4054018 0.3393817
## M49 0.50375536 0.5171263 0.5862023 0.4270994 0.4885724 0.4992087 0.5356458
## M50 0.32766391 0.6687247 0.7174531 0.6220000 0.6572413 0.6598824 0.7007774
## M51 0.27464746 0.5379825 0.4703780 0.3374158 0.4302614 0.5453630 0.5380648
## M52 0.29723554 0.6918697 0.6582684 0.5961975 0.6154504 0.6463294 0.6685479
## M53 0.24785449 0.5586967 0.6473224 0.5590610 0.5676807 0.5673771 0.6206825
## M54 0.40572549 0.6858040 0.7160511 0.5648049 0.6257990 0.6772421 0.7193381
## M55 0.52264363 0.3823970 0.3782767 0.1879797 0.3409750 0.4435028 0.4083586
## M56 0.31715127 0.7075628 0.7086940 0.6273132 0.6753041 0.6931913 0.6952335
## M57 0.33961084 0.6880037 0.6629811 0.5050792 0.6113427 0.6708304 0.6916469
## M58 0.56744162 0.4417319 0.3618333 0.2182240 0.3535202 0.4577280 0.4287156
## M59 0.29813129 0.5849894 0.6375600 0.5429385 0.5551936 0.5933024 0.6045886
## M60 0.31202962 0.6361321 0.7137912 0.5684572 0.6331791 0.6262486 0.6694046
## M61 0.30835273 0.5356032 0.3884316 0.3381107 0.4671253 0.5107471 0.4897799
## M62 0.18299387 0.5675728 0.5760460 0.5315807 0.5626596 0.4941050 0.5379053
## M63 0.33614663 0.6942619 0.7146297 0.5732848 0.6308258 0.6858706 0.6948287
## M29 M30 M31 M32 M33 M34 M35
## M1 0.4178225 0.3826603 0.5101444 0.4491311 0.4643834 0.2992731 0.4350556
## M2 0.4669634 0.5055339 0.6818617 0.5937515 0.6613732 0.3830585 0.6051265
## M3 0.5055613 0.4982545 0.7460880 0.6421308 0.6644876 0.3619056 0.5603202
## M4 0.4446808 0.5807407 0.6939652 0.6474061 0.6643074 0.3958279 0.6117605
## M5 0.5242113 0.5404429 0.7041842 0.5962912 0.6770374 0.3700924 0.6786661
## M6 0.4316458 0.5288117 0.6639134 0.6663733 0.6093925 0.3653330 0.6693292
## M7 0.3650334 0.3186184 0.4871885 0.4189599 0.4910528 0.3693312 0.5110175
## M8 0.5175670 0.5731563 0.7270608 0.6252472 0.6837936 0.4583846 0.6198552
## M9 0.4655609 0.5594014 0.6741831 0.6654321 0.6734176 0.4767703 0.6634017
## M10 0.5042525 0.5620848 0.7706722 0.6557783 0.6923130 0.4082927 0.6420570
## M11 0.4254940 0.4775611 0.6493449 0.6551173 0.6289594 0.5143166 0.6688372
## M12 0.4283498 0.4956239 0.6446088 0.6280865 0.6200568 0.4149687 0.6656885
## M13 0.3454983 0.4890821 0.6037950 0.6061130 0.5999901 0.4778058 0.6630043
## M14 0.3461469 0.4899169 0.6125982 0.5591574 0.5746950 0.4194263 0.5917499
## M15 0.5371283 0.4974189 0.8086787 0.6111966 0.7048444 0.3524835 0.6537474
## M16 0.5388412 0.4884291 0.7987842 0.6591955 0.7110186 0.4066623 0.6721024
## M17 0.4347466 0.5170065 0.6122296 0.7298153 0.6536918 0.4340188 0.6334996
## M18 0.5438497 0.6009382 0.8186980 0.7151911 0.7355010 0.4030416 0.7012471
## M19 0.5132409 0.5259709 0.7268862 0.7013440 0.6979137 0.4770943 0.6225167
## M20 0.5512428 0.4709997 0.7869735 0.6328264 0.6840921 0.3721765 0.5976378
## M21 0.4420975 0.5177127 0.7312913 0.6811099 0.6691762 0.3964798 0.6533055
## M22 0.6013058 0.6078970 0.4586536 0.3763807 0.4160094 0.1087122 0.3917224
## M23 0.4548511 0.5859859 0.7659949 0.6870505 0.6982989 0.4225784 0.6973493
## M24 0.4222960 0.5361215 0.6809044 0.7131327 0.6557396 0.4358801 0.6804859
## M25 0.2915302 0.4823795 0.5459138 0.5414077 0.5906335 0.4995428 0.5543159
## M26 0.3985023 0.5309867 0.6472983 0.6057425 0.6470017 0.4065747 0.6662757
## M27 0.4707307 0.5982012 0.7494609 0.6881784 0.6962419 0.3736270 0.7111562
## M28 0.4989311 0.6477256 0.7193354 0.6935677 0.6986920 0.4537160 0.6839432
## M29 1.0000000 0.6615619 0.6171626 0.4917939 0.5804658 0.1897147 0.4726928
## M30 0.6615619 1.0000000 0.5838290 0.5745085 0.5746655 0.2841742 0.5525574
## M31 0.6171626 0.5838290 1.0000000 0.7670293 0.7985993 0.4390536 0.6938415
## M32 0.4917939 0.5745085 0.7670293 1.0000000 0.6909054 0.3926139 0.6363141
## M33 0.5804658 0.5746655 0.7985993 0.6909054 1.0000000 0.4932050 0.6916455
## M34 0.1897147 0.2841742 0.4390536 0.3926139 0.4932050 1.0000000 0.4868312
## M35 0.4726928 0.5525574 0.6938415 0.6363141 0.6916455 0.4868312 1.0000000
## M36 0.4256571 0.5419311 0.6417378 0.7564657 0.6706005 0.5057829 0.6809835
## M37 0.4672469 0.5715674 0.7284792 0.7086240 0.7137808 0.4377997 0.7386955
## M38 0.6343733 0.6518692 0.5384281 0.6122783 0.5745309 0.2652636 0.5305205
## M39 0.1291790 0.1423535 0.3144901 0.2297453 0.2844803 0.2933813 0.3132371
## M40 0.6933838 0.6782263 0.5235208 0.4278018 0.4818754 0.1523028 0.3814957
## M41 0.4958703 0.5363464 0.7264701 0.7270749 0.7052270 0.4709077 0.6937293
## M42 0.3807356 0.3046562 0.5831084 0.4211550 0.4765251 0.2022211 0.4343372
## M43 0.4241831 0.3909936 0.6430177 0.5644928 0.5719253 0.2943211 0.5830023
## M44 0.3338571 0.4337837 0.5808941 0.7136989 0.5899044 0.4605905 0.5805489
## M45 0.4211802 0.5378552 0.6886517 0.7498883 0.6622127 0.4097775 0.7066968
## M46 0.3383968 0.4459470 0.5641824 0.7121977 0.6061915 0.4867555 0.6083310
## M47 0.5360188 0.5847390 0.7620482 0.7582207 0.7350597 0.4227953 0.7060947
## M48 0.6141278 0.5659521 0.4525050 0.3642784 0.3842901 0.0214835 0.3135535
## M49 0.6030809 0.6682537 0.5489058 0.6171942 0.5412645 0.3196712 0.5113589
## M50 0.4423943 0.5327441 0.6575019 0.6867621 0.7107265 0.5197406 0.7125100
## M51 0.4325035 0.3736333 0.6380569 0.5254588 0.5613270 0.2646676 0.5148133
## M52 0.4016518 0.5576490 0.6778674 0.7141288 0.6903653 0.4896738 0.6489159
## M53 0.3155678 0.4440762 0.5276107 0.6535580 0.5452947 0.4838015 0.5912200
## M54 0.4995740 0.5810306 0.7451117 0.7687058 0.7306449 0.4409689 0.6796420
## M55 0.6679651 0.6367275 0.5133525 0.3909470 0.4522011 0.0880885 0.3084745
## M56 0.4197858 0.5331362 0.6388049 0.6951879 0.6793742 0.4677872 0.7344272
## M57 0.4832819 0.5295004 0.7150514 0.8281977 0.7066803 0.4167253 0.6459859
## M58 0.7030980 0.6254931 0.5516216 0.4614461 0.4731052 0.1324431 0.4341678
## M59 0.3723679 0.4578178 0.5616921 0.6350556 0.6333749 0.4650506 0.6409672
## M60 0.3616126 0.5009663 0.5891075 0.7046742 0.6433599 0.4686222 0.6839582
## M61 0.4369358 0.3951828 0.5922354 0.4662818 0.4786616 0.1991668 0.4294275
## M62 0.2274277 0.3414321 0.4968327 0.5712807 0.4962292 0.4317373 0.5634985
## M63 0.4086633 0.5457402 0.6568074 0.7762348 0.6770276 0.4350547 0.6799602
## M36 M37 M38 M39 M40 M41 M42
## M1 0.3864130 0.4072344 0.37304937 0.269897394 0.37157371 0.4858458 0.3682592
## M2 0.5881541 0.6050421 0.43310781 0.319101854 0.41278635 0.6193167 0.4853848
## M3 0.5643923 0.5974517 0.45925474 0.361177949 0.45735411 0.5961205 0.5092397
## M4 0.6446825 0.6531507 0.51382639 0.329536674 0.38063986 0.6325387 0.4716771
## M5 0.5712593 0.6531559 0.46138425 0.349166069 0.43508681 0.5919097 0.5011734
## M6 0.6740804 0.6984232 0.51389196 0.303792528 0.40686440 0.6242997 0.4239969
## M7 0.4773295 0.5183772 0.31479155 0.292273113 0.27654136 0.4912837 