Likert Scale Reliability Assessment

Method :

Step1:

Ensure that scores from all statements share the same polarity. Recode the scores for statements with reverse polarity.

Step2:

Compute for the sum of scores for each of the 60 respondents. Each respondent is considered an independent observation.

Step3:

Sort all the 60 observations based from the highest to the lowest computed sum.

Step4:

Determine the 1st, 2nd and 3rd quartiles of the computed sum. Divide the observations into 4 groups with the 1st, 2nd and 3rd quartiles used as the group threshold values.

Step5:

Conduct median test for each of the 45 statements using the observations from group 1 (below the 1st quartile) and group 4 (above the 3rd quartile). Use = 0.05. Verify assumptions.

Step6:

Determine the statements with significant p-values computed from the median test. These statements will be retained as part of the final questionnaire. The remaining statements with insignificant p-values will be removed.

Step7:

Conduct pairwise correlation for the scores from all the remaining statements. Determine the statement-pairs with insignificant p-values and remove from the questionnaire. Use alpha = 0.05.

Working Data :

60x45 matrix with possible values belonging to the set { 1, 2, 3, 4, 5 }

Solution :

INITIALIZATION OF DIRECTORY AND LIBRARIES

######################################
# SETTING THE WORKING DIRECTORY
######################################
setwd("C:/Users/John/Desktop/Statistics Masters/Survey Operations/Likert Task")

######################################
# INSTALLING AND LOADING THE NECESSARY LIBRARIES
######################################
library("dplyr")
library("Hmisc")
library("agricolae")
library("psy")
library("corrplot")

DATA PREPARATION AND PROCESSING

######################################
# LOADING THE DATA
######################################
likert.df <- read.csv('LikertSampleDataFinal.csv',
                      na.strings=c("NA","NaN"," ",""),
                      stringsAsFactors = F)
dim(likert.df)

## [1] 60 49

colnames(likert.df)

##  [1] "Item"       "Student"    "Respondent" "Sum"        "S_1"       
##  [6] "S_2"        "S_3"        "S_4"        "S_5"        "S_6"       
## [11] "S_7"        "S_8"        "S_9"        "S_10"       "S_11"      
## [16] "S_12"       "S_13"       "S_14"       "S_15"       "S_16"      
## [21] "S_17"       "S_18"       "S_19"       "S_20"       "S_21"      
## [26] "S_22"       "S_23"       "S_24"       "S_25"       "S_26"      
## [31] "S_27"       "S_28"       "S_29"       "S_30"       "S_31"      
## [36] "S_32"       "S_33"       "S_34"       "S_35"       "S_36"      
## [41] "S_37"       "S_38"       "S_39"       "S_40"       "S_41"      
## [46] "S_42"       "S_43"       "S_44"       "S_45"

summary(likert.df)

##       Item         Student           Respondent             Sum       
##  Min.   : 1.00   Length:60          Length:60          Min.   : 45.0  
##  1st Qu.:15.75   Class :character   Class :character   1st Qu.: 94.5  
##  Median :30.50   Mode  :character   Mode  :character   Median :121.5  
##  Mean   :30.50                                         Mean   :118.5  
##  3rd Qu.:45.25                                         3rd Qu.:147.8  
##  Max.   :60.00                                         Max.   :196.0  
##       S_1            S_2             S_3             S_4       
##  Min.   :1.00   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:1.00   1st Qu.:2.000   1st Qu.:2.000   1st Qu.:2.000  
##  Median :2.00   Median :3.000   Median :3.000   Median :3.000  
##  Mean   :2.45   Mean   :2.633   Mean   :2.517   Mean   :2.617  
##  3rd Qu.:3.00   3rd Qu.:3.000   3rd Qu.:3.000   3rd Qu.:3.000  
##  Max.   :5.00   Max.   :5.000   Max.   :5.000   Max.   :5.000  
##       S_5             S_6            S_7           S_8       
##  Min.   :1.000   Min.   :1.00   Min.   :1.0   Min.   :1.000  
##  1st Qu.:2.000   1st Qu.:2.00   1st Qu.:2.0   1st Qu.:2.000  
##  Median :3.000   Median :3.00   Median :3.0   Median :2.000  
##  Mean   :2.667   Mean   :2.85   Mean   :2.6   Mean   :2.567  
##  3rd Qu.:3.000   3rd Qu.:4.00   3rd Qu.:3.0   3rd Qu.:3.000  
##  Max.   :5.000   Max.   :5.00   Max.   :5.0   Max.   :5.000  
##       S_9             S_10        S_11           S_12            S_13     
##  Min.   :1.000   Min.   :1   Min.   :1.00   Min.   :1.000   Min.   :1.00  
##  1st Qu.:2.000   1st Qu.:1   1st Qu.:1.00   1st Qu.:2.000   1st Qu.:1.75  
##  Median :3.000   Median :2   Median :2.00   Median :3.000   Median :2.00  
##  Mean   :2.933   Mean   :2   Mean   :2.35   Mean   :2.833   Mean   :2.35  
##  3rd Qu.:4.000   3rd Qu.:3   3rd Qu.:3.00   3rd Qu.:3.250   3rd Qu.:3.00  
##  Max.   :5.000   Max.   :4   Max.   :5.00   Max.   :5.000   Max.   :4.00  
##       S_14           S_15            S_16            S_17      
##  Min.   :1.00   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:1.75   1st Qu.:2.000   1st Qu.:2.000   1st Qu.:1.000  
##  Median :3.00   Median :3.000   Median :3.000   Median :2.000  
##  Mean   :2.50   Mean   :2.467   Mean   :2.583   Mean   :2.267  
##  3rd Qu.:3.00   3rd Qu.:3.000   3rd Qu.:3.000   3rd Qu.:3.000  
##  Max.   :5.00   Max.   :4.000   Max.   :5.000   Max.   :5.000  
##       S_18           S_19            S_20            S_21      
##  Min.   :1.00   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:1.00   1st Qu.:2.000   1st Qu.:1.000   1st Qu.:2.000  
##  Median :2.00   Median :3.000   Median :2.500   Median :3.000  
##  Mean   :2.35   Mean   :2.533   Mean   :2.417   Mean   :2.617  
##  3rd Qu.:3.00   3rd Qu.:3.000   3rd Qu.:3.000   3rd Qu.:4.000  
##  Max.   :5.00   Max.   :4.000   Max.   :5.000   Max.   :5.000  
##       S_22           S_23            S_24          S_25     
##  Min.   :1.00   Min.   :1.000   Min.   :1.0   Min.   :1.00  
##  1st Qu.:1.75   1st Qu.:1.000   1st Qu.:1.0   1st Qu.:2.00  
##  Median :3.00   Median :3.000   Median :3.0   Median :3.00  
##  Mean   :2.55   Mean   :2.617   Mean   :2.5   Mean   :2.75  
##  3rd Qu.:3.00   3rd Qu.:3.250   3rd Qu.:3.0   3rd Qu.:3.00  
##  Max.   :5.00   Max.   :5.000   Max.   :5.0   Max.   :5.00  
##       S_26            S_27            S_28            S_29    
##  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.0  
##  1st Qu.:2.000   1st Qu.:2.000   1st Qu.:1.000   1st Qu.:2.0  
##  Median :3.000   Median :3.000   Median :2.000   Median :3.0  
##  Mean   :2.833   Mean   :2.717   Mean   :2.133   Mean   :2.6  
##  3rd Qu.:3.250   3rd Qu.:3.000   3rd Qu.:3.000   3rd Qu.:3.0  
##  Max.   :5.000   Max.   :5.000   Max.   :4.000   Max.   :5.0  
##       S_30            S_31            S_32            S_33      
##  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:3.000   1st Qu.:2.000   1st Qu.:1.000   1st Qu.:3.000  
##  Median :4.000   Median :3.000   Median :2.000   Median :4.000  
##  Mean   :3.717   Mean   :2.783   Mean   :2.067   Mean   :3.617  
##  3rd Qu.:5.000   3rd Qu.:3.000   3rd Qu.:3.000   3rd Qu.:5.000  
##  Max.   :5.000   Max.   :5.000   Max.   :5.000   Max.   :5.000  
##       S_34           S_35            S_36          S_37      
##  Min.   :1.00   Min.   :1.000   Min.   :1.0   Min.   :1.000  
##  1st Qu.:3.00   1st Qu.:2.000   1st Qu.:2.0   1st Qu.:1.750  
##  Median :3.00   Median :3.000   Median :3.0   Median :3.000  
##  Mean   :3.25   Mean   :2.917   Mean   :2.7   Mean   :2.533  
##  3rd Qu.:4.00   3rd Qu.:4.000   3rd Qu.:3.0   3rd Qu.:3.000  
##  Max.   :5.00   Max.   :5.000   Max.   :5.0   Max.   :4.000  
##       S_38            S_39            S_40           S_41      
##  Min.   :1.000   Min.   :1.000   Min.   :1.00   Min.   :1.000  
##  1st Qu.:2.000   1st Qu.:2.000   1st Qu.:2.00   1st Qu.:2.000  
##  Median :3.000   Median :3.000   Median :3.00   Median :3.000  
##  Mean   :2.633   Mean   :2.883   Mean   :2.85   Mean   :2.717  
##  3rd Qu.:3.000   3rd Qu.:4.000   3rd Qu.:4.00   3rd Qu.:3.000  
##  Max.   :5.000   Max.   :5.000   Max.   :5.00   Max.   :5.000  
##       S_42            S_43           S_44            S_45      
##  Min.   :1.000   Min.   :1.00   Min.   :1.000   Min.   :1.000  
##  1st Qu.:2.000   1st Qu.:2.00   1st Qu.:2.000   1st Qu.:1.000  
##  Median :3.000   Median :2.50   Median :3.000   Median :2.000  
##  Mean   :2.583   Mean   :2.35   Mean   :2.883   Mean   :2.217  
##  3rd Qu.:3.000   3rd Qu.:3.00   3rd Qu.:4.000   3rd Qu.:3.000  
##  Max.   :5.000   Max.   :5.00   Max.   :5.000   Max.   :5.000

######################################
# SORTING THE DATA BY THE LIKERT SCORE SUM
######################################
(likert.df <- likert.df[order(-likert.df$Sum),])