0.4145879
## M8 0.6388161 0.6493976 0.48047738 0.350530298 0.44872572 0.6454668 0.4679101
## M9 0.7302718 0.6486655 0.53194386 0.296266288 0.38458744 0.6675664 0.5023382
## M10 0.5950718 0.6767648 0.50489355 0.330097839 0.45990474 0.6297138 0.4964774
## M11 0.7300000 0.6586810 0.50159991 0.279158149 0.36550361 0.7109185 0.3911294
## M12 0.6954439 0.6692258 0.50987470 0.252980017 0.37546972 0.6993372 0.4296611
## M13 0.6779232 0.6547742 0.45610968 0.295447926 0.29852572 0.6224969 0.4296355
## M14 0.6148917 0.6412764 0.40498596 0.229116974 0.36020746 0.6263188 0.3598198
## M15 0.5555003 0.6613086 0.43394861 0.341035916 0.51572094 0.6266186 0.6347479
## M16 0.5669813 0.6583048 0.49378713 0.365048338 0.46197556 0.6673294 0.5576191
## M17 0.8519033 0.6574280 0.58097305 0.229522681 0.32314278 0.7567621 0.3767726
## M18 0.6872386 0.7241316 0.52465300 0.337234975 0.51840572 0.7269017 0.5521470
## M19 0.6804249 0.6795389 0.49979320 0.338273445 0.40052005 0.6782729 0.4000761
## M20 0.5467926 0.6327602 0.43662542 0.264509906 0.50246062 0.6292417 0.6067985
## M21 0.6472245 0.7295526 0.47436855 0.277546083 0.39891030 0.6447393 0.4926507
## M22 0.3199285 0.3695970 0.55332716 0.067943278 0.62762438 0.3727837 0.2501566
## M23 0.6799672 0.7347880 0.49150093 0.277507693 0.41089952 0.7168162 0.5052378
## M24 0.7734864 0.6872682 0.53147070 0.279921282 0.38233642 0.7475057 0.3639925
## M25 0.6176030 0.5894992 0.36945240 0.256137146 0.21755056 0.5596755 0.3029725
## M26 0.6881620 0.6693518 0.47273570 0.282954405 0.32090831 0.6681295 0.4063433
## M27 0.6717349 0.7616197 0.49930866 0.300320597 0.45849067 0.7167492 0.5138724
## M28 0.7085218 0.7173846 0.52486497 0.307751992 0.40397550 0.7256181 0.4752663
## M29 0.4256571 0.4672469 0.63437335 0.129178974 0.69338381 0.4958703 0.3807356
## M30 0.5419311 0.5715674 0.65186919 0.142353513 0.67822634 0.5363464 0.3046562
## M31 0.6417378 0.7284792 0.53842812 0.314490081 0.52352085 0.7264701 0.5831084
## M32 0.7564657 0.7086240 0.61227832 0.229745253 0.42780182 0.7270749 0.4211550
## M33 0.6706005 0.7137808 0.57453094 0.284480283 0.48187540 0.7052270 0.4765251
## M34 0.5057829 0.4377997 0.26526361 0.293381250 0.15230284 0.4709077 0.2022211
## M35 0.6809835 0.7386955 0.53052053 0.313237075 0.38149575 0.6937293 0.4343372
## M36 1.0000000 0.7012156 0.61197537 0.235543480 0.34809744 0.7594945 0.3610534
## M37 0.7012156 1.0000000 0.51026541 0.334876067 0.43425590 0.6922366 0.4437945
## M38 0.6119754 0.5102654 1.00000000 0.064519866 0.64642223 0.5793456 0.2439219
## M39 0.2355435 0.3348761 0.06451987 1.000000000 0.05122598 0.2737056 0.2732853
## M40 0.3480974 0.4342559 0.64642223 0.051225980 1.00000000 0.3991457 0.3578115
## M41 0.7594945 0.6922366 0.57934562 0.273705611 0.39914569 1.0000000 0.4263348
## M42 0.3610534 0.4437945 0.24392186 0.273285257 0.35781151 0.4263348 1.0000000
## M43 0.5145395 0.6470388 0.39983808 0.285834795 0.35504468 0.5526731 0.6549848
## M44 0.7792120 0.5886985 0.53007637 0.225551166 0.29132148 0.6967909 0.3822842
## M45 0.7969230 0.6979801 0.59168362 0.260317254 0.42123977 0.7660906 0.4165681
## M46 0.7970018 0.5916392 0.54136174 0.201653991 0.26310755 0.6839109 0.3931141
## M47 0.7718747 0.6903321 0.67041169 0.263750336 0.48360890 0.8016357 0.4554694
## M48 0.2597688 0.3637210 0.52956820 -0.005574104 0.73428116 0.3555113 0.2710487
## M49 0.6314193 0.5063763 0.76154674 0.026678920 0.56064005 0.5718602 0.2380908
## M50 0.7599215 0.6826254 0.58352668 0.258194402 0.36396557 0.7657924 0.4091233
## M51 0.4935703 0.5481704 0.37327485 0.264910702 0.45083560 0.4779216 0.5758191
## M52 0.7091610 0.6802627 0.53321455 0.250977824 0.41377859 0.6957431 0.4221761
## M53 0.7468233 0.5585135 0.54558102 0.195333668 0.30721029 0.6717891 0.3324031
## M54 0.7471125 0.6894539 0.65014295 0.269847450 0.46861979 0.7453935 0.4466142
## M55 0.3033896 0.3905701 0.55268795 -0.005860015 0.76664649 0.3782122 0.3141414
## M56 0.7467079 0.7204558 0.51227994 0.292130124 0.39661072 0.6742052 0.4487642
## M57 0.7336365 0.6816436 0.59849689 0.287081162 0.41541252 0.7073629 0.4361345
## M58 0.3620354 0.4397443 0.60953040 0.039602355 0.77693298 0.4560185 0.3841606
## M59 0.6926410 0.6147808 0.46049779 0.292658525 0.33790137 0.6696432 0.3568494
## M60 0.8482842 0.6513749 0.56201250 0.191025130 0.34506542 0.7129793 0.3852448
## M61 0.3851431 0.4586800 0.32050072 0.262000760 0.37951629 0.4508776 0.7432324
## M62 0.6749648 0.5445955 0.38309714 0.169452562 0.18466193 0.5618421 0.3479959
## M63 0.7935760 0.7029747 0.57086276 0.213049826 0.40125799 0.7230982 0.3703576
## M43 M44 M45 M46 M47 M48 M49
## M1 0.4035903 0.3499932 0.4045192 0.3255800 0.4864959 0.314013548 0.33548856
## M2 0.5400041 0.5390487 0.5663508 0.5372544 0.6470131 0.365095325 0.46426391
## M3 0.5750424 0.5171287 0.5420711 0.5152131 0.6518542 0.363687005 0.44874451
## M4 0.5732013 0.5962100 0.5956580 0.5763453 0.6591348 0.328191816 0.50895304
## M5 0.6133471 0.5532469 0.5575695 0.5097800 0.6219662 0.305120190 0.43963306
## M6 0.6806723 0.6117503 0.6529462 0.6035093 0.6324232 0.339329543 0.48059989
## M7 0.4561533 0.4356509 0.4635993 0.4827717 0.4252873 0.191443947 0.28994692
## M8 0.5666176 0.5480657 0.5928143 0.5774322 0.6964761 0.351967826 0.48598877
## M9 0.5747446 0.6777309 0.6383920 0.6687278 0.6967317 0.282058217 0.51706262
## M10 0.5673990 0.5442984 0.5966822 0.5232889 0.6868430 0.342408058 0.48405695
## M11 0.5824232 0.6357979 0.6465732 0.6286322 0.6785125 0.240852505 0.52168552
## M12 0.5108464 0.5840255 0.6181649 0.5928864 0.6845984 0.304814473 0.49888681
## M13 0.5221566 0.6044987 0.6372439 0.6425985 0.6565836 0.213445857 0.45085150
## M14 0.4897790 0.5627781 0.5982440 0.5683830 0.6261321 0.315094559 0.46823912
## M15 0.6283987 0.4861803 0.5809731 0.4818276 0.6369472 0.395463558 0.42920777
## M16 0.6220023 0.5417883 0.6203218 0.5206538 0.6675506 0.385566633 0.47610281
## M17 0.4909755 0.7471870 0.7326862 0.7568419 0.7492154 0.239039520 0.59403973
## M18 0.6010605 0.5731481 0.6722386 0.5715789 0.7699705 0.399566773 0.52399704
## M19 0.5631593 0.6261531 0.6620596 0.6161680 0.7092568 0.354014990 0.53310437
## M20 0.6536049 0.4894444 0.5761714 0.5036936 0.6401267 0.424231446 0.45183405
## M21 0.6995459 0.5704794 0.6373409 0.5926976 0.6470103 0.357568337 0.50431731
## M22 0.3142351 0.2211559 0.3680985 0.2088088 0.4239901 0.501190537 0.50375536
## M23 0.6095350 0.5950274 0.6774040 0.5964134 0.7115047 0.354878882 0.51712632
## M24 0.5405112 0.6996579 0.7505532 0.6796113 0.7495860 0.323030653 0.58620230
## M25 0.4007808 0.6039262 0.5752226 0.6321379 0.5868824 0.178808101 0.42709938
## M26 0.5199778 0.5866241 0.6299708 0.6313291 0.6506367 0.297704918 0.48857242
## M27 0.6008874 0.5837408 0.6999370 0.5711902 0.7262369 0.405401799 0.49920872
## M28 0.5699942 0.6314790 0.6700669 0.6382368 0.7299606 0.339381668 0.53564583
## M29 0.4241831 0.3338571 0.4211802 0.3383968 0.5360188 0.614127805 0.60308085
## M30 0.3909936 0.4337837 0.5378552 0.4459470 0.5847390 0.565952073 0.66825371
## M31 0.6430177 0.5808941 0.6886517 0.5641824 0.7620482 0.452505038 0.54890576
## M32 0.5644928 0.7136989 0.7498883 0.7121977 0.7582207 0.364278394 0.61719419
## M33 0.5719253 0.5899044 0.6622127 0.6061915 0.7350597 0.384290060 0.54126453
## M34 0.2943211 0.4605905 0.4097775 0.4867555 0.4227953 0.021483502 0.31967119
## M35 0.5830023 0.5805489 0.7066968 0.6083310 0.7060947 0.313553473 0.51135894
## M36 0.5145395 0.7792120 0.7969230 0.7970018 0.7718747 0.259768757 0.63141934
## M37 0.6470388 0.5886985 0.6979801 0.5916392 0.6903321 0.363720999 0.50637634
## M38 0.3998381 0.5300764 0.5916836 0.5413617 0.6704117 0.529568200 0.76154674
## M39 0.2858348 0.2255512 0.2603173 0.2016540 0.2637503 -0.005574104 0.02667892
## M40 0.3550447 0.2913215 0.4212398 0.2631076 0.4836089 0.734281159 0.56064005
## M41 0.5526731 0.6967909 0.7660906 0.6839109 0.8016357 0.355511255 0.57186021
## M42 0.6549848 0.3822842 0.4165681 0.3931141 0.4554694 0.271048669 0.23809079
## M43 1.0000000 0.5463784 0.5871103 0.5437408 0.5451917 0.291062919 0.36330299
## M44 0.5463784 1.0000000 0.8174232 0.9165803 0.6847186 0.222159073 0.52519571
## M45 0.5871103 0.8174232 1.0000000 0.7764202 0.7850495 0.322967964 0.60765730
## M46 0.5437408 0.9165803 0.7764202 1.0000000 0.6883821 0.192255277 0.55713288
## M47 0.5451917 0.6847186 0.7850495 0.6883821 1.0000000 0.402165092 0.67197578
## M48 0.2910629 0.2221591 0.3229680 0.1922553 0.4021651 1.000000000 0.51997529
## M49 0.3633030 0.5251957 0.6076573 0.5571329 0.6719758 0.519975291 1.00000000
## M50 0.5816388 0.7443445 0.7601963 0.7313744 0.7720391 0.263774429 0.57818038
## M51 0.6406731 0.4450417 0.5290780 0.4449476 0.5376756 0.366977224 0.30543920
## M52 0.5414251 0.7089973 0.7310661 0.7007959 0.7287071 0.326747520 0.54948151
## M53 0.4956929 0.8263239 0.7269806 0.8658857 0.6953395 0.228282861 0.54120041
## M54 0.5343284 0.6649708 0.7416429 0.6814337 0.8593462 0.374876965 0.63967062
## M55 0.2924577 0.2812476 0.3774300 0.2605588 0.4468184 0.766056023 0.57372332
## M56 0.6238926 0.7643578 0.7667945 0.7578426 0.6998414 0.300159044 0.51795357
## M57 0.5769781 0.6750720 0.7249501 0.6744097 0.7440833 0.383987842 0.55721374
## M58 0.3754748 0.2886338 0.4229531 0.2840089 0.5071939 0.785920272 0.57492203
## M59 0.5156419 0.6786223 0.7384284 0.6843370 0.6743847 0.233386958 0.50820157
## M60 0.5314220 0.8087480 0.8060870 0.8173572 0.7297162 0.255234157 0.57187693
## M61 0.6725063 0.3954560 0.4531673 0.4053369 0.4740211 0.351006242 0.30607601
## M62 0.4702116 0.6873232 0.6377886 0.6973523 0.5411872 0.122633272 0.40771125
## M63 0.5416701 0.7584052 0.7993587 0.7311138 0.7436123 0.312826067 0.56118646
## M50 M51 M52 M53 M54 M55 M56
## M1 0.3848525 0.4224918 0.3847002 0.3295401 0.4895777 0.383265644 0.3790819
## M2 0.5657894 0.5482469 0.5809179 0.4991292 0.6530094 0.419046219 0.5611048
## M3 0.5510407 0.5486998 0.5957132 0.5039808 0.6590389 0.427217314 0.5817650
## M4 0.6138263 0.4901552 0.6158578 0.5835413 0.6262675 0.387585744 0.6272108
## M5 0.6049772 0.5585907 0.6241632 0.4868968 0.6199928 0.382484466 0.6565332
## M6 0.6356114 0.5053274 0.6103746 0.5746755 0.6223598 0.356734720 0.6952175
## M7 0.4445485 0.4257945 0.4493199 0.4230984 0.4321229 0.264703063 0.5139863
## M8 0.5894689 0.5415973 0.6208911 0.5468885 0.7068281 0.418005716 0.5998247
## M9 0.6494861 0.5434770 0.6440399 0.6442651 0.7066693 0.358025243 0.6857617
## M10 0.6374303 0.5793035 0.6314268 0.4873944 0.6749338 0.432138571 0.6063300
## M11 0.7734545 0.5236575 0.6332663 0.6035463 0.6657378 0.324000507 0.6467481
## M12 0.6784800 0.4797999 0.6172263 0.5866033 0.6388169 0.360559582 0.6244020
## M13 0.6638044 0.5019403 0.6188626 0.5910017 0.6545025 0.254991708 0.6859288
## M14 0.6152783 0.4616136 0.6276389 0.5500225 0.6077477 0.335235809 0.6269180
## M15 0.5811727 0.6318621 0.5900750 0.4595392 0.6421872 0.472039204 0.5700893
## M16 0.6233713 0.5968018 0.6090815 0.5024381 0.6956316 0.447053071 0.5937027
## M17 0.7556777 0.4503668 0.6786994 0.7401517 0.7037757 0.336523927 0.7061729
## M18 0.6545252 0.5905126 0.6579927 0.5540361 0.7119339 0.479480233 0.6714342
## M19 0.6345158 0.5325953 0.6562050 0.5807998 0.7005216 0.372173425 0.6936701
## M20 0.5767442 0.6099318 0.6581081 0.4950355 0.6013549 0.431148189 0.5889040
## M21 0.6427554 0.5437737 0.6385444 0.5479895 0.6419172 0.398863908 0.6974267
## M22 0.3276639 0.2746475 0.2972355 0.2478545 0.4057255 0.522643632 0.3171513
## M23 0.6687247 0.5379825 0.6918697 0.5586967 0.6858040 0.382397025 0.7075628
## M24 0.7174531 0.4703780 0.6582684 0.6473224 0.7160511 0.378276650 0.7086940
## M25 0.6220000 0.3374158 0.5961975 0.5590610 0.5648049 0.187979677 0.6273132
## M26 0.6572413 0.4302614 0.6154504 0.5676807 0.6257990 0.340974965 0.6753041
## M27 0.6598824 0.5453630 0.6463294 0.5673771 0.6772421 0.443502760 0.6931913
## M28 0.7007774 0.5380648 0.6685479 0.6206825 0.7193381 0.408358634 0.6952335
## M29 0.4423943 0.4325035 0.4016518 0.3155678 0.4995740 0.667965150 0.4197858
## M30 0.5327441 0.3736333 0.5576490 0.4440762 0.5810306 0.636727518 0.5331362
## M31 0.6575019 0.6380569 0.6778674 0.5276107 0.7451117 0.513352501 0.6388049
## M32 0.6867621 0.5254588 0.7141288 0.6535580 0.7687058 0.390946993 0.6951879
## M33 0.7107265 0.5613270 0.6903653 0.5452947 0.7306449 0.452201121 0.6793742
## M34 0.5197406 0.2646676 0.4896738 0.4838015 0.4409689 0.088088501 0.4677872
## M35 0.7125100 0.5148133 0.6489159 0.5912200 0.6796420 0.308474504 0.7344272
## M36 0.7599215 0.4935703 0.7091610 0.7468233 0.7471125 0.303389578 0.7467079
## M37 0.6826254 0.5481704 0.6802627 0.5585135 0.6894539 0.390570146 0.7204558
## M38 0.5835267 0.3732748 0.5332146 0.5455810 0.6501429 0.552687950 0.5122799
## M39 0.2581944 0.2649107 0.2509778 0.1953337 0.2698475 -0.005860015 0.2921301
## M40 0.3639656 0.4508356 0.4137786 0.3072103 0.4686198 0.766646494 0.3966107
## M41 0.7657924 0.4779216 0.6957431 0.6717891 0.7453935 0.378212175 0.6742052
## M42 0.4091233 0.5758191 0.4221761 0.3324031 0.4466142 0.314141397 0.4487642
## M43 0.5816388 0.6406731 0.5414251 0.4956929 0.5343284 0.292457669 0.6238926
## M44 0.7443445 0.4450417 0.7089973 0.8263239 0.6649708 0.281247574 0.7643578
## M45 0.7601963 0.5290780 0.7310661 0.7269806 0.7416429 0.377430010 0.7667945
## M46 0.7313744 0.4449476 0.7007959 0.8658857 0.6814337 0.260558823 0.7578426
## M47 0.7720391 0.5376756 