##    Item   Student Respondent Sum S_1 S_2 S_3 S_4 S_5 S_6 S_7 S_8 S_9 S_10
## 1     1     Jovit   18-20_yo 196   4   4   5   4   5   5   4   5   5    4
## 2     2   Twinkle     >50_yo 191   5   5   5   5   5   5   5   5   4    4
## 3     3     Benna  >30-50_yo 189   5   5   4   4   5   5   4   4   5    2
## 4     4       Sha   18-20_yo 179   5   5   4   5   5   5   4   5   5    4
## 5     5    Nicole   18-20_yo 178   4   4   3   4   4   5   4   4   3    2
## 6     6       Nix   18-20_yo 170   4   4   4   2   4   4   4   4   4    2
## 7     7     Wency     >50_yo 168   4   3   3   4   4   3   3   4   5    3
## 8     8      Jolo  >30-50_yo 167   4   4   3   3   3   4   4   4   4    4
## 9     9     Benna     >50_yo 167   3   4   3   3   4   4   5   5   4    3
## 10   10       Nix     >50_yo 166   4   4   3   3   4   4   3   3   2    2
## 11   11       Nix  >20-30_yo 161   4   4   2   4   4   4   4   4   3    2
## 12   12     Jovit  >30-50_yo 160   4   4   4   3   4   4   4   3   5    2
## 13   13 Christian  >20-30_yo 155   4   4   4   4   3   4   3   4   4    3
## 14   14    Dianne     >50_yo 152   3   3   3   4   3   3   4   4   3    3
## 15   15       Sha  >30-50_yo 150   3   4   4   3   4   5   3   4   3    3
## 16   16     Wency  >30-50_yo 147   3   3   3   4   4   4   3   3   4    2
## 17   17    Nicole     >50_yo 138   4   3   4   4   3   4   3   3   3    2
## 18   18     Wency   18-20_yo 136   3   3   3   3   3   3   3   3   3    3
## 19   19     Marco   18-20_yo 135   3   3   3   3   3   3   3   3   3    3
## 20   20      Jolo     >50_yo 135   3   3   3   3   3   3   3   3   3    3
## 21   21     Marco  >20-30_yo 133   4   4   2   2   3   4   3   3   5    2
## 22   22      Jolo  >20-30_yo 132   3   3   3   2   2   2   3   3   4    2
## 23   23       Max     >50_yo 131   3   3   3   3   3   3   3   3   1    1
## 24   24     Sonny  >20-30_yo 129   3   3   3   3   3   3   3   3   3    2
## 25   25    Dianne   18-20_yo 127   2   3   2   2   2   3   3   4   3    3
## 26   26     Jovit     >50_yo 127   1   2   3   4   3   3   3   3   3    2
## 27   27     Jason  >20-30_yo 126   2   2   3   3   3   2   3   2   4    2
## 28   28       Sha     >50_yo 125   3   3   3   3   3   3   2   3   3    3
## 29   29       Kat   18-20_yo 122   3   2   2   3   3   3   2   2   3    2
## 30   30     Sonny   18-20_yo 122   2   3   3   3   2   3   3   2   2    2
## 31   31     Jason  >30-50_yo 121   2   2   3   3   2   3   3   2   3    2
## 32   32       Max  >20-30_yo 120   1   3   3   1   4   2   3   2   3    1
## 33   33     Benna  >20-30_yo 119   2   3   2   3   3   3   3   2   3    3
## 34   34    Dianne  >30-50_yo 115   1   3   3   3   3   3   1   1   3    1
## 35   35     Jovit  >20-30_yo 114   2   3   3   4   2   3   3   3   3    1
## 36   36       Kat  >20-30_yo 114   2   2   2   2   3   3   2   2   3    2
## 37   37      Jolo   18-20_yo 107   1   2   2   2   2   3   2   2   3    2
## 38   38    Dianne  >20-30_yo 106   2   2   3   2   3   4   3   2   1    2
## 39   39     Jason   18-20_yo 104   3   3   3   3   3   2   2   2   2    1
## 40   40     Marco  >30-50_yo 103   1   3   2   2   3   2   3   2   4    3
## 41   41     Benna   18-20_yo 100   3   2   3   1   2   3   3   2   3    1
## 42   42       Nix  >30-50_yo  98   1   1   1   1   1   3   3   3   1    1
## 43   43 Christian     >50_yo  97   2   2   1   3   2   2   3   1   2    3
## 44   44 Christian  >30-50_yo  96   1   1   1   3   2   2   1   2   3    1
## 45   45    Nicole  >30-50_yo  95   1   1   1   3   2   2   2   2   2    2
## 46   46    Nicole  >20-30_yo  93   1   2   2   2   2   2   2   2   2    1
## 47   47     Wency  >20-30_yo  90   2   2   2   2   2   2   2   2   2    2
## 48   48 Christian   18-20_yo  82   2   2   2   2   2   2   2   2   2    2
## 49   49     Sonny     >50_yo  79   2   2   1   1   1   2   1   1   2    1
## 50   50       Max   18-20_yo  79   1   2   2   2   1   2   1   2   1    1
## 51   51   Twinkle  >30-50_yo  65   1   1   1   1   1   1   1   1   5    1
## 52   52       Sha  >20-30_yo  64   2   2   2   1   2   1   1   1   1    1
## 53   53   Twinkle  >20-30_yo  61   1   1   1   1   1   1   1   1   4    1
## 54   54       Kat     >50_yo  57   1   1   1   1   1   1   1   1   5    1
## 55   55   Twinkle   18-20_yo  57   1   1   1   1   1   1   1   1   1    1
## 56   56       Max  >30-50_yo  56   2   1   2   1   1   2   1   1   2    1
## 57   57       Kat  >30-50_yo  55   1   1   1   3   1   1   1   1   1    1
## 58   58     Marco     >50_yo  53   1   1   1   1   1   1   1   1   1    1
## 59   59     Jason     >50_yo  51   1   1   1   1   1   1   1   1   1    1
## 60   60     Sonny  >30-50_yo  45   1   1   1   1   1   1   1   1   1    1
##    S_11 S_12 S_13 S_14 S_15 S_16 S_17 S_18 S_19 S_20 S_21 S_22 S_23 S_24
## 1     5    5    4    5    4    4    4    5    4    4    5    4    4    3
## 2     4    5    4    4    3    3    5    4    3    5    5    5    5    4
## 3     4    5    3    4    4    4    4    4    4    4    4    4    5    4
## 4     4    5    3    4    4    3    4    4    3    4    4    3    5    4
## 5     4    5    3    5    3    5    3    4    3    4    5    3    4    5
## 6     4    4    4    4    4    2    4    4    4    4    4    4    4    4
## 7     4    4    4    4    4    4    4    4    4    4    4    3    4    4
## 8     4    4    3    4    4    4    3    3    4    4    4    4    4    4
## 9     4    4    4    3    3    4    3    4    3    3    4    4    4    4
## 10    4    4    4    4    3    4    2    4    4    4    4    4    4    4
## 11    3    4    4    3    3    3    3    3    3    3    4    4    4    4
## 12    4    5    4    4    3    3    2    3    3    4    4    4    3    4
## 13    3    4    2    2    3    4    3    3    4    3    4    3    3    4
## 14    4    3    4    4    4    3    3    3    3    4    3    3    4    4
## 15    3    3    3    3    3    4    3    4    3    3    3    4    3    3
## 16    3    4    3    3    3    4    4    4    4    3    4    3    4    3
## 17    3    3    2    3    4    4    2    2    2    2    4    3    2    4
## 18    3    3    2    2    3    3    3    4    4    3    3    3    4    2
## 19    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 20    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 21    3    3    1    1    2    4    1    1    4    1    2    3    5    3
## 22    2    4    4    2    2    4    3    2    4    4    2    3    3    2
## 23    3    3    3    3    3    3    1    1    3    3    3    3    3    3
## 24    2    3    2    2    3    3    2    3    3    3    3    3    3    3
## 25    2    2    3    3    2    2    2    3    3    3    3    3    3    3
## 26    3    3    2    3    2    4    3    3    3    4    3    3    3    2
## 27    2    3    3    2    3    2    3    3    3    3    3    2    2    2
## 28    2    3    2    3    3    3    2    2    3    2    3    3    3    3
## 29    3    3    1    3    3    3    3    2    2    1    2    3    3    3
## 30    2    3    3    3    2    2    3    3    3    2    2    2    3    3
## 31    2    3    2    3    3    3    2    2    2    1    2    2    2    2
## 32    1    3    4    3    2    2    1    1    3    3    4    3    2    2
## 33    3    2    1    2    2    3    2    2    3    2    3    2    3    2
## 34    1    3    2    3    2    3    2    1    2    3    2    3    3    1
## 35    2    3    2    3    2    2    3    3    3    4    3    3    2    2
## 36    3    3    1    3    3    3    2    2    2    1    1    1    3    3
## 37    2    2    2    2    2    2    2    1    2    2    3    3    2    3
## 38    2    3    3    3    2    2    1    2    2    2    2    3    3    3
## 39    1    1    2    2    3    2    3    3    3    2    1    1    1    1
## 40    3    3    2    2    2    2    2    2    2    3    2    2    2    2
## 41    1    3    2    2    2    2    3    2    3    1    2    1    3    1
## 42    1    3    3    3    3    1    1    1    1    1    3    1    1    3
## 43    2    2    1    3    2    2    3    2    2    1    2    1    1    1
## 44    1    3    2    1    3    1    1    1    1    1    2    3    1    1
## 45    2    2    2    2    2    2    2    2    3    2    3    2    2    3
## 46    1    2    2    1    2    3    2    2    2    1    1    3    1    2
## 47    2    2    2    2    2    2    2    2    2    2    2    2    2    2
## 48    2    2    2    2    1    1    1    1    1    1    2    3    3    2
## 49    1    2    2    1    3    3    1    1    2    2    2    2    1    1
## 50    1    2    1    1    2    2    2    3    2    3    1    3    2    2
## 51    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 52    1    1    1    1    1    2    1    1    1    1    1    1    1    1
## 53    1    1    2    1    1    1    1    1    1    1    1    1    1    1
## 54    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 55    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 56    1    2    1    1    1    1    1    1    1    1    1    1    1    1
## 57    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 58    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 59    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 60    1    1    1    1    1    1    1    1    1    1    1    1    1    1
##    S_25 S_26 S_27 S_28 S_29 S_30 S_31 S_32 S_33 S_34 S_35 S_36 S_37 S_38
## 1     4    4    5    3    4    4    4    3    5    5    4    4    4    5
## 2     3    4    4    3    4    3    3    5    3    4    4    4    3    5
## 3     5    5    4    3    4    5    4    3    3    5    4    4    4    4
## 4     5    4    4    4    4    3    3    4    3    4    4    4    4    3
## 5     3    4    3    3    5    4    4    3    5    5    5    4    3    5
## 6     4    4    2    4    4    4    2    4    4    4    4    4    4    4
## 7     4    4    4    3    4    3    3    3    3    4    4    4    4    4
## 8     3    4    3    4    4    5    4    2    3    4    3    5    3    3
## 9     5    4    4    3    3    3    3    3    3    4    4    4    3    4
## 10    4    4    4    2    4    5    5    1    4    5    5    4    3    4
## 11    4    4    3    2    4    5    3    3    5    5    3    3    3    4
## 12    4    3    3    1    2    5    4    2    4    4    4    4    4    4
## 13    4    3    3    3    3    4    4    3    4    4    4    4    4    4
## 14    3    4    3    3    3    4    4    2    4    3    4    3    4    4
## 15    3    4    3    3    4    3    3    4    3    4    4    3    4    3
## 16    3    3    3    3    3    3    3    3    4    3    3    3    3    3
## 17    2    4    3    2    2    2    2    2    4    4    4    3    3    3
## 18    3    3    3    3    3    3    3    3    3    3    3    4    3    3
## 19    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 20    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 21    3    3    4    1    3    4    4    2    5    5    4    2    4    2
## 22    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 23    3    3    3    3    3    5    3    3    3    5    3    3    3    3
## 24    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 25    3    3    3    3    2    4    4    3    5    3    4    2    2    3
## 26    2    3    3    3    3    3    3    3    3    4    2    3    2    3
## 27    4    3    4    3    3    3    3    2    4    4    3    3    3    2
## 28    3    3    3    3    3    4    3    1    4    3    3    3    3    2
## 29    3    3    3    2    3    5    3    3    3    3    3    3    1    3
## 30    3    3    3    3    3    4    3    3    3    4    3    3    3    3
## 31    3    3    3    3    3    4    4    1    3    4    3    3    3    3
## 32    3    3    4    1    4    4    3    1    3    4    4    3    3    2
## 33    3    3    3    2    3    4    3    3    4    2    4    3    3    2
## 34    3    3    3    3    3    4    3    1    5    3    5    3    3    1
## 35    2    2    2    3    2    2    2    3    3    4    2    3    2    3
## 36    3    3    3    2    3    5    3    1    4    3    3    3    3    2
## 37    3    2    2    1    3    4    3    1    4    4    3    3    3    4
## 38    3    3    2    1    2    5    2    1    5    3    3    2    2    3
## 39    3    3    3    3    3    2    4    1    1    4    3    3    3    3
## 40    3    2    2    2    2    2    2    2    3    3    3    3    2    2
## 41    2    2    3    1    1    5    3    1    5    3    2    1    3    2
## 42    3    3    3    1    3    4    3    1    4    1    3    3    3    3
## 43    2    3    2    1    2    4    2    1    1    3    2    3    1    3
## 44    4    4    3    1    2    5    5    1    5    3    3    2    1    2
## 45    2    2    2    2    2    3    2    2    3    3    2    2    2    2
## 46    3    3    3    1    2    5    3    1    4    3    3    2    2    2
## 47    2    2    2    2    2    2    2    2    2    2    2    2    2    2
## 48    2    2    3    1    1    4    1    2    2    1    1    2    1    2
## 49    1    3    3    1    2    5    2    1    5    1    3    1    3    1
## 50    2    3    2    1    2    2    1    2    2    2    1    2    1    2
## 51    1    1    1    1    1    5    1    1    5    3    3    1    1    1
## 52    2    2    2    1    1    5    2    1    5    1    2    2    1    1
## 53    1    1    1    1    1    5    1    1    5    4    1    1    1    1
## 54    1    1    1    1    1    5    1    1    5    1    1    1    1    1
## 55    1    1    1    1    1    1    5    1    5    5    1    1    1    1
## 56    1    1    1    1    1    5    1    1    1    2    1    1    1    1
## 57    1    1    1    1    1    3    1    1    3    3    1    1    1    1
## 58    1    1    1    1    1    5    1    1    5    1    1    1    1    1
## 59    1    1    1    1    1    1    1    1    5    1    1    1    1    1
## 60    1    1    1    1    1    1    1    1    1    1    1    1    1    1
##    S_39 S_40 S_41 S_42 S_43 S_44 S_45
## 1     5    5    5    5    4    4    5
## 2     5    4    5    4    5    4    5
## 3     5    5    4    4    4    5    5
## 4     4    3    4    4    3    4    3
## 5     5    4    4    4    3    5    4
## 6     4    4    4    4    4    4    4
## 7     4    4    4    4    3    3    4
## 8     3    5    4    4    3    4    4
## 9     4    4    4    4    3    4    5
## 10    5    4    5    4    3    3    3
## 11    4    4    4    3    3    5    4
## 12    4    3    4    4    3    4    3
## 13    4    3    3    3    3    3    3
## 14    4    3    3    3    2    3    4
## 15    4    3    4    3    2    3    2
## 16    3    4    3    3    3    3    3
## 17    5    3    3    2    3    5    4
## 18    4    3    3    3    2    3    3
## 19    3    3    3    3    3    3    3
## 20    3    3    3    3    3    3    3
## 21    5    5    3    2    3    2    1
## 22    3    3    3    3    3    4    3
## 23    3    3    3    3    3    3    3
## 24    3    2    3    3    3    3    3
## 25    3    2    2    3    3    3    3
## 26    3    2    3    3    3    2    3
## 27    3    4    3    3    2    4    1
## 28    3    3    3    3    2    2    2
## 29    3    4    3    3    3    3    2
## 30    3    2    2    3    2    3    2
## 31    3    5    3    3    3    4    1
## 32    4    3    3    3    3    4    1
## 33    3    2    3    3    2    3    2
## 34    3    3    3    3    2    4    1
## 35    3    2    3    2    2    1    2
## 36    3    2    3    3    3    4    1
## 37    3    2    2    2    2    4    1
## 38    1    2    1    2    1    4    1
## 39    3    5    2    2    1    1    1
## 40    2    3    3    2    2    1    1
## 41    1    1    2    3    3    4    1
## 42    3    3    3    3    1    4    1
## 43    3    4    3    2    3    3    3
## 44    2    4    3    2    2    2    1
## 45    2    2    2    2    2    3    2
## 46    2    1    2    2    1    4    1
## 47    2    2    2    2    2    2    2
## 48    1    2    2    1    2    4    1
## 49    3    1    1    1    1    1    1
## 50    1    2    3    2    2    1    1
## 51    1    5    1    1    1    1    1
## 52    1    1    1    1    1    1    1
## 53    1    1    1    1    1    2    1
## 54    1    1    1    1    1    1    1
## 55    1    1    1    1    1    1    1
## 56    2    1    1    1    1    1    1
## 57    1    1    1    1    3    1    1
## 58    1    1    1    1    1    1    1
## 59    1    3    1    1    1    1    1
## 60    1    1    1    1    1    1    1