0.7287071 0.6953395 0.8593462 0.446818358 0.6998414
## M48 0.2637744 0.3669772 0.3267475 0.2282829 0.3748770 0.766056023 0.3001590
## M49 0.5781804 0.3054392 0.5494815 0.5412004 0.6396706 0.573723319 0.5179536
## M50 1.0000000 0.5024473 0.7681344 0.7192942 0.7563639 0.322215033 0.7513089
## M51 0.5024473 1.0000000 0.5149766 0.4140079 0.5425272 0.396848654 0.5190770
## M52 0.7681344 0.5149766 1.0000000 0.7207166 0.7578951 0.381259075 0.7318156
## M53 0.7192942 0.4140079 0.7207166 1.0000000 0.6907153 0.284833719 0.6920531
## M54 0.7563639 0.5425272 0.7578951 0.6907153 1.0000000 0.430321002 0.7215722
## M55 0.3222150 0.3968487 0.3812591 0.2848337 0.4303210 1.000000000 0.3073160
## M56 0.7513089 0.5190770 0.7318156 0.6920531 0.7215722 0.307316019 1.0000000
## M57 0.7025193 0.5540293 0.7035937 0.6521755 0.7653410 0.360793352 0.7077371
## M58 0.3844297 0.4760747 0.3956941 0.2762989 0.4779152 0.795528813 0.3646453
## M59 0.7187136 0.4445077 0.6882078 0.6808989 0.6470386 0.277648364 0.7560239
## M60 0.7671022 0.4826068 0.7390168 0.8076609 0.7252878 0.293404587 0.7671920
## M61 0.4401463 0.5396581 0.4939405 0.3562808 0.4610561 0.373973101 0.4484564
## M62 0.6506509 0.3977098 0.6639907 0.7145395 0.5443448 0.124254371 0.6683474
## M63 0.7509776 0.5346794 0.7571553 0.7432825 0.7358871 0.357151775 0.7326750
## M57 M58 M59 M60 M61 M62 M63
## M1 0.4144613 0.40566508 0.2880050 0.3432942 0.3698628 0.2234211 0.3738716
## M2 0.5771374 0.40107061 0.4970002 0.5183160 0.4883801 0.4147514 0.5632419
## M3 0.6232211 0.43263042 0.4696283 0.5305361 0.5273762 0.4037703 0.5708411
## M4 0.6175142 0.38260512 0.5710317 0.5832719 0.4890578 0.4869849 0.6396421
## M5 0.5974404 0.40271250 0.5403731 0.5386269 0.5327361 0.4500102 0.6039417
## M6 0.6479697 0.39223428 0.5708515 0.6458525 0.4664917 0.5308664 0.6636587
## M7 0.4191692 0.28064830 0.4267509 0.4380789 0.3570427 0.4214689 0.4476430
## M8 0.6354736 0.45639569 0.5220011 0.5623527 0.4979879 0.4275457 0.5739886
## M9 0.6474076 0.36714178 0.5959968 0.6930458 0.5009237 0.5746850 0.6669951
## M10 0.6409329 0.46966517 0.4799934 0.5447904 0.4948258 0.4266049 0.6059574
## M11 0.5909837 0.39289559 0.6145506 0.6912711 0.3911245 0.5736499 0.6517208
## M12 0.6133397 0.39007844 0.5288328 0.6397456 0.4420496 0.5494893 0.6562481
## M13 0.5576389 0.27568633 0.5974590 0.6452051 0.4140903 0.6146896 0.5995649
## M14 0.5453173 0.31397969 0.5377333 0.5845962 0.4032669 0.5426786 0.6028620
## M15 0.6141441 0.51478767 0.4419483 0.5073639 0.6144400 0.4413277 0.5910301
## M16 0.6466834 0.48306918 0.5136099 0.5207059 0.5454978 0.4481349 0.6056741
## M17 0.6972638 0.33038436 0.6767602 0.7859641 0.3787609 0.6446261 0.7390437
## M18 0.7059466 0.51465950 0.6085219 0.6237941 0.5550687 0.4822119 0.6873391
## M19 0.6925341 0.40567886 0.6255496 0.6100774 0.4368657 0.5253699 0.6585640
## M20 0.6242115 0.51544377 0.4896203 0.5175627 0.6126459 0.4523872 0.5674291
## M21 0.6575278 0.43852992 0.6064084 0.6081248 0.4977011 0.5208965 0.6073881
## M22 0.3396108 0.56744162 0.2981313 0.3120296 0.3083527 0.1829939 0.3361466
## M23 0.6880037 0.44173191 0.5849894 0.6361321 0.5356032 0.5675728 0.6942619
## M24 0.6629811 0.36183327 0.6375600 0.7137912 0.3884316 0.5760460 0.7146297
## M25 0.5050792 0.21822400 0.5429385 0.5684572 0.3381107 0.5315807 0.5732848
## M26 0.6113427 0.35352019 0.5551936 0.6331791 0.4671253 0.5626596 0.6308258
## M27 0.6708304 0.45772805 0.5933024 0.6262486 0.5107471 0.4941050 0.6858706
## M28 0.6916469 0.42871557 0.6045886 0.6694046 0.4897799 0.5379053 0.6948287
## M29 0.4832819 0.70309797 0.3723679 0.3616126 0.4369358 0.2274277 0.4086633
## M30 0.5295004 0.62549312 0.4578178 0.5009663 0.3951828 0.3414321 0.5457402
## M31 0.7150514 0.55162158 0.5616921 0.5891075 0.5922354 0.4968327 0.6568074
## M32 0.8281977 0.46144609 0.6350556 0.7046742 0.4662818 0.5712807 0.7762348
## M33 0.7066803 0.47310521 0.6333749 0.6433599 0.4786616 0.4962292 0.6770276
## M34 0.4167253 0.13244305 0.4650506 0.4686222 0.1991668 0.4317373 0.4350547
## M35 0.6459859 0.43416784 0.6409672 0.6839582 0.4294275 0.5634985 0.6799602
## M36 0.7336365 0.36203540 0.6926410 0.8482842 0.3851431 0.6749648 0.7935760
## M37 0.6816436 0.43974426 0.6147808 0.6513749 0.4586800 0.5445955 0.7029747
## M38 0.5984969 0.60953040 0.4604978 0.5620125 0.3205007 0.3830971 0.5708628
## M39 0.2870812 0.03960235 0.2926585 0.1910251 0.2620008 0.1694526 0.2130498
## M40 0.4154125 0.77693298 0.3379014 0.3450654 0.3795163 0.1846619 0.4012580
## M41 0.7073629 0.45601854 0.6696432 0.7129793 0.4508776 0.5618421 0.7230982
## M42 0.4361345 0.38416057 0.3568494 0.3852448 0.7432324 0.3479959 0.3703576
## M43 0.5769781 0.37547478 0.5156419 0.5314220 0.6725063 0.4702116 0.5416701
## M44 0.6750720 0.28863382 0.6786223 0.8087480 0.3954560 0.6873232 0.7584052
## M45 0.7249501 0.42295308 0.7384284 0.8060870 0.4531673 0.6377886 0.7993587
## M46 0.6744097 0.28400893 0.6843370 0.8173572 0.4053369 0.6973523 0.7311138
## M47 0.7440833 0.50719390 0.6743847 0.7297162 0.4740211 0.5411872 0.7436123
## M48 0.3839878 0.78592027 0.2333870 0.2552342 0.3510062 0.1226333 0.3128261
## M49 0.5572137 0.57492203 0.5082016 0.5718769 0.3060760 0.4077113 0.5611865
## M50 0.7025193 0.38442966 0.7187136 0.7671022 0.4401463 0.6506509 0.7509776
## M51 0.5540293 0.47607472 0.4445077 0.4826068 0.5396581 0.3977098 0.5346794
## M52 0.7035937 0.39569405 0.6882078 0.7390168 0.4939405 0.6639907 0.7571553
## M53 0.6521755 0.27629892 0.6808989 0.8076609 0.3562808 0.7145395 0.7432825
## M54 0.7653410 0.47791520 0.6470386 0.7252878 0.4610561 0.5443448 0.7358871
## M55 0.3607934 0.79552881 0.2776484 0.2934046 0.3739731 0.1242544 0.3571518
## M56 0.7077371 0.36464526 0.7560239 0.7671920 0.4484564 0.6683474 0.7326750
## M57 1.0000000 0.45732471 0.6441500 0.7184266 0.4803280 0.5913265 0.8201105
## M58 0.4573247 1.00000000 0.3071023 0.3242004 0.4399612 0.1806682 0.4175741
## M59 0.6441500 0.30710229 1.0000000 0.7413406 0.3133344 0.6587280 0.6789043
## M60 0.7184266 0.32420042 0.7413406 1.0000000 0.3555133 0.7472296 0.8129710
## M61 0.4803280 0.43996119 0.3133344 0.3555133 1.0000000 0.3272938 0.4315524
## M62 0.5913265 0.18066821 0.6587280 0.7472296 0.3272938 1.0000000 0.6754247
## M63 0.8201105 0.41757407 0.6789043 0.8129710 0.4315524 0.6754247 1.0000000
##assumption set up (We must use a fake regression analysis because, while EFA is regrerssion to the extreme , you still have to screen it with a regular regres. analysis)
random = rchisq(nrow(haluknoutliers), 7)
fake = lm(random~., data = haluknoutliers)
standardized = rstudent(fake)
fitted = scale(fake$fitted.values)
#Bu analizlerde her;ey sifirin trafinda mitoplaniyor diye kontrol ediyoruz.
##normality (the previos code was the set up, lets now look at the histogram) (Hersey sifirin etrafinda -2, 2 araliginda toplanmis.Bu gayet normal gorunuyor)
hist(standardized)
##linearity (burada da 0 trfinda -2 ve 2 aradinda toplanmis noktalar, bu da gayet iyi.)
qqnorm(standardized)
abline(0,1)
##homegeneity (buraa da noktalarin 0 trafinda toplanmasini istiyoruz, bu da gayet iyi)
plot(fitted, standardized)
abline(0,0)
abline(v = 0)
##Running EFA Analysis (Simdiye kadar olan asamada datamizi hazirladik. Simdi analiz icin uygun ve temiz bir dataset imiz var)
library(psych)
##
## Attaching package: 'psych'
## The following object is masked from 'package:lavaan':
##
## cor2cov
library(GPArotation)
##Correlation adequacy Bartlett's test (p.value = 0 cikti. anlamli bir etki var. Analize devasm etmek icin koreleasyonlarin yeterli buyuklukte oldugunu soyluyor)
cortest.bartlett(correl, n = nrow(haluknoutliers))
## $chisq
## [1] 17903.29
##
## $p.value
## [1] 0
##
## $df
## [1] 1953
##Sampling adequacy KMO test (Overall MSA{mean sampling adequacy} nin en az .7 olmasi lazim, bizim .97)
KMO(correl)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = correl)
## Overall MSA = 0.97
## MSA for each item =
## M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16
## 0.96 0.97 0.98 0.97 0.97 0.98 0.97 0.98 0.98 0.98 0.98 0.97 0.98 0.96 0.97 0.98
## M17 M18 M19 M20 M21 M22 M23 M24 M25 M26 M27 M28 M29 M30 M31 M32
## 0.98 0.98 0.99 0.96 0.97 0.96 0.98 0.98 0.97 0.96 0.98 0.98 0.97 0.97 0.98 0.97
## M33 M34 M35 M36 M37 M38 M39 M40 M41 M42 M43 M44 M45 M46 M47 M48
## 0.99 0.96 0.97 0.98 0.99 0.96 0.92 0.94 0.99 0.95 0.97 0.95 0.97 0.96 0.98 0.93
## M49 M50 M51 M52 M53 M54 M55 M56 M57 M58 M59 M60 M61 M62 M63
## 0.97 0.98 0.97 0.98 0.97 0.98 0.94 0.98 0.98 0.95 0.98 0.98 0.96 0.98 0.98
##How many factors should I have? (Bizim teorik alt yapi 3 tane diyordu. Simdi asagidaki analizlerde teoriye dayanmayan opsiyonlari incleyecegiz)
##How many factors? (fa.parallel, paralele analiz komutu)
##paralel analiz 4 faktor var dio, scree plot gorseline bakinca da 3 faktor var gbi gorunuyor. 4. cizgi uzerinde cok )
nofactors = fa.parallel(haluknoutliers, fm="ml", fa = "fa")
## Parallel analysis suggests that the number of factors = 3 and the number of components = NA
sum(nofactors$fa.values > 1.0) ##old kaiser criterion (bu kritere gore 3 faktor gosteriyor)
## [1] 3
sum(nofactors$fa.values > 0.7) ##new kaiser criterion (bu kritere gore 5 faktor gosteriyor)
## [1] 5
#Yani elimizde 4 faktor, 3 faktor, 3 faktor ve 5 faktor onerileri var.
#Bu verilere gore 3 faktor common ground (orta yol) gibi gorunuyor. Bu y]zden 3u deneyerek analize devam ediyoruz.
##Tabi istersek diger faktor sayilarina gore de deneme yapabiliriz
##simple structure with a 3 factor model
round1 = fa(haluknoutliers, nfactors = 3, rotate = "oblimin", fm = "ml")
round1
## Factor Analysis using method = ml
## Call: fa(r = haluknoutliers, nfactors = 3, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML3 ML1 ML2 h2 u2 com
## M1 0.59 -0.10 0.15 0.37 0.63 1.2
## M2 0.73 0.04 0.05 0.62 0.38 1.0
## M3 0.81 -0.04 0.07 0.67 0.33 1.0
## M4 0.64 0.20 0.01 0.65 0.35 1.2
## M5 0.81 0.02 0.00 0.68 0.32 1.0
## M6 0.54 0.30 0.02 0.63 0.37 1.6
## M7 0.56 0.12 -0.08 0.38 0.62 1.1
## M8 0.75 0.07 0.06 0.69 0.31 1.0
## M9 0.54 0.37 -0.02 0.70 0.30 1.8
## M10 0.80 0.01 0.07 0.72 0.28 1.0
## M11 0.43 0.44 -0.01 0.65 0.35 2.0
## M12 0.47 0.38 0.01 0.62 0.38 1.9
## M13 0.46 0.44 -0.12 0.62 0.38 2.1
## M14 0.49 0.33 -0.03 0.56 0.44 1.8
## M15 0.89 -0.13 0.11 0.74 0.26 1.1
## M16 0.87 -0.05 0.07 0.75 0.25 1.0
## M17 0.16 0.74 0.02 0.76 0.24 1.1
## M18 0.76 0.10 0.11 0.80 0.20 1.1
## M19 0.62 0.25 0.02 0.69 0.31 1.3
## M20 0.80 -0.06 0.13 0.69 0.31 1.1
## M21 0.65 0.20 0.03 0.67 0.33 1.2
## M22 0.13 -0.01 0.61 0.46 0.54 1.1
## M23 0.65 0.23 0.03 0.72 0.28 1.3
## M24 0.39 0.51 0.03 0.71 0.29 1.9
## M25 0.35 0.48 -0.14 0.52 0.48 2.0
## M26 0.48 0.39 -0.02 0.62 0.38 1.9
## M27 0.66 0.20 0.07 0.73 0.27 1.2
## M28 0.58 0.33 0.03 0.73 0.27 1.6
## M29 0.26 -0.03 0.66 0.66 0.34 1.3
## M30 0.15 0.24 0.57 0.63 0.37 1.5
## M31 0.79 0.03 0.17 0.82 0.18 1.1
## M32 0.30 0.52 0.15 0.72 0.28 1.8
## M33 0.57 0.24 0.14 0.71 0.29 1.5
## M34 0.29 0.40 -0.18 0.33 0.67 2.3
## M35 0.50 0.36 0.03 0.66 0.34 1.8
## M36 0.10 0.82 0.04 0.83 0.17 1.0
## M37 0.56 0.30 0.05 0.69 0.31 1.5
## M38 -0.16 0.52 0.61 0.68 0.32 2.1
## M39 0.64 -0.11 -0.28 0.23 0.77 1.4
## M40 0.09 -0.03 0.84 0.76 0.24 1.0
## M41 0.34 0.52 0.10 0.72 0.28 1.8
## M42 0.75 -0.16 0.01 0.42 0.58 1.1
## M43 0.67 0.10 -0.02 0.54 0.46 1.0
## M44 -0.02 0.91 -0.01 0.79 0.21 1.0
## M45 0.11 0.74 0.12 0.78 0.22 1.1
## M46 -0.03 0.93 -0.03 0.81 0.19 1.0
## M47 0.31 0.52 0.21 0.78 0.22 2.0
## M48 0.02 -0.07 0.85 0.70 0.30 1.0
## M49 -0.17 0.55 0.57 0.66 0.34 2.2
## M50 0.21 0.68 0.04 0.75 0.25 1.2
## M51 0.62 0.00 0.12 0.48 0.52 1.1
## M52 0.27 0.58 0.08 0.70 0.30 1.5
## M53 -0.09 0.93 0.03 0.76 0.24 1.0
## M54 0.32 0.50 0.18 0.74 0.26 2.0
## M55 0.07 -0.06 0.85 0.75 0.25 1.0
## M56 0.29 0.63 0.00 0.74 0.26 1.4
## M57 0.31 0.51 0.13 0.69 0.31 1.8
## M58 0.11 -0.05 0.85 0.79 0.21 1.0
## M59 0.10 0.72 0.02 0.63 0.37 1.0
## M60 -0.04 0.93 0.04 0.84 0.16 1.0
## M61 0.68 -0.13 0.11 0.43 0.57 1.1
## M62 0.05 0.79 -0.14 0.61 0.39 1.1
## M63 0.15 0.72 0.10 0.76 0.24 1.1
##
## ML3 ML1 ML2
## SS loadings 19.50 15.93 6.33
## Proportion Var 0.31 0.25 0.10
## Cumulative Var 0.31 0.56 0.66
## Proportion Explained 0.47 0.38 0.15
## Cumulative Proportion 0.47 0.85 1.00
##
## With factor correlations of
## ML3 ML1 ML2
## ML3 1.00 0.71 0.51
## ML1 0.71 1.00 0.36
## ML2 0.51 0.36 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 1953 and the objective function was 78.81 with Chi Square of 17903.29
## The degrees of freedom for the model are 1767 and the objective function was 16.3
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic number of observations is 250 with the empirical chi square 1081.65 with prob < 1
## The total number of observations was 250 with Likelihood Chi Square = 3669.74 with prob < 2.2e-135
##
## Tucker Lewis Index of factoring reliability = 0.867
## RMSEA index = 0.066 and the 90 % confidence intervals are 0.063 0.069
## BIC = -6086.68
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML3 ML1 ML2
## Correlation of (regression) scores with factors 0.99 0.99 0.97
## Multiple R square of scores with factors 0.98 0.98 0.95
## Minimum correlation of possible factor scores 0.96 0.96 0.89
#simdi -bad- olarak isaretledigimiz iki faktore giren ifadeleri cikartiyoruz