######################################
# DETERMINING THE RANGE AND QUARTILES
######################################
(likert.range <- range(likert.df$Sum))

## [1]  45 196

(likert.quartile <- quantile(likert.df$Sum))

##     0%    25%    50%    75%   100% 
##  45.00  94.50 121.50 147.75 196.00

(quartile1 <- likert.quartile[[2]])

## [1] 94.5

(quartile2 <- likert.quartile[[3]])

## [1] 121.5

(quartile3 <- likert.quartile[[4]])

## [1] 147.75

######################################
# CREATING A QUARTILE VARIABLE
######################################
likert.df <- likert.df %>% 
             mutate(
               Quartile=cut(Sum, 
               breaks=c(-Inf, quartile1, quartile2, quartile3, Inf),
               labels=c("Quartile1", "Quartile2", "Quartile3", "Quartile4")))
(likert.df)

##    Item   Student Respondent Sum S_1 S_2 S_3 S_4 S_5 S_6 S_7 S_8 S_9 S_10
## 1     1     Jovit   18-20_yo 196   4   4   5   4   5   5   4   5   5    4
## 2     2   Twinkle     >50_yo 191   5   5   5   5   5   5   5   5   4    4
## 3     3     Benna  >30-50_yo 189   5   5   4   4   5   5   4   4   5    2
## 4     4       Sha   18-20_yo 179   5   5   4   5   5   5   4   5   5    4
## 5     5    Nicole   18-20_yo 178   4   4   3   4   4   5   4   4   3    2
## 6     6       Nix   18-20_yo 170   4   4   4   2   4   4   4   4   4    2
## 7     7     Wency     >50_yo 168   4   3   3   4   4   3   3   4   5    3
## 8     8      Jolo  >30-50_yo 167   4   4   3   3   3   4   4   4   4    4
## 9     9     Benna     >50_yo 167   3   4   3   3   4   4   5   5   4    3
## 10   10       Nix     >50_yo 166   4   4   3   3   4   4   3   3   2    2
## 11   11       Nix  >20-30_yo 161   4   4   2   4   4   4   4   4   3    2
## 12   12     Jovit  >30-50_yo 160   4   4   4   3   4   4   4   3   5    2
## 13   13 Christian  >20-30_yo 155   4   4   4   4   3   4   3   4   4    3
## 14   14    Dianne     >50_yo 152   3   3   3   4   3   3   4   4   3    3
## 15   15       Sha  >30-50_yo 150   3   4   4   3   4   5   3   4   3    3
## 16   16     Wency  >30-50_yo 147   3   3   3   4   4   4   3   3   4    2
## 17   17    Nicole     >50_yo 138   4   3   4   4   3   4   3   3   3    2
## 18   18     Wency   18-20_yo 136   3   3   3   3   3   3   3   3   3    3
## 19   19     Marco   18-20_yo 135   3   3   3   3   3   3   3   3   3    3
## 20   20      Jolo     >50_yo 135   3   3   3   3   3   3   3   3   3    3
## 21   21     Marco  >20-30_yo 133   4   4   2   2   3   4   3   3   5    2
## 22   22      Jolo  >20-30_yo 132   3   3   3   2   2   2   3   3   4    2
## 23   23       Max     >50_yo 131   3   3   3   3   3   3   3   3   1    1
## 24   24     Sonny  >20-30_yo 129   3   3   3   3   3   3   3   3   3    2
## 25   25    Dianne   18-20_yo 127   2   3   2   2   2   3   3   4   3    3
## 26   26     Jovit     >50_yo 127   1   2   3   4   3   3   3   3   3    2
## 27   27     Jason  >20-30_yo 126   2   2   3   3   3   2   3   2   4    2
## 28   28       Sha     >50_yo 125   3   3   3   3   3   3   2   3   3    3
## 29   29       Kat   18-20_yo 122   3   2   2   3   3   3   2   2   3    2
## 30   30     Sonny   18-20_yo 122   2   3   3   3   2   3   3   2   2    2
## 31   31     Jason  >30-50_yo 121   2   2   3   3   2   3   3   2   3    2
## 32   32       Max  >20-30_yo 120   1   3   3   1   4   2   3   2   3    1
## 33   33     Benna  >20-30_yo 119   2   3   2   3   3   3   3   2   3    3
## 34   34    Dianne  >30-50_yo 115   1   3   3   3   3   3   1   1   3    1
## 35   35     Jovit  >20-30_yo 114   2   3   3   4   2   3   3   3   3    1
## 36   36       Kat  >20-30_yo 114   2   2   2   2   3   3   2   2   3    2
## 37   37      Jolo   18-20_yo 107   1   2   2   2   2   3   2   2   3    2
## 38   38    Dianne  >20-30_yo 106   2   2   3   2   3   4   3   2   1    2
## 39   39     Jason   18-20_yo 104   3   3   3   3   3   2   2   2   2    1
## 40   40     Marco  >30-50_yo 103   1   3   2   2   3   2   3   2   4    3
## 41   41     Benna   18-20_yo 100   3   2   3   1   2   3   3   2   3    1
## 42   42       Nix  >30-50_yo  98   1   1   1   1   1   3   3   3   1    1
## 43   43 Christian     >50_yo  97   2   2   1   3   2   2   3   1   2    3
## 44   44 Christian  >30-50_yo  96   1   1   1   3   2   2   1   2   3    1
## 45   45    Nicole  >30-50_yo  95   1   1   1   3   2   2   2   2   2    2
## 46   46    Nicole  >20-30_yo  93   1   2   2   2   2   2   2   2   2    1
## 47   47     Wency  >20-30_yo  90   2   2   2   2   2   2   2   2   2    2
## 48   48 Christian   18-20_yo  82   2   2   2   2   2   2   2   2   2    2
## 49   49     Sonny     >50_yo  79   2   2   1   1   1   2   1   1   2    1
## 50   50       Max   18-20_yo  79   1   2   2   2   1   2   1   2   1    1
## 51   51   Twinkle  >30-50_yo  65   1   1   1   1   1   1   1   1   5    1
## 52   52       Sha  >20-30_yo  64   2   2   2   1   2   1   1   1   1    1
## 53   53   Twinkle  >20-30_yo  61   1   1   1   1   1   1   1   1   4    1
## 54   54       Kat     >50_yo  57   1   1   1   1   1   1   1   1   5    1
## 55   55   Twinkle   18-20_yo  57   1   1   1   1   1   1   1   1   1    1
## 56   56       Max  >30-50_yo  56   2   1   2   1   1   2   1   1   2    1
## 57   57       Kat  >30-50_yo  55   1   1   1   3   1   1   1   1   1    1
## 58   58     Marco     >50_yo  53   1   1   1   1   1   1   1   1   1    1
## 59   59     Jason     >50_yo  51   1   1   1   1   1   1   1   1   1    1
## 60   60     Sonny  >30-50_yo  45   1   1   1   1   1   1   1   1   1    1
##    S_11 S_12 S_13 S_14 S_15 S_16 S_17 S_18 S_19 S_20 S_21 S_22 S_23 S_24
## 1     5    5    4    5    4    4    4    5    4    4    5    4    4    3
## 2     4    5    4    4    3    3    5    4    3    5    5    5    5    4
## 3     4    5    3    4    4    4    4    4    4    4    4    4    5    4
## 4     4    5    3    4    4    3    4    4    3    4    4    3    5    4
## 5     4    5    3    5    3    5    3    4    3    4    5    3    4    5
## 6     4    4    4    4    4    2    4    4    4    4    4    4    4    4
## 7     4    4    4    4    4    4    4    4    4    4    4    3    4    4
## 8     4    4    3    4    4    4    3    3    4    4    4    4    4    4
## 9     4    4    4    3    3    4    3    4    3    3    4    4    4    4
## 10    4    4    4    4    3    4    2    4    4    4    4    4    4    4
## 11    3    4    4    3    3    3    3    3    3    3    4    4    4    4
## 12    4    5    4    4    3    3    2    3    3    4    4    4    3    4
## 13    3    4    2    2    3    4    3    3    4    3    4    3    3    4
## 14    4    3    4    4    4    3    3    3    3    4    3    3    4    4
## 15    3    3    3    3    3    4    3    4    3    3    3    4    3    3
## 16    3    4    3    3    3    4    4    4    4    3    4    3    4    3
## 17    3    3    2    3    4    4    2    2    2    2    4    3    2    4
## 18    3    3    2    2    3    3    3    4    4    3    3    3    4    2
## 19    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 20    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 21    3    3    1    1    2    4    1    1    4    1    2    3    5    3
## 22    2    4    4    2    2    4    3    2    4    4    2    3    3    2
## 23    3    3    3    3    3    3    1    1    3    3    3    3    3    3
## 24    2    3    2    2    3    3    2    3    3    3    3    3    3    3
## 25    2    2    3    3    2    2    2    3    3    3    3    3    3    3
## 26    3    3    2    3    2    4    3    3    3    4    3    3    3    2
## 27    2    3    3    2    3    2    3    3    3    3    3    2    2    2
## 28    2    3    2    3    3    3    2    2    3    2    3    3    3    3
## 29    3    3    1    3    3    3    3    2    2    1    2    3    3    3
## 30    2    3    3    3    2    2    3    3    3    2    2    2    3    3
## 31    2    3    2    3    3    3    2    2    2    1    2    2    2    2
## 32    1    3    4    3    2    2    1    1    3    3    4    3    2    2
## 33    3    2    1    2    2    3    2    2    3    2    3    2    3    2
## 34    1    3    2    3    2    3    2    1    2    3    2    3    3    1
## 35    2    3    2    3    2    2    3    3    3    4    3    3    2    2
## 36    3    3    1    3    3    3    2    2    2    1    1    1    3    3
## 37    2    2    2    2    2    2    2    1    2    2    3    3    2    3
## 38    2    3    3    3    2    2    1    2    2    2    2    3    3    3
## 39    1    1    2    2    3    2    3    3    3    2    1    1    1    1
## 40    3    3    2    2    2    2    2    2    2    3    2    2    2    2
## 41    1    3    2    2    2    2    3    2    3    1    2    1    3    1
## 42    1    3    3    3    3    1    1    1    1    1    3    1    1    3
## 43    2    2    1    3    2    2    3    2    2    1    2    1    1    1
## 44    1    3    2    1    3    1    1    1    1    1    2    3    1    1
## 45    2    2    2    2    2    2    2    2    3    2    3    2    2    3
## 46    1    2    2    1    2    3    2    2    2    1    1    3    1    2
## 47    2    2    2    2    2    2    2    2    2    2    2    2    2    2
## 48    2    2    2    2    1    1    1    1    1    1    2    3    3    2
## 49    1    2    2    1    3    3    1    1    2    2    2    2    1    1
## 50    1    2    1    1    2    2    2    3    2    3    1    3    2    2
## 51    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 52    1    1    1    1    1    2    1    1    1    1    1    1    1    1
## 53    1    1    2    1    1    1    1    1    1    1    1    1    1    1
## 54    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 55    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 56    1    2    1    1    1    1    1    1    1    1    1    1    1    1
## 57    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 58    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 59    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 60    1    1    1    1    1    1    1    1    1    1    1    1    1    1
##    S_25 S_26 S_27 S_28 S_29 S_30 S_31 S_32 S_33 S_34 S_35 S_36 S_37 S_38
## 1     4    4    5    3    4    4    4    3    5    5    4    4    4    5
## 2     3    4    4    3    4    3    3    5    3    4    4    4    3    5
## 3     5    5    4    3    4    5    4    3    3    5    4    4    4    4
## 4     5    4    4    4    4    3    3    4    3    4    4    4    4    3
## 5     3    4    3    3    5    4    4    3    5    5    5    4    3    5
## 6     4    4    2    4    4    4    2    4    4    4    4    4    4    4
## 7     4    4    4    3    4    3    3    3    3    4    4    4    4    4
## 8     3    4    3    4    4    5    4    2    3    4    3    5    3    3
## 9     5    4    4    3    3    3    3    3    3    4    4    4    3    4
## 10    4    4    4    2    4    5    5    1    4    5    5    4    3    4
## 11    4    4    3    2    4    5    3    3    5    5    3    3    3    4
## 12    4    3    3    1    2    5    4    2    4    4    4    4    4    4
## 13    4    3    3    3    3    4    4    3    4    4    4    4    4    4
## 14    3    4    3    3    3    4    4    2    4    3    4    3    4    4
## 15    3    4    3    3    4    3    3    4    3    4    4    3    4    3
## 16    3    3    3    3    3    3    3    3    4    3    3    3    3    3
## 17    2    4    3    2    2    2    2    2    4    4    4    3    3    3
## 18    3    3    3    3    3    3    3    3    3    3    3    4    3    3
## 19    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 20    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 21    3    3    4    1    3    4    4    2    5    5    4    2    4    2
## 22    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 23    3    3    3    3    3    5    3    3    3    5    3    3    3    3
## 24    3    3    3    3    3    3    3    3    3    3    3    3    3    3
## 25    3    3    3    3    2    4    4    3    5    3    4    2    2    3
## 26    2    3    3    3    3    3    3    3    3    4    2    3    2    3
## 27    4    3    4    3    3    3    3    2    4    4    3    3    3    2
## 28    3    3    3    3    3    4    3    1    4    3    3    3    3    2
## 29    3    3    3    2    3    5    3    3    3    3    3    3    1    3
## 30    3    3    3    3    3    4    3    3    3    4    3    3    3    3
## 31    3    3    3    3    3    4    4    1    3    4    3    3    3    3
## 32    3    3    4    1    4    4    3    1    3    4    4    3    3    2
## 33    3    3    3    2    3    4    3    3    4    2    4    3    3    2
## 34    3    3    3    3    3    4    3    1    5    3    5    3    3    1
## 35    2    2    2    3    2    2    2    3    3    4    2    3    2    3
## 36    3    3    3    2    3    5    3    1    4    3    3    3    3    2
## 37    3    2    2    1    3    4    3    1    4    4    3    3    3    4
## 38    3    3    2    1    2    5    2    1    5    3    3    2    2    3
## 39    3    3    3    3    3    2    4    1    1    4    3    3    3    3
## 40    3    2    2    2    2    2    2    2    3    3    3    3    2    2
## 41    2    2    3    1    1    5    3    1    5    3    2    1    3    2
## 42    3    3    3    1    3    4    3    1    4    1    3    3    3    3
## 43    2    3    2    1    2    4    2    1    1    3    2    3    1    3
## 44    4    4    3    1    2    5    5    1    5    3    3    2    1    2
## 45    2    2    2    2    2    3    2    2    3    3    2    2    2    2
## 46    3    3    3    1    2    5    3    1    4    3    3    2    2    2
## 47    2    2    2    2    2    2    2    2    2    2    2    2    2    2
## 48    2    2    3    1    1    4    1    2    2    1    1    2    1    2
## 49    1    3    3    1    2    5    2    1    5    1    3    1    3    1
## 50    2    3    2    1    2    2    1    2    2    2    1    2    1    2
## 51    1    1    1    1    1    5    1    1    5    3    3    1    1    1
## 52    2    2    2    1    1    5    2    1    5    1    2    2    1    1
## 53    1    1    1    1    1    5    1    1    5    4    1    1    1    1
## 54    1    1    1    1    1    5    1    1    5    1    1    1    1    1
## 55    1    1    1    1    1    1    5    1    5    5    1    1    1    1
## 56    1    1    1    1    1    5    1    1    1    2    1    1    1    1
## 57    1    1    1    1    1    3    1    1    3    3    1    1    1    1
## 58    1    1    1    1    1    5    1    1    5    1    1    1    1    1
## 59    1    1    1    1    1    1    1    1    5    1    1    1    1    1
## 60    1    1    1    1    1    1    1    1    1    1    1    1    1    1
##    S_39 S_40 S_41 S_42 S_43 S_44 S_45  Quartile
## 1     5    5    5    5    4    4    5 Quartile4
## 2     5    4    5    4    5    4    5 Quartile4
## 3     5    5    4    4    4    5    5 Quartile4
## 4     4    3    4    4    3    4    3 Quartile4
## 5     5    4    4    4    3    5    4 Quartile4
## 6     4    4    4    4    4    4    4 Quartile4
## 7     4    4    4    4    3    3    4 Quartile4
## 8     3    5    4    4    3    4    4 Quartile4
## 9     4    4    4    4    3    4    5 Quartile4
## 10    5    4    5    4    3    3    3 Quartile4
## 11    4    4    4    3    3    5    4 Quartile4
## 12    4    3    4    4    3    4    3 Quartile4
## 13    4    3    3    3    3    3    3 Quartile4
## 14    4    3    3    3    2    3    4 Quartile4
## 15    4    3    4    3    2    3    2 Quartile4
## 16    3    4    3    3    3    3    3 Quartile3
## 17    5    3    3    2    3    5    4 Quartile3
## 18    4    3    3    3    2    3    3 Quartile3
## 19    3    3    3    3    3    3    3 Quartile3
## 20    3    3    3    3    3    3    3 Quartile3
## 21    5    5    3    2    3    2    1 Quartile3
## 22    3    3    3    3    3    4    3 Quartile3
## 23    3    3    3    3    3    3    3 Quartile3
## 24    3    2    3    3    3    3    3 Quartile3
## 25    3    2    2    3    3    3    3 Quartile3
## 26    3    2    3    3    3    2    3 Quartile3
## 27    3    4    3    3    2    4    1 Quartile3
## 28    3    3    3    3    2    2    2 Quartile3
## 29    3    4    3    3    3    3    2 Quartile3
## 30    3    2    2    3    2    3    2 Quartile3
## 31    3    5    3    3    3    4    1 Quartile2
## 32    4    3    3    3    3    4    1 Quartile2
## 33    3    2    3    3    2    3    2 Quartile2
## 34    3    3    3    3    2    4    1 Quartile2
## 35    3    2    3    2    2    1    2 Quartile2
## 36    3    2    3    3    3    4    1 Quartile2
## 37    3    2    2    2    2    4    1 Quartile2
## 38    1    2    1    2    1    4    1 Quartile2
## 39    3    5    2    2    1    1    1 Quartile2
## 40    2    3    3    2    2    1    1 Quartile2
## 41    1    1    2    3    3    4    1 Quartile2
## 42    3    3    3    3    1    4    1 Quartile2
## 43    3    4    3    2    3    3    3 Quartile2
## 44    2    4    3    2    2    2    1 Quartile2
## 45    2    2    2    2    2    3    2 Quartile2
## 46    2    1    2    2    1    4    1 Quartile1
## 47    2    2    2    2    2    2    2 Quartile1
## 48    1    2    2    1    2    4    1 Quartile1
## 49    3    1    1    1    1    1    1 Quartile1
## 50    1    2    3    2    2    1    1 Quartile1
## 51    1    5    1    1    1    1    1 Quartile1
## 52    1    1    1    1    1    1    1 Quartile1
## 53    1    1    1    1    1    2    1 Quartile1
## 54    1    1    1    1    1    1    1 Quartile1
## 55    1    1    1    1    1    1    1 Quartile1
## 56    2    1    1    1    1    1    1 Quartile1
## 57    1    1    1    1    3    1    1 Quartile1
## 58    1    1    1    1    1    1    1 Quartile1
## 59    1    3    1    1    1    1    1 Quartile1
## 60    1    1    1    1    1    1    1 Quartile1

######################################
# CREATING THE DATASET CONTAINING Q1 AND Q4 ONLY
######################################
(likert.df.q1q4 <- likert.df[likert.df$Quartile=="Quartile1" | likert.df$Quartile=="Quartile4",])

##    Item   Student Respondent Sum S_1 S_2 S_3 S_4 S_5 S_6 S_7 S_8 S_9 S_10
## 1     1     Jovit   18-20_yo 196   4   4   5   4   5   5   4   5   5    4
## 2     2   Twinkle     >50_yo 191   5   5   5   5   5   5   5   5   4    4
## 3     3     Benna  >30-50_yo 189   5   5   4   4   5   5   4   4   5    2
## 4     4       Sha   18-20_yo 179   5   5   4   5   5   5   4   5   5    4
## 5     5    Nicole   18-20_yo 178   4   4   3   4   4   5   4   4   3    2
## 6     6       Nix   18-20_yo 170   4   4   4   2   4   4   4   4   4    2
## 7     7     Wency     >50_yo 168   4   3   3   4   4   3   3   4   5    3
## 8     8      Jolo  >30-50_yo 167   4   4   3   3   3   4   4   4   4    4
## 9     9     Benna     >50_yo 167   3   4   3   3   4   4   5   5   4    3
## 10   10       Nix     >50_yo 166   4   4   3   3   4   4   3   3   2    2
## 11   11       Nix  >20-30_yo 161   4   4   2   4   4   4   4   4   3    2
## 12   12     Jovit  >30-50_yo 160   4   4   4   3   4   4   4   3   5    2
## 13   13 Christian  >20-30_yo 155   4   4   4   4   3   4   3   4   4    3
## 14   14    Dianne     >50_yo 152   3   3   3   4   3   3   4   4   3    3
## 15   15       Sha  >30-50_yo 150   3   4   4   3   4   5   3   4   3    3
## 46   46    Nicole  >20-30_yo  93   1   2   2   2   2   2   2   2   2    1
## 47   47     Wency  >20-30_yo  90   2   2   2   2   2   2   2   2   2    2
## 48   48 Christian   18-20_yo  82   2   2   2   2   2   2   2   2   2    2
## 49   49     Sonny     >50_yo  79   2   2   1   1   1   2   1   1   2    1
## 50   50       Max   18-20_yo  79   1   2   2   2   1   2   1   2   1    1
## 51   51   Twinkle  >30-50_yo  65   1   1   1   1   1   1   1   1   5    1
## 52   52       Sha  >20-30_yo  64   2   2   2   1   2   1   1   1   1    1
## 53   53   Twinkle  >20-30_yo  61   1   1   1   1   1   1   1   1   4    1
## 54   54       Kat     >50_yo  57   1   1   1   1   1   1   1   1   5    1
## 55   55   Twinkle   18-20_yo  57   1   1   1   1   1   1   1   1   1    1
## 56   56       Max  >30-50_yo  56   2   1   2   1   1   2   1   1   2    1
## 57   57       Kat  >30-50_yo  55   1   1   1   3   1   1   1   1   1    1
## 58   58     Marco     >50_yo  53   1   1   1   1   1   1   1   1   1    1
## 59   59     Jason     >50_yo  51   1   1   1   1   1   1   1   1   1    1
## 60   60     Sonny  >30-50_yo  45   1   1   1   1   1   1   1   1   1    1
##    S_11 S_12 S_13 S_14 S_15 S_16 S_17 S_18 S_19 S_20 S_21 S_22 S_23 S_24
## 1     5    5    4    5    4    4    4    5    4    4    5    4    4    3
## 2     4    5    4    4    3    3    5    4    3    5    5    5    5    4
## 3     4    5    3    4    4    4    4    4    4    4    4    4    5    4
## 4     4    5    3    4    4    3    4    4    3    4    4    3    5    4
## 5     4    5    3    5    3    5    3    4    3    4    5    3    4    5
## 6     4    4    4    4    4    2    4    4    4    4    4    4    4    4
## 7     4    4    4    4    4    4    4    4    4    4    4    3    4    4
## 8     4    4    3    4    4    4    3    3    4    4    4    4    4    4
## 9     4    4    4    3    3    4    3    4    3    3    4    4    4    4
## 10    4    4    4    4    3    4    2    4    4    4    4    4    4    4
## 11    3    4    4    3    3    3    3    3    3    3    4    4    4    4
## 12    4    5    4    4    3    3    2    3    3    4    4    4    3    4
## 13    3    4    2    2    3    4    3    3    4    3    4    3    3    4
## 14    4    3    4    4    4    3    3    3    3    4    3    3    4    4
## 15    3    3    3    3    3    4    3    4    3    3    3    4    3    3
## 46    1    2    2    1    2    3    2    2    2    1    1    3    1    2
## 47    2    2    2    2    2    2    2    2    2    2    2    2    2    2
## 48    2    2    2    2    1    1    1    1    1    1    2    3    3    2
## 49    1    2    2    1    3    3    1    1    2    2    2    2    1    1
## 50    1    2    1    1    2    2    2    3    2    3    1    3    2    2
## 51    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 52    1    1    1    1    1    2    1    1    1    1    1    1    1    1
## 53    1    1    2    1    1    1    1    1    1    1    1    1    1    1
## 54    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 55    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 56    1    2    1    1    1    1    1    1    1    1    1    1    1    1
## 57    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 58    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 59    1    1    1    1    1    1    1    1    1    1    1    1    1    1
## 60    1    1    1    1    1    1    1    1    1    1    1    1    1    1
##    S_25 S_26 S_27 S_28 S_29 S_30 S_31 S_32 S_33 S_34 S_35 S_36 S_37 S_38
## 1     4    4    5    3    4    4    4    3    5    5    4    4    4    5
## 2     3    4    4    3    4    3    3    5    3    4    4    4    3    5
## 3     5    5    4    3    4    5    4    3    3    5    4    4    4    4
## 4     5    4    4    4    4    3    3    4    3    4    4    4    4    3
## 5     3    4    3    3    5    4    4    3    5    5    5    4    3    5
## 6     4    4    2    4    4    4    2    4    4    4    4    4    4    4
## 7     4    4    4    3    4    3    3    3    3    4    4    4    4    4
## 8     3    4    3    4    4    5    4    2    3    4    3    5    3    3
## 9     5    4    4    3    3    3    3    3    3    4    4    4    3    4
## 10    4    4    4    2    4    5    5    1    4    5    5    4    3    4
## 11    4    4    3    2    4    5    3    3    5    5    3    3    3    4
## 12    4    3    3    1    2    5    4    2    4    4    4    4    4    4
## 13    4    3    3    3    3    4    4    3    4    4    4    4    4    4
## 14    3    4    3    3    3    4    4    2    4    3    4    3    4    4
## 15    3    4    3    3    4    3    3    4    3    4    4    3    4    3
## 46    3    3    3    1    2    5    3    1    4    3    3    2    2    2
## 47    2    2    2    2    2    2    2    2    2    2    2    2    2    2
## 48    2    2    3    1    1    4    1    2    2    1    1    2    1    2
## 49    1    3    3    1    2    5    2    1    5    1    3    1    3    1
## 50    2    3    2    1    2    2    1    2    2    2    1    2    1    2
## 51    1    1    1    1    1    5    1    1    5    3    3    1    1    1
## 52    2    2    2    1    1    5    2    1    5    1    2    2    1    1
## 53    1    1    1    1    1    5    1    1    5    4    1    1    1    1
## 54    1    1    1    1    1    5    1    1    5    1    1    1    1    1
## 55    1    1    1    1    1    1    5    1    5    5    1    1    1    1
## 56    1    1    1    1    1    5    1    1    1    2    1    1    1    1
## 57    1    1    1    1    1    3    1    1    3    3    1    1    1    1
## 58    1    1    1    1    1    5    1    1    5    1    1    1    1    1
## 59    1    1    1    1    1    1    1    1    5    1    1    1    1    1
## 60    1    1    1    1    1    1    1    1    1    1    1    1    1    1
##    S_39 S_40 S_41 S_42 S_43 S_44 S_45  Quartile
## 1     5    5    5    5    4    4    5 Quartile4
## 2     5    4    5    4    5    4    5 Quartile4
## 3     5    5    4    4    4    5    5 Quartile4
## 4     4    3    4    4    3    4    3 Quartile4
## 5     5    4    4    4    3    5    4 Quartile4
## 6     4    4    4    4    4    4    4 Quartile4
## 7     4    4    4    4    3    3    4 Quartile4
## 8     3    5    4    4    3    4    4 Quartile4
## 9     4    4    4    4    3    4    5 Quartile4
## 10    5    4    5    4    3    3    3 Quartile4
## 11    4    4    4    3    3    5    4 Quartile4
## 12    4    3    4    4    3    4    3 Quartile4
## 13    4    3    3    3    3    3    3 Quartile4
## 14    4    3    3    3    2    3    4 Quartile4
## 15    4    3    4    3    2    3    2 Quartile4
## 46    2    1    2    2    1    4    1 Quartile1
## 47    2    2    2    2    2    2    2 Quartile1
## 48    1    2    2    1    2    4    1 Quartile1
## 49    3    1    1    1    1    1    1 Quartile1
## 50    1    2    3    2    2    1    1 Quartile1
## 51    1    5    1    1    1    1    1 Quartile1
## 52    1    1    1    1    1    1    1 Quartile1
## 53    1    1    1    1    1    2    1 Quartile1
## 54    1    1    1    1    1    1    1 Quartile1
## 55    1    1    1    1    1    1    1 Quartile1
## 56    2    1    1    1    1    1    1 Quartile1
## 57    1    1    1    1    3    1    1 Quartile1
## 58    1    1    1    1    1    1    1 Quartile1
## 59    1    3    1    1    1    1    1 Quartile1
## 60    1    1    1    1    1    1    1 Quartile1