round2 = fa(haluknoutliers[ , -c(6,9,11,12,13,14,24,25,26,28,32,35,37,38,41,47,49,54,57)], nfactors = 3, rotate = "oblimin", fm = "ml")
round2
## Factor Analysis using method = ml
## Call: fa(r = haluknoutliers[, -c(6, 9, 11, 12, 13, 14, 24, 25, 26,
## 28, 32, 35, 37, 38, 41, 47, 49, 54, 57)], nfactors = 3, rotate = "oblimin",
## fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML3 ML2 h2 u2 com
## M1 0.61 -0.10 0.11 0.38 0.62 1.1
## M2 0.75 0.05 0.01 0.63 0.37 1.0
## M3 0.85 -0.04 0.01 0.69 0.31 1.0
## M4 0.64 0.21 -0.01 0.64 0.36 1.2
## M5 0.82 0.04 -0.03 0.68 0.32 1.0
## M7 0.53 0.15 -0.07 0.37 0.63 1.2
## M8 0.76 0.07 0.02 0.69 0.31 1.0
## M10 0.82 0.01 0.02 0.72 0.28 1.0
## M15 0.89 -0.10 0.08 0.75 0.25 1.0
## M16 0.91 -0.05 0.01 0.77 0.23 1.0
## M17 0.16 0.73 0.01 0.74 0.26 1.1
## M18 0.76 0.11 0.08 0.80 0.20 1.1
## M19 0.64 0.25 -0.01 0.69 0.31 1.3
## M20 0.82 -0.04 0.08 0.71 0.29 1.0
## M21 0.64 0.22 0.01 0.66 0.34 1.2
## M22 0.13 0.00 0.58 0.44 0.56 1.1
## M23 0.64 0.24 0.01 0.71 0.29 1.3
## M27 0.61 0.23 0.08 0.70 0.30 1.3
## M29 0.26 -0.02 0.63 0.64 0.36 1.3
## M30 0.10 0.26 0.58 0.62 0.38 1.5
## M31 0.81 0.04 0.12 0.83 0.17 1.0
## M33 0.59 0.24 0.10 0.71 0.29 1.4
## M34 0.30 0.39 -0.19 0.33 0.67 2.4
## M36 0.11 0.81 0.03 0.80 0.20 1.0
## M39 0.66 -0.11 -0.30 0.23 0.77 1.5
## M40 0.03 0.02 0.85 0.77 0.23 1.0
## M42 0.73 -0.11 0.00 0.43 0.57 1.0
## M43 0.66 0.14 -0.04 0.54 0.46 1.1
## M44 -0.05 0.94 -0.01 0.83 0.17 1.0
## M45 0.10 0.76 0.12 0.78 0.22 1.1
## M46 -0.05 0.96 -0.03 0.84 0.16 1.0
## M48 -0.07 -0.01 0.90 0.73 0.27 1.0
## M50 0.22 0.68 0.03 0.74 0.26 1.2
## M51 0.59 0.05 0.12 0.48 0.52 1.1
## M52 0.27 0.60 0.07 0.70 0.30 1.4
## M53 -0.11 0.95 0.03 0.78 0.22 1.0
## M55 -0.01 0.00 0.89 0.77 0.23 1.0
## M56 0.24 0.66 0.02 0.74 0.26 1.3
## M58 0.05 0.00 0.87 0.81 0.19 1.0
## M59 0.08 0.73 0.03 0.64 0.36 1.0
## M60 -0.07 0.95 0.05 0.85 0.15 1.0
## M61 0.66 -0.09 0.09 0.44 0.56 1.1
## M62 0.02 0.81 -0.12 0.63 0.37 1.0
## M63 0.13 0.73 0.10 0.76 0.24 1.1
##
## ML1 ML3 ML2
## SS loadings 13.93 10.31 4.91
## Proportion Var 0.32 0.23 0.11
## Cumulative Var 0.32 0.55 0.66
## Proportion Explained 0.48 0.35 0.17
## Cumulative Proportion 0.48 0.83 1.00
##
## With factor correlations of
## ML1 ML3 ML2
## ML1 1.00 0.71 0.56
## ML3 0.71 1.00 0.35
## ML2 0.56 0.35 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 946 and the objective function was 49.66 with Chi Square of 11596.14
## The degrees of freedom for the model are 817 and the objective function was 7.46
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic number of observations is 250 with the empirical chi square 499.34 with prob < 1
## The total number of observations was 250 with Likelihood Chi Square = 1726.45 with prob < 3.1e-67
##
## Tucker Lewis Index of factoring reliability = 0.9
## RMSEA index = 0.067 and the 90 % confidence intervals are 0.062 0.071
## BIC = -2784.58
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML1 ML3 ML2
## Correlation of (regression) scores with factors 0.99 0.99 0.97
## Multiple R square of scores with factors 0.98 0.98 0.94
## Minimum correlation of possible factor scores 0.95 0.95 0.89
#round3
round3 = fa(haluknoutliers[ , -c(6,9,11,12,13,14,24,25,26,28,32,35,37,38,41,47,49,54,57,34)], nfactors = 3, rotate = "oblimin", fm = "ml")
round3
## Factor Analysis using method = ml
## Call: fa(r = haluknoutliers[, -c(6, 9, 11, 12, 13, 14, 24, 25, 26,
## 28, 32, 35, 37, 38, 41, 47, 49, 54, 57, 34)], nfactors = 3,
## rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML3 ML2 h2 u2 com
## M1 0.61 -0.10 0.11 0.38 0.62 1.1
## M2 0.75 0.05 0.01 0.63 0.37 1.0
## M3 0.85 -0.04 0.01 0.69 0.31 1.0
## M4 0.64 0.21 -0.01 0.64 0.36 1.2
## M5 0.82 0.04 -0.03 0.68 0.32 1.0
## M7 0.53 0.15 -0.07 0.37 0.63 1.2
## M8 0.76 0.07 0.02 0.69 0.31 1.0
## M10 0.82 0.01 0.02 0.72 0.28 1.0
## M15 0.89 -0.10 0.07 0.75 0.25 1.0
## M16 0.91 -0.05 0.01 0.77 0.23 1.0
## M17 0.16 0.73 0.01 0.74 0.26 1.1
## M18 0.76 0.11 0.08 0.80 0.20 1.1
## M19 0.64 0.25 -0.02 0.69 0.31 1.3
## M20 0.83 -0.04 0.08 0.71 0.29 1.0
## M21 0.64 0.22 0.01 0.66 0.34 1.2
## M22 0.13 0.00 0.59 0.44 0.56 1.1
## M23 0.64 0.24 0.01 0.71 0.29 1.3
## M27 0.61 0.23 0.08 0.70 0.30 1.3
## M29 0.25 -0.02 0.64 0.64 0.36 1.3
## M30 0.10 0.26 0.58 0.62 0.38 1.4
## M31 0.81 0.04 0.12 0.82 0.18 1.0
## M33 0.59 0.24 0.10 0.71 0.29 1.4
## M36 0.11 0.81 0.03 0.80 0.20 1.0
## M39 0.66 -0.11 -0.30 0.23 0.77 1.5
## M40 0.03 0.02 0.86 0.77 0.23 1.0
## M42 0.73 -0.11 -0.01 0.43 0.57 1.0
## M43 0.66 0.14 -0.05 0.54 0.46 1.1
## M44 -0.04 0.94 -0.01 0.83 0.17 1.0
## M45 0.10 0.76 0.11 0.78 0.22 1.1
## M46 -0.05 0.96 -0.03 0.84 0.16 1.0
## M48 -0.08 -0.02 0.90 0.72 0.28 1.0
## M50 0.21 0.68 0.03 0.73 0.27 1.2
## M51 0.59 0.05 0.11 0.48 0.52 1.1
## M52 0.27 0.60 0.07 0.70 0.30 1.4
## M53 -0.11 0.95 0.03 0.78 0.22 1.0
## M55 -0.02 0.00 0.89 0.77 0.23 1.0
## M56 0.25 0.66 0.01 0.74 0.26 1.3
## M58 0.04 -0.01 0.88 0.81 0.19 1.0
## M59 0.08 0.73 0.03 0.64 0.36 1.0
## M60 -0.07 0.95 0.05 0.85 0.15 1.0
## M61 0.67 -0.09 0.09 0.44 0.56 1.1
## M62 0.02 0.81 -0.13 0.63 0.37 1.1
## M63 0.13 0.73 0.09 0.76 0.24 1.1
##
## ML1 ML3 ML2
## SS loadings 13.80 10.09 4.93
## Proportion Var 0.32 0.23 0.11
## Cumulative Var 0.32 0.56 0.67
## Proportion Explained 0.48 0.35 0.17
## Cumulative Proportion 0.48 0.83 1.00
##
## With factor correlations of
## ML1 ML3 ML2
## ML1 1.00 0.71 0.57
## ML3 0.71 1.00 0.36
## ML2 0.57 0.36 1.00
##
## Mean item complexity = 1.1
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 903 and the objective function was 49.02 with Chi Square of 11463.07
## The degrees of freedom for the model are 777 and the objective function was 7.2
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic number of observations is 250 with the empirical chi square 465.62 with prob < 1
## The total number of observations was 250 with Likelihood Chi Square = 1669.18 with prob < 3.3e-67
##
## Tucker Lewis Index of factoring reliability = 0.901
## RMSEA index = 0.068 and the 90 % confidence intervals are 0.063 0.072
## BIC = -2621
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML1 ML3 ML2
## Correlation of (regression) scores with factors 0.99 0.99 0.97
## Multiple R square of scores with factors 0.98 0.98 0.95
## Minimum correlation of possible factor scores 0.95 0.95 0.89
#Now we have our final model. what can we do with it?