DATA ANALYSIS

######################################
# CONDUCTING THE MEDIAN TEST
######################################

######################################
# TESTING FOR THE MEDIAN TEST ASSUMPTIONS
# ASSUMPTION 1 : INDEPENDENCE OF OBSERVATIONS
# ASSUMPTION 2 : AT LEAST ORDINAL MEASURES
######################################

######################################
# TRYING THE BASE MEDIAN TEST FUNCTION
######################################
likert.df.q1q4.mediantest<-with(
  likert.df.q1q4,Median.test(S_45,Quartile,
  console=FALSE,
  correct=TRUE,
  group=FALSE))

likert.df.q1q4.mediantest$comparison

##                         median chisq pvalue signif.
## Quartile1 and Quartile4      2 26.25      0     ***

likert.df.q1q4.mediantest$medians

##           Median  r Min Max Q25 Q75
## Quartile1      1 15   1   2   1 1.0
## Quartile4      4 15   2   5   3 4.5

######################################
# TRYING MANUAL MEDIAN TEST
######################################

likert.df.q1q4.s1 <- likert.df.q1q4[,c(5,50)]
likert.df.q1q4.s1$MedianGroup <- ifelse(likert.df.q1q4.s1$S_1>median(likert.df.q1q4.s1$S_1),"high","low")
likert.df.q1q4.s1$Quartile <- factor(likert.df.q1q4.s1$Quartile)
likert.df.q1q4.s1.table <- table(likert.df.q1q4.s1$Quartile,
                                 likert.df.q1q4.s1$MedianGroup)
likert.df.q1q4.s1.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s1.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s1.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s2 <- likert.df.q1q4[,c(6,50)]
likert.df.q1q4.s2$MedianGroup <- ifelse(likert.df.q1q4.s2$S_2>median(likert.df.q1q4.s2$S_2),"high","low")
likert.df.q1q4.s2$Quartile <- factor(likert.df.q1q4.s2$Quartile)
likert.df.q1q4.s2.table <- table(likert.df.q1q4.s2$Quartile,
                                 likert.df.q1q4.s2$MedianGroup)
likert.df.q1q4.s2.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s2.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s2.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s3 <- likert.df.q1q4[,c(7,50)]
likert.df.q1q4.s3$MedianGroup <- ifelse(likert.df.q1q4.s3$S_3>median(likert.df.q1q4.s3$S_3),"high","low")
likert.df.q1q4.s3$Quartile <- factor(likert.df.q1q4.s3$Quartile)
likert.df.q1q4.s3.table <- table(likert.df.q1q4.s3$Quartile,
                                 likert.df.q1q4.s3$MedianGroup)
likert.df.q1q4.s3.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   14   1

chisq.test(likert.df.q1q4.s3.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s3.table
## X-squared = 22.634, df = 1, p-value = 1.96e-06

likert.df.q1q4.s4 <- likert.df.q1q4[,c(8,50)]
likert.df.q1q4.s4$MedianGroup <- ifelse(likert.df.q1q4.s4$S_4>median(likert.df.q1q4.s4$S_4),"high","low")
likert.df.q1q4.s4$Quartile <- factor(likert.df.q1q4.s4$Quartile)
likert.df.q1q4.s4.table <- table(likert.df.q1q4.s4$Quartile,
                                 likert.df.q1q4.s4$MedianGroup)
likert.df.q1q4.s4.table

##            
##             high low
##   Quartile1    1  14
##   Quartile4   14   1

chisq.test(likert.df.q1q4.s4.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s4.table
## X-squared = 19.2, df = 1, p-value = 1.177e-05

likert.df.q1q4.s5 <- likert.df.q1q4[,c(9,50)]
likert.df.q1q4.s5$MedianGroup <- ifelse(likert.df.q1q4.s5$S_5>median(likert.df.q1q4.s5$S_5),"high","low")
likert.df.q1q4.s5$Quartile <- factor(likert.df.q1q4.s5$Quartile)
likert.df.q1q4.s5.table <- table(likert.df.q1q4.s5$Quartile,
                                 likert.df.q1q4.s5$MedianGroup)
likert.df.q1q4.s5.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s5.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s5.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s6 <- likert.df.q1q4[,c(10,50)]
likert.df.q1q4.s6$MedianGroup <- ifelse(likert.df.q1q4.s6$S_6>median(likert.df.q1q4.s6$S_6),"high","low")
likert.df.q1q4.s6$Quartile <- factor(likert.df.q1q4.s6$Quartile)
likert.df.q1q4.s6.table <- table(likert.df.q1q4.s6$Quartile,
                                 likert.df.q1q4.s6$MedianGroup)
likert.df.q1q4.s6.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s6.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s6.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s7 <- likert.df.q1q4[,c(11,50)]
likert.df.q1q4.s7$MedianGroup <- ifelse(likert.df.q1q4.s7$S_7>median(likert.df.q1q4.s7$S_7),"high","low")
likert.df.q1q4.s7$Quartile <- factor(likert.df.q1q4.s7$Quartile)
likert.df.q1q4.s7.table <- table(likert.df.q1q4.s7$Quartile,
                                 likert.df.q1q4.s7$MedianGroup)
likert.df.q1q4.s7.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s7.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s7.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s8 <- likert.df.q1q4[,c(12,50)]
likert.df.q1q4.s8$MedianGroup <- ifelse(likert.df.q1q4.s8$S_8>median(likert.df.q1q4.s8$S_8),"high","low")
likert.df.q1q4.s8$Quartile <- factor(likert.df.q1q4.s8$Quartile)
likert.df.q1q4.s8.table <- table(likert.df.q1q4.s8$Quartile,
                                 likert.df.q1q4.s8$MedianGroup)
likert.df.q1q4.s8.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s8.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s8.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s9 <- likert.df.q1q4[,c(13,50)]
likert.df.q1q4.s9$MedianGroup <- ifelse(likert.df.q1q4.s9$S_9>median(likert.df.q1q4.s9$S_9),"high","low")
likert.df.q1q4.s9$Quartile <- factor(likert.df.q1q4.s9$Quartile)
likert.df.q1q4.s9.table <- table(likert.df.q1q4.s9$Quartile,
                                 likert.df.q1q4.s9$MedianGroup)
likert.df.q1q4.s9.table

##            
##             high low
##   Quartile1    3  12
##   Quartile4   10   5

chisq.test(likert.df.q1q4.s9.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s9.table
## X-squared = 4.8869, df = 1, p-value = 0.02706

likert.df.q1q4.s10 <- likert.df.q1q4[,c(14,50)]
likert.df.q1q4.s10$MedianGroup <- ifelse(likert.df.q1q4.s10$S_10>median(likert.df.q1q4.s10$S_10),"high","low")
likert.df.q1q4.s10$Quartile <- factor(likert.df.q1q4.s10$Quartile)
likert.df.q1q4.s10.table <- table(likert.df.q1q4.s10$Quartile,
                                  likert.df.q1q4.s10$MedianGroup)
likert.df.q1q4.s10.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4    9   6

chisq.test(likert.df.q1q4.s10.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s10.table
## X-squared = 10.159, df = 1, p-value = 0.001436

fisher.test(likert.df.q1q4.s10.table)

## 
##  Fisher's Exact Test for Count Data
## 
## data:  likert.df.q1q4.s10.table
## p-value = 0.0006997
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.0000000 0.2994113
## sample estimates:
## odds ratio 
##          0

likert.df.q1q4.s11 <- likert.df.q1q4[,c(15,50)]
likert.df.q1q4.s11$MedianGroup <- ifelse(likert.df.q1q4.s11$S_11>median(likert.df.q1q4.s11$S_11),"high","low")
likert.df.q1q4.s11$Quartile <- factor(likert.df.q1q4.s11$Quartile)
likert.df.q1q4.s11.table <- table(likert.df.q1q4.s11$Quartile,
                                  likert.df.q1q4.s11$MedianGroup)
likert.df.q1q4.s11.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s11.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s11.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s12 <- likert.df.q1q4[,c(16,50)]
likert.df.q1q4.s12$MedianGroup <- ifelse(likert.df.q1q4.s12$S_12>median(likert.df.q1q4.s12$S_12),"high","low")
likert.df.q1q4.s12$Quartile <- factor(likert.df.q1q4.s12$Quartile)
likert.df.q1q4.s12.table <- table(likert.df.q1q4.s12$Quartile,
                                  likert.df.q1q4.s12$MedianGroup)
likert.df.q1q4.s12.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s12.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s12.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s13 <- likert.df.q1q4[,c(17,50)]
likert.df.q1q4.s13$MedianGroup <- ifelse(likert.df.q1q4.s13$S_13>median(likert.df.q1q4.s13$S_13),"high","low")
likert.df.q1q4.s13$Quartile <- factor(likert.df.q1q4.s13$Quartile)
likert.df.q1q4.s13.table <- table(likert.df.q1q4.s13$Quartile,
                                  likert.df.q1q4.s13$MedianGroup)
likert.df.q1q4.s13.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   14   1

chisq.test(likert.df.q1q4.s13.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s13.table
## X-squared = 22.634, df = 1, p-value = 1.96e-06

likert.df.q1q4.s14 <- likert.df.q1q4[,c(18,50)]
likert.df.q1q4.s14$MedianGroup <- ifelse(likert.df.q1q4.s14$S_14>median(likert.df.q1q4.s14$S_14),"high","low")
likert.df.q1q4.s14$Quartile <- factor(likert.df.q1q4.s14$Quartile)
likert.df.q1q4.s14.table <- table(likert.df.q1q4.s14$Quartile,
                                  likert.df.q1q4.s14$MedianGroup)
likert.df.q1q4.s14.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   14   1

chisq.test(likert.df.q1q4.s14.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s14.table
## X-squared = 22.634, df = 1, p-value = 1.96e-06

likert.df.q1q4.s15 <- likert.df.q1q4[,c(19,50)]
likert.df.q1q4.s15$MedianGroup <- ifelse(likert.df.q1q4.s15$S_15>median(likert.df.q1q4.s15$S_15),"high","low")
likert.df.q1q4.s15$Quartile <- factor(likert.df.q1q4.s15$Quartile)
likert.df.q1q4.s15.table <- table(likert.df.q1q4.s15$Quartile,
                                  likert.df.q1q4.s15$MedianGroup)
likert.df.q1q4.s15.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4    7   8

chisq.test(likert.df.q1q4.s15.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s15.table
## X-squared = 6.7081, df = 1, p-value = 0.009598

fisher.test(likert.df.q1q4.s15.table)

## 
##  Fisher's Exact Test for Count Data
## 
## data:  likert.df.q1q4.s15.table
## p-value = 0.006322
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.0000000 0.5054614
## sample estimates:
## odds ratio 
##          0

likert.df.q1q4.s16 <- likert.df.q1q4[,c(20,50)]
likert.df.q1q4.s16$MedianGroup <- ifelse(likert.df.q1q4.s16$S_16>median(likert.df.q1q4.s16$S_16),"high","low")
likert.df.q1q4.s16$Quartile <- factor(likert.df.q1q4.s16$Quartile)
likert.df.q1q4.s16.table <- table(likert.df.q1q4.s16$Quartile,
                                  likert.df.q1q4.s16$MedianGroup)
likert.df.q1q4.s16.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4    9   6

chisq.test(likert.df.q1q4.s16.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s16.table
## X-squared = 10.159, df = 1, p-value = 0.001436

fisher.test(likert.df.q1q4.s16.table)

## 
##  Fisher's Exact Test for Count Data
## 
## data:  likert.df.q1q4.s16.table
## p-value = 0.0006997
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.0000000 0.2994113
## sample estimates:
## odds ratio 
##          0

likert.df.q1q4.s17 <- likert.df.q1q4[,c(21,50)]
likert.df.q1q4.s17$MedianGroup <- ifelse(likert.df.q1q4.s17$S_17>median(likert.df.q1q4.s17$S_17),"high","low")
likert.df.q1q4.s17$Quartile <- factor(likert.df.q1q4.s17$Quartile)
likert.df.q1q4.s17.table <- table(likert.df.q1q4.s17$Quartile,
                                  likert.df.q1q4.s17$MedianGroup)
likert.df.q1q4.s17.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   13   2

chisq.test(likert.df.q1q4.s17.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s17.table
## X-squared = 19.548, df = 1, p-value = 9.813e-06

likert.df.q1q4.s18 <- likert.df.q1q4[,c(22,50)]
likert.df.q1q4.s18$MedianGroup <- ifelse(likert.df.q1q4.s18$S_18>median(likert.df.q1q4.s18$S_18),"high","low")
likert.df.q1q4.s18$Quartile <- factor(likert.df.q1q4.s18$Quartile)
likert.df.q1q4.s18.table <- table(likert.df.q1q4.s18$Quartile,
                                  likert.df.q1q4.s18$MedianGroup)
likert.df.q1q4.s18.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   10   5

chisq.test(likert.df.q1q4.s18.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s18.table
## X-squared = 12.15, df = 1, p-value = 0.0004909

likert.df.q1q4.s19 <- likert.df.q1q4[,c(23,50)]
likert.df.q1q4.s19$MedianGroup <- ifelse(likert.df.q1q4.s19$S_19>median(likert.df.q1q4.s19$S_19),"high","low")
likert.df.q1q4.s19$Quartile <- factor(likert.df.q1q4.s19$Quartile)
likert.df.q1q4.s19.table <- table(likert.df.q1q4.s19$Quartile,
                                  likert.df.q1q4.s19$MedianGroup)
likert.df.q1q4.s19.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s19.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s19.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s20 <- likert.df.q1q4[,c(24,50)]
likert.df.q1q4.s20$MedianGroup <- ifelse(likert.df.q1q4.s20$S_20>median(likert.df.q1q4.s20$S_20),"high","low")
likert.df.q1q4.s20$Quartile <- factor(likert.df.q1q4.s20$Quartile)
likert.df.q1q4.s20.table <- table(likert.df.q1q4.s20$Quartile,
                                  likert.df.q1q4.s20$MedianGroup)
likert.df.q1q4.s20.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   11   4

chisq.test(likert.df.q1q4.s20.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s20.table
## X-squared = 14.354, df = 1, p-value = 0.0001515

likert.df.q1q4.s21 <- likert.df.q1q4[,c(25,50)]
likert.df.q1q4.s21$MedianGroup <- ifelse(likert.df.q1q4.s21$S_21>median(likert.df.q1q4.s21$S_21),"high","low")
likert.df.q1q4.s21$Quartile <- factor(likert.df.q1q4.s21$Quartile)
likert.df.q1q4.s21.table <- table(likert.df.q1q4.s21$Quartile,
                                  likert.df.q1q4.s21$MedianGroup)
likert.df.q1q4.s21.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s21.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s21.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s22 <- likert.df.q1q4[,c(26,50)]
likert.df.q1q4.s22$MedianGroup <- ifelse(likert.df.q1q4.s22$S_22>median(likert.df.q1q4.s22$S_22),"high","low")
likert.df.q1q4.s22$Quartile <- factor(likert.df.q1q4.s22$Quartile)
likert.df.q1q4.s22.table <- table(likert.df.q1q4.s22$Quartile,
                                  likert.df.q1q4.s22$MedianGroup)
likert.df.q1q4.s22.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   10   5

chisq.test(likert.df.q1q4.s22.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s22.table
## X-squared = 12.15, df = 1, p-value = 0.0004909

likert.df.q1q4.s23 <- likert.df.q1q4[,c(27,50)]
likert.df.q1q4.s23$MedianGroup <- ifelse(likert.df.q1q4.s23$S_23>median(likert.df.q1q4.s23$S_23),"high","low")
likert.df.q1q4.s23$Quartile <- factor(likert.df.q1q4.s23$Quartile)
likert.df.q1q4.s23.table <- table(likert.df.q1q4.s23$Quartile,
                                  likert.df.q1q4.s23$MedianGroup)
likert.df.q1q4.s23.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   12   3

chisq.test(likert.df.q1q4.s23.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s23.table
## X-squared = 16.806, df = 1, p-value = 4.141e-05

likert.df.q1q4.s24 <- likert.df.q1q4[,c(28,50)]
likert.df.q1q4.s24$MedianGroup <- ifelse(likert.df.q1q4.s24$S_24>median(likert.df.q1q4.s24$S_24),"high","low")
likert.df.q1q4.s24$Quartile <- factor(likert.df.q1q4.s24$Quartile)
likert.df.q1q4.s24.table <- table(likert.df.q1q4.s24$Quartile,
                                  likert.df.q1q4.s24$MedianGroup)
likert.df.q1q4.s24.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s24.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s24.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s25 <- likert.df.q1q4[,c(29,50)]
likert.df.q1q4.s25$MedianGroup <- ifelse(likert.df.q1q4.s25$S_25>median(likert.df.q1q4.s25$S_25),"high","low")
likert.df.q1q4.s25$Quartile <- factor(likert.df.q1q4.s25$Quartile)
likert.df.q1q4.s25.table <- table(likert.df.q1q4.s25$Quartile,
                                  likert.df.q1q4.s25$MedianGroup)
likert.df.q1q4.s25.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   10   5

chisq.test(likert.df.q1q4.s25.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s25.table
## X-squared = 12.15, df = 1, p-value = 0.0004909

likert.df.q1q4.s26 <- likert.df.q1q4[,c(30,50)]
likert.df.q1q4.s26$MedianGroup <- ifelse(likert.df.q1q4.s26$S_26>median(likert.df.q1q4.s26$S_26),"high","low")
likert.df.q1q4.s26$Quartile <- factor(likert.df.q1q4.s26$Quartile)
likert.df.q1q4.s26.table <- table(likert.df.q1q4.s26$Quartile,
                                  likert.df.q1q4.s26$MedianGroup)
likert.df.q1q4.s26.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   13   2

chisq.test(likert.df.q1q4.s26.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s26.table
## X-squared = 19.548, df = 1, p-value = 9.813e-06

likert.df.q1q4.s27 <- likert.df.q1q4[,c(31,50)]
likert.df.q1q4.s27$MedianGroup <- ifelse(likert.df.q1q4.s27$S_27>median(likert.df.q1q4.s27$S_27),"high","low")
likert.df.q1q4.s27$Quartile <- factor(likert.df.q1q4.s27$Quartile)
likert.df.q1q4.s27.table <- table(likert.df.q1q4.s27$Quartile,
                                  likert.df.q1q4.s27$MedianGroup)
likert.df.q1q4.s27.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4    7   8

chisq.test(likert.df.q1q4.s27.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s27.table
## X-squared = 6.7081, df = 1, p-value = 0.009598

fisher.test(likert.df.q1q4.s27.table)

## 
##  Fisher's Exact Test for Count Data
## 
## data:  likert.df.q1q4.s27.table
## p-value = 0.006322
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.0000000 0.5054614
## sample estimates:
## odds ratio 
##          0

likert.df.q1q4.s28 <- likert.df.q1q4[,c(32,50)]
likert.df.q1q4.s28$MedianGroup <- ifelse(likert.df.q1q4.s28$S_28>median(likert.df.q1q4.s28$S_28),"high","low")
likert.df.q1q4.s28$Quartile <- factor(likert.df.q1q4.s28$Quartile)
likert.df.q1q4.s28.table <- table(likert.df.q1q4.s28$Quartile,
                                  likert.df.q1q4.s28$MedianGroup)
likert.df.q1q4.s28.table

##            
##             high low
##   Quartile1    1  14
##   Quartile4   14   1

chisq.test(likert.df.q1q4.s28.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s28.table
## X-squared = 19.2, df = 1, p-value = 1.177e-05

likert.df.q1q4.s29 <- likert.df.q1q4[,c(33,50)]
likert.df.q1q4.s29$MedianGroup <- ifelse(likert.df.q1q4.s29$S_29>median(likert.df.q1q4.s29$S_29),"high","low")
likert.df.q1q4.s29$Quartile <- factor(likert.df.q1q4.s29$Quartile)
likert.df.q1q4.s29.table <- table(likert.df.q1q4.s29$Quartile,
                                  likert.df.q1q4.s29$MedianGroup)
likert.df.q1q4.s29.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   14   1

chisq.test(likert.df.q1q4.s29.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s29.table
## X-squared = 22.634, df = 1, p-value = 1.96e-06

likert.df.q1q4.s30 <- likert.df.q1q4[,c(34,50)]
likert.df.q1q4.s30$MedianGroup <- ifelse(likert.df.q1q4.s30$S_30>median(likert.df.q1q4.s30$S_30),"high","low")
likert.df.q1q4.s30$Quartile <- factor(likert.df.q1q4.s30$Quartile)
likert.df.q1q4.s30.table <- table(likert.df.q1q4.s30$Quartile,
                                  likert.df.q1q4.s30$MedianGroup)
likert.df.q1q4.s30.table

##            
##             high low
##   Quartile1    8   7
##   Quartile4    5  10

chisq.test(likert.df.q1q4.s30.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s30.table
## X-squared = 0.54299, df = 1, p-value = 0.4612

likert.df.q1q4.s31 <- likert.df.q1q4[,c(35,50)]
likert.df.q1q4.s31$MedianGroup <- ifelse(likert.df.q1q4.s31$S_31>median(likert.df.q1q4.s31$S_31),"high","low")
likert.df.q1q4.s31$Quartile <- factor(likert.df.q1q4.s31$Quartile)
likert.df.q1q4.s31.table <- table(likert.df.q1q4.s31$Quartile,
                                  likert.df.q1q4.s31$MedianGroup)
likert.df.q1q4.s31.table

##            
##             high low
##   Quartile1    1  14
##   Quartile4    8   7

chisq.test(likert.df.q1q4.s31.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s31.table
## X-squared = 5.7143, df = 1, p-value = 0.01683

fisher.test(likert.df.q1q4.s31.table)