# ML1, ML2 ve ML3 un arasinda koreleasyon guclu (ML1 ve Ml3 arasinda r = 0.71, ML2 ve ML3 r = 0.36, ML1 ve ML2 r = 0.57)
# Tucker Lewis Index of factoring reliability = 0.9 (0.9 ve ustu olmasi beklenirmis kaynak: https://pdfs.semanticscholar.org/2ad3/e0e8ad810061673f718a88e430598f42d932.pdf)
# The root mean square of the residuals (RMSR) is 0.03 (bunun .05 den kucuk olmasi beklenirmis: kaynak: https://stats.idre.ucla.edu/wp-content/uploads/2016/02/part2-1.pdf)
# RMSEA index = 0.067 and the 90 % confidence intervals are 0.062 0.07 (0.06 ve alti olmasi beklenirmis: kaynak: https://en.wikipedia.org/wiki/Confirmatory_factor_analysis)
#The last thing we want is CFI. It is one of the most commonly reported values in factor analysis
finalmodel = fa(haluknoutliers[ , -c(6,9,11,12,13,14,24,25,26,28,32,35,37,38,41,47,49,54,57,34)], nfactors = 3, rotate = "oblimin", fm = "ml")
1 - ((finalmodel$STATISTIC-finalmodel$dof)/
(finalmodel$null.chisq-finalmodel$null.dof))
## [1] 0.915514
# 0.91 verdi CFI degerini
#Reliability
factor1 = c(1, 2, 3, 4, 5, 7, 8, 10, 15, 16, 18, 19, 20, 21, 23, 27, 31, 33, 39, 42, 43, 51, 61)
factor2 = c(22, 29, 30, 40, 48, 55, 58)
factor3 = c(17, 36, 44, 45, 46, 50, 52, 53, 56, 59, 60, 62, 63)
psych::alpha(haluknoutliers[ , factor1])
##
## Reliability analysis
## Call: psych::alpha(x = haluknoutliers[, factor1])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.97 0.97 0.98 0.59 33 0.0026 3.6 0.78 0.63
##
## lower alpha upper 95% confidence boundaries
## 0.97 0.97 0.98
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## M1 0.97 0.97 0.98 0.60 34 0.0026 0.017 0.64
## M2 0.97 0.97 0.98 0.59 32 0.0028 0.019 0.62
## M3 0.97 0.97 0.98 0.59 31 0.0028 0.019 0.62
## M4 0.97 0.97 0.98 0.59 32 0.0028 0.019 0.62
## M5 0.97 0.97 0.98 0.59 31 0.0028 0.019 0.62
## M7 0.97 0.97 0.98 0.60 34 0.0026 0.018 0.64
## M8 0.97 0.97 0.98 0.59 31 0.0028 0.018 0.62
## M10 0.97 0.97 0.98 0.59 31 0.0028 0.018 0.62
## M15 0.97 0.97 0.98 0.59 31 0.0028 0.018 0.61
## M16 0.97 0.97 0.98 0.59 31 0.0028 0.018 0.61
## M18 0.97 0.97 0.98 0.58 31 0.0028 0.018 0.62
## M19 0.97 0.97 0.98 0.59 32 0.0028 0.018 0.62
## M20 0.97 0.97 0.98 0.59 31 0.0028 0.018 0.62
## M21 0.97 0.97 0.98 0.59 32 0.0028 0.018 0.61
## M23 0.97 0.97 0.98 0.59 32 0.0028 0.018 0.62
## M27 0.97 0.97 0.98 0.59 32 0.0028 0.018 0.62
## M31 0.97 0.97 0.98 0.58 31 0.0028 0.017 0.61
## M33 0.97 0.97 0.98 0.59 32 0.0028 0.018 0.62
## M39 0.97 0.97 0.98 0.62 36 0.0025 0.011 0.64
## M42 0.97 0.97 0.98 0.60 33 0.0027 0.018 0.64
## M43 0.97 0.97 0.98 0.59 32 0.0027 0.019 0.63
## M51 0.97 0.97 0.98 0.60 33 0.0027 0.019 0.64
## M61 0.97 0.97 0.98 0.60 33 0.0027 0.018 0.64
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## M1 250 0.63 0.63 0.61 0.59 3.9 0.95
## M2 250 0.81 0.81 0.80 0.79 3.8 0.91
## M3 250 0.84 0.84 0.83 0.82 3.8 0.92
## M4 250 0.80 0.80 0.79 0.78 3.5 1.08
## M5 250 0.84 0.83 0.83 0.82 3.6 1.04
## M7 250 0.64 0.63 0.61 0.60 3.2 1.09
## M8 250 0.84 0.84 0.83 0.82 3.5 1.05
## M10 250 0.84 0.84 0.84 0.82 3.5 1.08
## M15 250 0.85 0.86 0.85 0.84 3.8 0.98
## M16 250 0.87 0.87 0.87 0.86 3.8 0.99
## M18 250 0.89 0.88 0.89 0.87 3.6 1.01
## M19 250 0.83 0.82 0.82 0.81 3.2 1.11
## M20 250 0.84 0.84 0.84 0.82 3.8 0.93
## M21 250 0.81 0.81 0.80 0.79 3.4 1.00
## M23 250 0.83 0.83 0.83 0.81 3.3 0.99
## M27 250 0.83 0.83 0.82 0.81 3.4 1.06
## M31 250 0.89 0.89 0.90 0.88 3.7 0.98
## M33 250 0.82 0.82 0.81 0.80 3.6 1.05
## M39 250 0.44 0.43 0.39 0.39 2.9 1.08
## M42 250 0.68 0.68 0.67 0.65 3.8 0.94
## M43 250 0.76 0.76 0.76 0.74 3.5 1.02
## M51 250 0.71 0.72 0.70 0.69 3.9 0.83
## M61 250 0.68 0.69 0.68 0.65 3.8 0.93
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## M1 0.03 0.06 0.14 0.53 0.23 0
## M2 0.02 0.10 0.16 0.54 0.19 0
## M3 0.02 0.08 0.17 0.51 0.22 0
## M4 0.04 0.17 0.22 0.41 0.16 0
## M5 0.04 0.14 0.19 0.47 0.16 0
## M7 0.04 0.24 0.26 0.34 0.12 0
## M8 0.04 0.17 0.20 0.45 0.15 0
## M10 0.04 0.18 0.14 0.47 0.17 0
## M15 0.02 0.12 0.12 0.54 0.20 0
## M16 0.02 0.12 0.10 0.53 0.23 0
## M18 0.03 0.15 0.22 0.46 0.15 0
## M19 0.06 0.26 0.25 0.32 0.12 0
## M20 0.03 0.08 0.14 0.56 0.20 0
## M21 0.03 0.17 0.25 0.43 0.12 0
## M23 0.03 0.20 0.28 0.41 0.08 0
## M27 0.05 0.19 0.24 0.40 0.12 0
## M31 0.03 0.11 0.16 0.52 0.18 0
## M33 0.02 0.18 0.16 0.46 0.18 0
## M39 0.08 0.32 0.26 0.28 0.06 0
## M42 0.03 0.08 0.12 0.56 0.21 0
## M43 0.04 0.14 0.23 0.46 0.14 0
## M51 0.02 0.06 0.11 0.61 0.20 0
## M61 0.03 0.07 0.13 0.58 0.19 0
psych::alpha(haluknoutliers[ , factor2])
##
## Reliability analysis
## Call: psych::alpha(x = haluknoutliers[, factor2])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.93 0.93 0.93 0.66 14 0.0071 3.8 0.82 0.66
##
## lower alpha upper 95% confidence boundaries
## 0.91 0.93 0.94
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## M22 0.93 0.93 0.93 0.70 14 0.0073 0.0050 0.69
## M29 0.91 0.92 0.92 0.66 12 0.0085 0.0102 0.64
## M30 0.92 0.93 0.92 0.67 12 0.0079 0.0096 0.69
## M40 0.91 0.91 0.91 0.64 11 0.0090 0.0081 0.63
## M48 0.92 0.92 0.92 0.66 12 0.0083 0.0059 0.66
## M55 0.91 0.92 0.91 0.65 11 0.0087 0.0064 0.63
## M58 0.91 0.92 0.91 0.64 11 0.0089 0.0063 0.64
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## M22 250 0.76 0.75 0.69 0.67 3.6 1.08
## M29 250 0.84 0.84 0.80 0.78 3.8 1.03
## M30 250 0.83 0.81 0.76 0.74 3.3 1.21
## M40 250 0.89 0.89 0.88 0.85 4.0 0.87
## M48 250 0.83 0.84 0.82 0.77 3.9 0.92
## M55 250 0.86 0.87 0.86 0.82 3.9 0.87
## M58 250 0.88 0.89 0.88 0.84 4.0 0.90
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## M22 0.04 0.15 0.14 0.47 0.19 0
## M29 0.04 0.10 0.15 0.49 0.22 0
## M30 0.06 0.27 0.18 0.32 0.18 0
## M40 0.02 0.06 0.12 0.56 0.24 0
## M48 0.02 0.07 0.17 0.49 0.25 0
## M55 0.02 0.04 0.16 0.55 0.22 0
## M58 0.02 0.04 0.16 0.49 0.29 0
psych::alpha(haluknoutliers[ , factor3])
##
## Reliability analysis
## Call: psych::alpha(x = haluknoutliers[, factor3])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.97 0.97 0.98 0.74 37 0.0024 2.8 0.99 0.74
##
## lower alpha upper 95% confidence boundaries
## 0.97 0.97 0.98
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## M17 0.97 0.97 0.97 0.74 35 0.0026 0.0030 0.74
## M36 0.97 0.97 0.97 0.74 34 0.0027 0.0028 0.74
## M44 0.97 0.97 0.97 0.74 34 0.0027 0.0026 0.74
## M45 0.97 0.97 0.97 0.74 34 0.0026 0.0030 0.74
## M46 0.97 0.97 0.97 0.74 34 0.0027 0.0025 0.74
## M50 0.97 0.97 0.98 0.74 35 0.0026 0.0033 0.74
## M52 0.97 0.97 0.98 0.75 35 0.0025 0.0032 0.75
## M53 0.97 0.97 0.97 0.74 34 0.0026 0.0030 0.75
## M56 0.97 0.97 0.98 0.74 35 0.0026 0.0033 0.74
## M59 0.97 0.97 0.98 0.75 36 0.0025 0.0029 0.75
## M60 0.97 0.97 0.97 0.73 33 0.0027 0.0029 0.73
## M62 0.97 0.97 0.98 0.75 37 0.0025 0.0024 0.75
## M63 0.97 0.97 0.97 0.74 34 0.0026 0.0032 0.74
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## M17 250 0.87 0.86 0.85 0.84 2.7 1.19