## 
##  Fisher's Exact Test for Count Data
## 
## data:  likert.df.q1q4.s31.table
## p-value = 0.01419
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.001323691 0.678290071
## sample estimates:
## odds ratio 
## 0.06892393

likert.df.q1q4.s32 <- likert.df.q1q4[,c(36,50)]
likert.df.q1q4.s32$MedianGroup <- ifelse(likert.df.q1q4.s32$S_32>median(likert.df.q1q4.s32$S_32),"high","low")
likert.df.q1q4.s32$Quartile <- factor(likert.df.q1q4.s32$Quartile)
likert.df.q1q4.s32.table <- table(likert.df.q1q4.s32$Quartile,
                                  likert.df.q1q4.s32$MedianGroup)
likert.df.q1q4.s32.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   11   4

chisq.test(likert.df.q1q4.s32.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s32.table
## X-squared = 14.354, df = 1, p-value = 0.0001515

likert.df.q1q4.s33 <- likert.df.q1q4[,c(37,50)]
likert.df.q1q4.s33$MedianGroup <- ifelse(likert.df.q1q4.s33$S_33>median(likert.df.q1q4.s33$S_33),"high","low")
likert.df.q1q4.s33$Quartile <- factor(likert.df.q1q4.s33$Quartile)
likert.df.q1q4.s33.table <- table(likert.df.q1q4.s33$Quartile,
                                  likert.df.q1q4.s33$MedianGroup)
likert.df.q1q4.s33.table

##            
##             high low
##   Quartile1    8   7
##   Quartile4    3  12

chisq.test(likert.df.q1q4.s33.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s33.table
## X-squared = 2.2967, df = 1, p-value = 0.1297

likert.df.q1q4.s34 <- likert.df.q1q4[,c(38,50)]
likert.df.q1q4.s34$MedianGroup <- ifelse(likert.df.q1q4.s34$S_34>median(likert.df.q1q4.s34$S_34),"high","low")
likert.df.q1q4.s34$Quartile <- factor(likert.df.q1q4.s34$Quartile)
likert.df.q1q4.s34.table <- table(likert.df.q1q4.s34$Quartile,
                                  likert.df.q1q4.s34$MedianGroup)
likert.df.q1q4.s34.table

##            
##             high low
##   Quartile1    1  14
##   Quartile4    5  10

chisq.test(likert.df.q1q4.s34.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s34.table
## X-squared = 1.875, df = 1, p-value = 0.1709

fisher.test(likert.df.q1q4.s34.table)

## 
##  Fisher's Exact Test for Count Data
## 
## data:  likert.df.q1q4.s34.table
## p-value = 0.1686
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.002829566 1.661668864
## sample estimates:
## odds ratio 
##  0.1519383

likert.df.q1q4.s35 <- likert.df.q1q4[,c(39,50)]
likert.df.q1q4.s35$MedianGroup <- ifelse(likert.df.q1q4.s35$S_35>median(likert.df.q1q4.s35$S_35),"high","low")
likert.df.q1q4.s35$Quartile <- factor(likert.df.q1q4.s35$Quartile)
likert.df.q1q4.s35.table <- table(likert.df.q1q4.s35$Quartile,
                                  likert.df.q1q4.s35$MedianGroup)
likert.df.q1q4.s35.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   13   2

chisq.test(likert.df.q1q4.s35.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s35.table
## X-squared = 19.548, df = 1, p-value = 9.813e-06

likert.df.q1q4.s36 <- likert.df.q1q4[,c(40,50)]
likert.df.q1q4.s36$MedianGroup <- ifelse(likert.df.q1q4.s36$S_36>median(likert.df.q1q4.s36$S_36),"high","low")
likert.df.q1q4.s36$Quartile <- factor(likert.df.q1q4.s36$Quartile)
likert.df.q1q4.s36.table <- table(likert.df.q1q4.s36$Quartile,
                                  likert.df.q1q4.s36$MedianGroup)
likert.df.q1q4.s36.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s36.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s36.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s37 <- likert.df.q1q4[,c(41,50)]
likert.df.q1q4.s37$MedianGroup <- ifelse(likert.df.q1q4.s37$S_37>median(likert.df.q1q4.s37$S_37),"high","low")
likert.df.q1q4.s37$Quartile <- factor(likert.df.q1q4.s37$Quartile)
likert.df.q1q4.s37.table <- table(likert.df.q1q4.s37$Quartile,
                                  likert.df.q1q4.s37$MedianGroup)
likert.df.q1q4.s37.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4    9   6

chisq.test(likert.df.q1q4.s37.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s37.table
## X-squared = 10.159, df = 1, p-value = 0.001436

fisher.test(likert.df.q1q4.s37.table)

## 
##  Fisher's Exact Test for Count Data
## 
## data:  likert.df.q1q4.s37.table
## p-value = 0.0006997
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.0000000 0.2994113
## sample estimates:
## odds ratio 
##          0

likert.df.q1q4.s38 <- likert.df.q1q4[,c(42,50)]
likert.df.q1q4.s38$MedianGroup <- ifelse(likert.df.q1q4.s38$S_38>median(likert.df.q1q4.s38$S_38),"high","low")
likert.df.q1q4.s38$Quartile <- factor(likert.df.q1q4.s38$Quartile)
likert.df.q1q4.s38.table <- table(likert.df.q1q4.s38$Quartile,
                                  likert.df.q1q4.s38$MedianGroup)
likert.df.q1q4.s38.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s38.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s38.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s39 <- likert.df.q1q4[,c(43,50)]
likert.df.q1q4.s39$MedianGroup <- ifelse(likert.df.q1q4.s39$S_39>median(likert.df.q1q4.s39$S_39),"high","low")
likert.df.q1q4.s39$Quartile <- factor(likert.df.q1q4.s39$Quartile)
likert.df.q1q4.s39.table <- table(likert.df.q1q4.s39$Quartile,
                                  likert.df.q1q4.s39$MedianGroup)
likert.df.q1q4.s39.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   14   1

chisq.test(likert.df.q1q4.s39.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s39.table
## X-squared = 22.634, df = 1, p-value = 1.96e-06

likert.df.q1q4.s40 <- likert.df.q1q4[,c(44,50)]
likert.df.q1q4.s40$MedianGroup <- ifelse(likert.df.q1q4.s40$S_40>median(likert.df.q1q4.s40$S_40),"high","low")
likert.df.q1q4.s40$Quartile <- factor(likert.df.q1q4.s40$Quartile)
likert.df.q1q4.s40.table <- table(likert.df.q1q4.s40$Quartile,
                                  likert.df.q1q4.s40$MedianGroup)
likert.df.q1q4.s40.table

##            
##             high low
##   Quartile1    1  14
##   Quartile4   10   5

chisq.test(likert.df.q1q4.s40.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s40.table
## X-squared = 9.1866, df = 1, p-value = 0.002438

likert.df.q1q4.s41 <- likert.df.q1q4[,c(45,50)]
likert.df.q1q4.s41$MedianGroup <- ifelse(likert.df.q1q4.s41$S_41>median(likert.df.q1q4.s41$S_41),"high","low")
likert.df.q1q4.s41$Quartile <- factor(likert.df.q1q4.s41$Quartile)
likert.df.q1q4.s41.table <- table(likert.df.q1q4.s41$Quartile,
                                  likert.df.q1q4.s41$MedianGroup)
likert.df.q1q4.s41.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   13   2

chisq.test(likert.df.q1q4.s41.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s41.table
## X-squared = 19.548, df = 1, p-value = 9.813e-06

likert.df.q1q4.s42 <- likert.df.q1q4[,c(46,50)]
likert.df.q1q4.s42$MedianGroup <- ifelse(likert.df.q1q4.s42$S_42>median(likert.df.q1q4.s42$S_42),"high","low")
likert.df.q1q4.s42$Quartile <- factor(likert.df.q1q4.s42$Quartile)
likert.df.q1q4.s42.table <- table(likert.df.q1q4.s42$Quartile,
                                  likert.df.q1q4.s42$MedianGroup)
likert.df.q1q4.s42.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   15   0

chisq.test(likert.df.q1q4.s42.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s42.table
## X-squared = 26.133, df = 1, p-value = 3.186e-07

likert.df.q1q4.s43 <- likert.df.q1q4[,c(47,50)]
likert.df.q1q4.s43$MedianGroup <- ifelse(likert.df.q1q4.s43$S_43>median(likert.df.q1q4.s43$S_43),"high","low")
likert.df.q1q4.s43$Quartile <- factor(likert.df.q1q4.s43$Quartile)
likert.df.q1q4.s43.table <- table(likert.df.q1q4.s43$Quartile,
                                  likert.df.q1q4.s43$MedianGroup)
likert.df.q1q4.s43.table

##            
##             high low
##   Quartile1    1  14
##   Quartile4   13   2

chisq.test(likert.df.q1q4.s43.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s43.table
## X-squared = 16.205, df = 1, p-value = 5.683e-05

likert.df.q1q4.s44 <- likert.df.q1q4[,c(48,50)]
likert.df.q1q4.s44$MedianGroup <- ifelse(likert.df.q1q4.s44$S_44>median(likert.df.q1q4.s44$S_44),"high","low")
likert.df.q1q4.s44$Quartile <- factor(likert.df.q1q4.s44$Quartile)
likert.df.q1q4.s44.table <- table(likert.df.q1q4.s44$Quartile,
                                  likert.df.q1q4.s44$MedianGroup)
likert.df.q1q4.s44.table

##            
##             high low
##   Quartile1    2  13
##   Quartile4   10   5

chisq.test(likert.df.q1q4.s44.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s44.table
## X-squared = 6.8056, df = 1, p-value = 0.009087

likert.df.q1q4.s45 <- likert.df.q1q4[,c(49,50)]
likert.df.q1q4.s45$MedianGroup <- ifelse(likert.df.q1q4.s45$S_45>median(likert.df.q1q4.s45$S_45),"high","low")
likert.df.q1q4.s45$Quartile <- factor(likert.df.q1q4.s45$Quartile)
likert.df.q1q4.s45.table <- table(likert.df.q1q4.s45$Quartile,
                                  likert.df.q1q4.s45$MedianGroup)
likert.df.q1q4.s45.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4   14   1

chisq.test(likert.df.q1q4.s45.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s45.table
## X-squared = 22.634, df = 1, p-value = 1.96e-06

likert.df.q1q4.s27 <- likert.df.q1q4[,c(31,50)]
likert.df.q1q4.s27$MedianGroup <- ifelse(likert.df.q1q4.s27$S_27>median(likert.df.q1q4.s27$S_27),"high","low")
likert.df.q1q4.s27$Quartile <- factor(likert.df.q1q4.s27$Quartile)
likert.df.q1q4.s27.table <- table(likert.df.q1q4.s27$Quartile,
                                  likert.df.q1q4.s27$MedianGroup)
likert.df.q1q4.s27.table

##            
##             high low
##   Quartile1    0  15
##   Quartile4    7   8

chisq.test(likert.df.q1q4.s27.table)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  likert.df.q1q4.s27.table
## X-squared = 6.7081, df = 1, p-value = 0.009598

fisher.test(likert.df.q1q4.s27.table)

## 
##  Fisher's Exact Test for Count Data
## 
## data:  likert.df.q1q4.s27.table
## p-value = 0.006322
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.0000000 0.5054614
## sample estimates:
## odds ratio 
##          0

######################################
# LOOPING THE MEDIAN TEST FOR ALL VARIABLES
######################################
for(column_no in c(1:45)){
  likert.df.q1q4.mediantest<-with(likert.df.q1q4,
                                  Median.test(as.numeric(unlist(likert.df.q1q4[column_no+4])),
                                              Quartile,
                                              correct=TRUE,
                                              console=FALSE,
                                              group=FALSE))
  median_name <- (paste0("likert.df.q1q4.mediantest.median_S", column_no)) 
  comparison_name <- (paste0("likert.df.q1q4.mediantest.comparison_S", column_no))
  likert.df.q1q4.mediantest.median <- likert.df.q1q4.mediantest$medians
  likert.df.q1q4.mediantest.comparison <- likert.df.q1q4.mediantest$comparison
  assign(median_name,likert.df.q1q4.mediantest.median)
  assign(comparison_name,likert.df.q1q4.mediantest.comparison)
}

######################################
# CONSOLIDATING THE RESULTS 
######################################

######################################
# CONSOLIDATING THE VARIABLE NAMES 
######################################
column_name <- c()
for(column_no in c(1:45)){
  column_name[column_no] <- (paste0("S_", column_no)) 
}
column_name

##  [1] "S_1"  "S_2"  "S_3"  "S_4"  "S_5"  "S_6"  "S_7"  "S_8"  "S_9"  "S_10"
## [11] "S_11" "S_12" "S_13" "S_14" "S_15" "S_16" "S_17" "S_18" "S_19" "S_20"
## [21] "S_21" "S_22" "S_23" "S_24" "S_25" "S_26" "S_27" "S_28" "S_29" "S_30"
## [31] "S_31" "S_32" "S_33" "S_34" "S_35" "S_36" "S_37" "S_38" "S_39" "S_40"
## [41] "S_41" "S_42" "S_43" "S_44" "S_45"