## M36 250 0.90 0.90 0.89 0.88 2.9 1.21
## M44 250 0.90 0.90 0.90 0.88 2.7 1.16
## M45 250 0.89 0.89 0.88 0.87 2.9 1.21
## M46 250 0.90 0.90 0.90 0.88 2.6 1.18
## M50 250 0.87 0.87 0.86 0.85 3.0 1.13
## M52 250 0.84 0.85 0.83 0.82 3.0 1.10
## M53 250 0.88 0.88 0.87 0.86 2.7 1.13
## M56 250 0.87 0.87 0.85 0.84 2.8 1.12
## M59 250 0.83 0.83 0.81 0.80 2.8 1.14
## M60 250 0.92 0.92 0.92 0.91 2.7 1.10
## M62 250 0.80 0.80 0.78 0.77 2.4 0.98
## M63 250 0.88 0.88 0.87 0.86 3.1 1.14
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## M17 0.14 0.37 0.21 0.19 0.09 0
## M36 0.12 0.36 0.18 0.23 0.11 0
## M44 0.13 0.36 0.24 0.18 0.09 0
## M45 0.12 0.30 0.22 0.26 0.11 0
## M46 0.17 0.40 0.20 0.15 0.08 0
## M50 0.10 0.28 0.29 0.25 0.09 0
## M52 0.10 0.24 0.32 0.27 0.08 0
## M53 0.11 0.39 0.23 0.20 0.08 0
## M56 0.10 0.36 0.27 0.18 0.09 0
## M59 0.10 0.35 0.25 0.22 0.09 0
## M60 0.10 0.40 0.24 0.20 0.07 0
## M62 0.17 0.48 0.22 0.10 0.03 0
## M63 0.08 0.28 0.24 0.30 0.10 0
#factor1 de raw_alpha 0.97 cikti. cok iyi deger. Eger iy icikmssaydi tablodan hangi idafedenin raw alpha deger idusukmus diye bakip cikarirdik
#factor2 icin raw alpha 0.93
#factor3 icin raw alpha 0.97
#3 faktorun de reliability si cok yuksek cikti. Guzel
# Finally THEORY. What do th factors mean? Look at the question themes and give the factors a label. Burda sen faktor altindaki sorularda ortak cikan seye gore temasini yszarsin (bilissel, duygusal neyse artik)
# Eger faktorlerden birinde reverse coded olan itemlerin hepsi toplanmissa bu durumdan endise edebilirmissin. Ama zaten ole istiyorsan sorun yokmus. Ben kontrol etmedim reverseler ayni yerde mi toplanmis bir bak
##create new factor scores
haluknoutliers$f1 = apply(haluknoutliers[ , factor1], 1, mean) ##creates avarage scores
haluknoutliers$f2 = apply(haluknoutliers[ , factor2], 1, mean) ##creates avarage scores
haluknoutliers$f3 = apply(haluknoutliers[ , factor3], 1, mean) ##creates avarage scores
summary(haluknoutliers)
## M1 M2 M3 M4 M5
## Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:3.000 1st Qu.:3.00 1st Qu.:3.000 1st Qu.:3.000
## Median :4.000 Median :4.000 Median :4.00 Median :4.000 Median :4.000
## Mean :3.864 Mean :3.788 Mean :3.84 Mean :3.484 Mean :3.584
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.000
## M6 M7 M8 M9
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.000 1st Qu.:2.000
## Median :4.000 Median :3.000 Median :4.000 Median :3.000
## Mean :3.312 Mean :3.244 Mean :3.512 Mean :3.012
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## M10 M11 M12 M13 M14
## Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:2.00 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000
## Median :4.000 Median :3.00 Median :3.000 Median :2.000 Median :3.000
## Mean :3.548 Mean :2.94 Mean :2.996 Mean :2.568 Mean :2.824
## 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000
## M15 M16 M17 M18
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:4.000 1st Qu.:2.000 1st Qu.:3.000
## Median :4.000 Median :4.000 Median :2.000 Median :4.000
## Mean :3.764 Mean :3.832 Mean :2.736 Mean :3.552
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## M19 M20 M21 M22 M23
## Min. :1.000 Min. :1.00 Min. :1.00 Min. :1.000 Min. :1.0
## 1st Qu.:2.000 1st Qu.:4.00 1st Qu.:3.00 1st Qu.:3.000 1st Qu.:3.0
## Median :3.000 Median :4.00 Median :4.00 Median :4.000 Median :3.0
## Mean :3.188 Mean :3.82 Mean :3.44 Mean :3.624 Mean :3.3
## 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:4.0
## Max. :5.000 Max. :5.00 Max. :5.00 Max. :5.000 Max. :5.0
## M24 M25 M26 M27
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.000
## Median :3.000 Median :2.000 Median :3.000 Median :4.000
## Mean :3.112 Mean :2.448 Mean :2.972 Mean :3.352
## 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## M28 M29 M30 M31 M32
## Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:3.00 1st Qu.:2.000 1st Qu.:3.000 1st Qu.:2.000
## Median :3.000 Median :4.00 Median :3.000 Median :4.000 Median :4.000
## Mean :3.112 Mean :3.76 Mean :3.288 Mean :3.708 Mean :3.368
## 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000
## M33 M34 M35 M36 M37
## Min. :1.0 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.0 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000
## Median :4.0 Median :2.000 Median :3.000 Median :3.000 Median :4.000
## Mean :3.6 Mean :2.636 Mean :3.292 Mean :2.856 Mean :3.272
## 3rd Qu.:4.0 3rd Qu.:3.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.0 Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## M38 M39 M40 M41
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:4.000 1st Qu.:3.000
## Median :4.000 Median :3.000 Median :4.000 Median :3.500
## Mean :3.396 Mean :2.912 Mean :3.952 Mean :3.396
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## M42 M43 M44 M45
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:2.000
## Median :4.000 Median :4.000 Median :3.000 Median :3.000
## Mean :3.836 Mean :3.512 Mean :2.732 Mean :2.948
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## M46 M47 M48 M49 M50
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.00
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.000 1st Qu.:2.00 1st Qu.:2.00
## Median :2.000 Median :3.000 Median :4.000 Median :3.00 Median :3.00
## Mean :2.588 Mean :3.244 Mean :3.892 Mean :3.16 Mean :2.96
## 3rd Qu.:3.000 3rd Qu.:4.000 3rd Qu.:4.750 3rd Qu.:4.00 3rd Qu.:4.00
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.00 Max. :5.00
## M51 M52 M53 M54 M55
## Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:4.00 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.00 1st Qu.:4.000
## Median :4.00 Median :3.000 Median :2.500 Median :3.00 Median :4.000
## Mean :3.92 Mean :2.996 Mean :2.736 Mean :3.22 Mean :3.892
## 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:4.000
## Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.00 Max. :5.000
## M56 M57 M58 M59 M60
## Min. :1.0 Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.:2.0 1st Qu.:2.000 1st Qu.:4.00 1st Qu.:2.000 1st Qu.:2.000
## Median :3.0 Median :4.000 Median :4.00 Median :3.000 Median :3.000
## Mean :2.8 Mean :3.316 Mean :3.98 Mean :2.844 Mean :2.748
## 3rd Qu.:4.0 3rd Qu.:4.000 3rd Qu.:5.00 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.0 Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.000
## M61 M62 M63 f1
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.087
## 1st Qu.:4.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.217
## Median :4.000 Median :2.000 Median :3.000 Median :3.696
## Mean :3.828 Mean :2.356 Mean :3.052 Mean :3.584
## 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:4.000 3rd Qu.:4.033
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## f2 f3
## Min. :1.000 Min. :1.000
## 1st Qu.:3.286 1st Qu.:2.000
## Median :3.857 Median :2.692
## Mean :3.770 Mean :2.796
## 3rd Qu.:4.250 3rd Qu.:3.462
## Max. :5.000 Max. :5.000
sd(haluknoutliers$f1)
## [1] 0.7820226
sd(haluknoutliers$f2)
## [1] 0.8244563
sd(haluknoutliers$f3)
## [1] 0.9934199
#tablodan da g,rebilirsin f1 mean 3.58, f2 mean 3.77, f3 mean 2.78 (factor 1 ve 2, faktor 3 e gore daha onemli gorunuyor)