######################################
# CONSOLIDATING THE Q1 MEDIAN PER VARIABLE
######################################
q1median_percolumn <- c()
for(column_no in c(1:45)){
  q1median_column_name <- (paste0("likert.df.q1q4.mediantest.median_S", column_no))
  q1median_column_name <- eval(as.name(paste(q1median_column_name)))
  q1median_percolumn[column_no] <- q1median_column_name[[1]][1] 
}
q1median_percolumn

##  [1] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 5 2 1
## [36] 1 1 1 1 1 1 1 1 1 1

######################################
# CONSOLIDATING THE Q4 MEDIAN PER VARIABLE
######################################
q4median_percolumn <- c()
for(column_no in c(1:45)){
  q4median_column_name <- (paste0("likert.df.q1q4.mediantest.median_S", column_no))
  q4median_column_name <- eval(as.name(paste(q4median_column_name)))
  q4median_percolumn[column_no] <- q4median_column_name[[1]][2] 
}
q4median_percolumn

##  [1] 4 4 4 4 4 4 4 4 4 3 4 4 4 4 3 4 3 4 3 4 4 4 4 4 4 4 3 3 4 4 4 3 4 4 4
## [36] 4 4 4 4 4 4 4 3 4 4

######################################
# CONSOLIDATING THE Q1+Q4 MEDIAN PER VARIABLE
######################################
allmedian_percolumn <- c()
for(column_no in c(1:45)){
  allmedian_column_name <- (paste0("likert.df.q1q4.mediantest.comparison_S", column_no))
  allmedian_column_name <- eval(as.name(paste(allmedian_column_name)))
  allmedian_percolumn[column_no] <- allmedian_column_name[[1]] 
}
allmedian_percolumn

##  [1] 2.5 2.5 2.0 2.5 2.5 2.5 2.5 2.5 3.0 2.0 2.5 2.5 2.0 2.0 3.0 3.0 2.0
## [18] 3.0 2.5 3.0 2.5 3.0 3.0 2.5 3.0 3.0 3.0 1.5 2.0 4.0 3.0 2.0 4.0 4.0
## [35] 3.0 2.5 3.0 2.5 3.0 3.0 3.0 2.5 2.0 3.0 2.0

######################################
# CONSOLIDATING THE CHI-SQUARE TEST STATISTIC PER VARIABLE 
######################################
chisquare_percolumn <- c()
for(column_no in c(1:45)){
  chisquare_column_name <- (paste0("likert.df.q1q4.mediantest.comparison_S", column_no))
  chisquare_column_name <- eval(as.name(paste(chisquare_column_name)))
  chisquare_percolumn[column_no] <- chisquare_column_name[[2]] 
}
chisquare_percolumn

##  [1] 30.000000 30.000000 26.250000 22.533333 30.000000 30.000000 30.000000
##  [8] 30.000000  6.651584 12.857143 30.000000 30.000000 26.250000 26.250000
## [15]  9.130435 12.857143 22.941176 15.000000 30.000000 17.368421 30.000000
## [22] 15.000000 20.000000 30.000000 15.000000 22.941176  9.130435 22.533333
## [29] 26.250000  1.221719  7.777778 17.368421  3.588517  3.333333 22.941176
## [36] 30.000000 12.857143 30.000000 26.250000 11.626794 22.941176 30.000000
## [43] 19.285714  8.888889 26.250000

######################################
# CONSOLIDATING THE P-VALUE PER VARIABLE 
######################################
pvalue_percolumn <- c()
for(column_no in c(1:45)){
  pvalue_column_name <- (paste0("likert.df.q1q4.mediantest.comparison_S", column_no))
  pvalue_column_name <- eval(as.name(paste(pvalue_column_name)))
  pvalue_percolumn[column_no] <- pvalue_column_name[[3]] 
}
pvalue_percolumn

##  [1] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0099 0.0003
## [11] 0.0000 0.0000 0.0000 0.0000 0.0025 0.0003 0.0000 0.0001 0.0000 0.0000
## [21] 0.0000 0.0001 0.0000 0.0000 0.0001 0.0000 0.0025 0.0000 0.0000 0.2690
## [31] 0.0053 0.0000 0.0582 0.0679 0.0000 0.0000 0.0003 0.0000 0.0000 0.0007
## [41] 0.0000 0.0000 0.0000 0.0029 0.0000

######################################
# COLLATING ALL DATA
######################################
likert.df.results <- cbind(column_name,
                           q1median_percolumn,
                           q4median_percolumn,
                           allmedian_percolumn,
                           chisquare_percolumn,
                           pvalue_percolumn)

######################################
# TRANSFORMING DATA TYPES AND FORMATS
######################################

likert.df.results <- as.data.frame(likert.df.results)
likert.df.results$q1median_percolumn <- as.numeric(as.character(q1median_percolumn))
likert.df.results$q4median_percolumn <- as.numeric(as.character(q4median_percolumn))
likert.df.results$allmedian_percolumn <- as.numeric(as.character(allmedian_percolumn))
likert.df.results$chisquare_percolumn <- as.numeric(as.character(chisquare_percolumn))
likert.df.results$pvalue_percolumn <- as.numeric(as.character(pvalue_percolumn))

summary(likert.df.results)

##   column_name q1median_percolumn q4median_percolumn allmedian_percolumn
##  S_1    : 1   Min.   :1.000      Min.   :3.000      Min.   :1.500      
##  S_10   : 1   1st Qu.:1.000      1st Qu.:4.000      1st Qu.:2.500      
##  S_11   : 1   Median :1.000      Median :4.000      Median :2.500      
##  S_12   : 1   Mean   :1.222      Mean   :3.822      Mean   :2.667      
##  S_13   : 1   3rd Qu.:1.000      3rd Qu.:4.000      3rd Qu.:3.000      
##  S_14   : 1   Max.   :5.000      Max.   :4.000      Max.   :4.000      
##  (Other):39                                                            
##  chisquare_percolumn pvalue_percolumn  
##  Min.   : 1.222      Min.   :0.000000  
##  1st Qu.:12.857      1st Qu.:0.000000  
##  Median :22.941      Median :0.000000  
##  Mean   :20.739      Mean   :0.009336  
##  3rd Qu.:30.000      3rd Qu.:0.000300  
##  Max.   :30.000      Max.   :0.269000  
## 

colnames(likert.df.results) <- c("Statements",
                                 "Q1_Median",
                                 "Q4_Median",
                                 "Q1Q4_Median",
                                 "ChiSquare_TestStat",
                                 "P_Value")

summary(likert.df.results)

##    Statements   Q1_Median       Q4_Median      Q1Q4_Median   
##  S_1    : 1   Min.   :1.000   Min.   :3.000   Min.   :1.500  
##  S_10   : 1   1st Qu.:1.000   1st Qu.:4.000   1st Qu.:2.500  
##  S_11   : 1   Median :1.000   Median :4.000   Median :2.500  
##  S_12   : 1   Mean   :1.222   Mean   :3.822   Mean   :2.667  
##  S_13   : 1   3rd Qu.:1.000   3rd Qu.:4.000   3rd Qu.:3.000  
##  S_14   : 1   Max.   :5.000   Max.   :4.000   Max.   :4.000  
##  (Other):39                                                  
##  ChiSquare_TestStat    P_Value        
##  Min.   : 1.222     Min.   :0.000000  
##  1st Qu.:12.857     1st Qu.:0.000000  
##  Median :22.941     Median :0.000000  
##  Mean   :20.739     Mean   :0.009336  
##  3rd Qu.:30.000     3rd Qu.:0.000300  
##  Max.   :30.000     Max.   :0.269000  
## 

######################################
# EVALUATING THE P-VALUES
######################################
likert.df.results$Classification <- ifelse(likert.df.results$P_Value<0.05,
                                           "Include",
                                           "Exclude")

likert.df.results.table <- table(likert.df.results$Classification)
likert.df.results.table

## 
## Exclude Include 
##       3      42

prop.table(likert.df.results.table)

## 
##    Exclude    Include 
## 0.06666667 0.93333333

######################################
# FORMATTING THE FINAL OUTPUT
######################################
gc()

##           used  (Mb) gc trigger  (Mb) max used  (Mb)
## Ncells 2055109 109.8    4167531 222.6  4167531 222.6
## Vcells 3559393  27.2    8388608  64.0  6402443  48.9

likert.df.results$Q1_Median <- format(likert.df.results$Q1_Median,nsmall=2)
likert.df.results$Q4_Median <- format(likert.df.results$Q4_Median,nsmall=2)
likert.df.results$Q1Q4_Median <- format(likert.df.results$Q1Q4_Median,nsmall=2)
likert.df.results$ChiSquare_TestStat <- format(round(likert.df.results$ChiSquare_TestStat,digits=2),nsmall=2)
likert.df.results$P_Value <- format(likert.df.results$P_Value,nsmall=5)

######################################
# VIEWING THE FINAL OUTPUT
######################################
(likert.df.results)

##    Statements Q1_Median Q4_Median Q1Q4_Median ChiSquare_TestStat P_Value
## 1         S_1      1.00      4.00        2.50              30.00 0.00000
## 2         S_2      1.00      4.00        2.50              30.00 0.00000
## 3         S_3      1.00      4.00        2.00              26.25 0.00000
## 4         S_4      1.00      4.00        2.50              22.53 0.00000
## 5         S_5      1.00      4.00        2.50              30.00 0.00000
## 6         S_6      1.00      4.00        2.50              30.00 0.00000
## 7         S_7      1.00      4.00        2.50              30.00 0.00000
## 8         S_8      1.00      4.00        2.50              30.00 0.00000
## 9         S_9      2.00      4.00        3.00               6.65 0.00990
## 10       S_10      1.00      3.00        2.00              12.86 0.00030
## 11       S_11      1.00      4.00        2.50              30.00 0.00000
## 12       S_12      1.00      4.00        2.50              30.00 0.00000
## 13       S_13      1.00      4.00        2.00              26.25 0.00000
## 14       S_14      1.00      4.00        2.00              26.25 0.00000
## 15       S_15      1.00      3.00        3.00               9.13 0.00250
## 16       S_16      1.00      4.00        3.00              12.86 0.00030
## 17       S_17      1.00      3.00        2.00              22.94 0.00000
## 18       S_18      1.00      4.00        3.00              15.00 0.00010
## 19       S_19      1.00      3.00        2.50              30.00 0.00000
## 20       S_20      1.00      4.00        3.00              17.37 0.00000
## 21       S_21      1.00      4.00        2.50              30.00 0.00000
## 22       S_22      1.00      4.00        3.00              15.00 0.00010
## 23       S_23      1.00      4.00        3.00              20.00 0.00000
## 24       S_24      1.00      4.00        2.50              30.00 0.00000
## 25       S_25      1.00      4.00        3.00              15.00 0.00010
## 26       S_26      1.00      4.00        3.00              22.94 0.00000
## 27       S_27      1.00      3.00        3.00               9.13 0.00250
## 28       S_28      1.00      3.00        1.50              22.53 0.00000
## 29       S_29      1.00      4.00        2.00              26.25 0.00000
## 30       S_30      5.00      4.00        4.00               1.22 0.26900
## 31       S_31      1.00      4.00        3.00               7.78 0.00530
## 32       S_32      1.00      3.00        2.00              17.37 0.00000
## 33       S_33      5.00      4.00        4.00               3.59 0.05820
## 34       S_34      2.00      4.00        4.00               3.33 0.06790
## 35       S_35      1.00      4.00        3.00              22.94 0.00000
## 36       S_36      1.00      4.00        2.50              30.00 0.00000
## 37       S_37      1.00      4.00        3.00              12.86 0.00030
## 38       S_38      1.00      4.00        2.50              30.00 0.00000
## 39       S_39      1.00      4.00        3.00              26.25 0.00000
## 40       S_40      1.00      4.00        3.00              11.63 0.00070
## 41       S_41      1.00      4.00        3.00              22.94 0.00000
## 42       S_42      1.00      4.00        2.50              30.00 0.00000
## 43       S_43      1.00      3.00        2.00              19.29 0.00000
## 44       S_44      1.00      4.00        3.00               8.89 0.00290
## 45       S_45      1.00      4.00        2.00              26.25 0.00000
##    Classification
## 1         Include
## 2         Include
## 3         Include
## 4         Include
## 5         Include
## 6         Include
## 7         Include
## 8         Include
## 9         Include
## 10        Include
## 11        Include
## 12        Include
## 13        Include
## 14        Include
## 15        Include
## 16        Include
## 17        Include
## 18        Include
## 19        Include
## 20        Include
## 21        Include
## 22        Include
## 23        Include
## 24        Include
## 25        Include
## 26        Include
## 27        Include
## 28        Include
## 29        Include
## 30        Exclude
## 31        Include
## 32        Include
## 33        Exclude
## 34        Exclude
## 35        Include
## 36        Include
## 37        Include
## 38        Include
## 39        Include
## 40        Include
## 41        Include
## 42        Include
## 43        Include
## 44        Include
## 45        Include

######################################
# MEDIAN TEST SUMMARY
######################################
cat("Number of statements to be excluded is equal to", 
  nrow(likert.df.results[likert.df.results$Classification=="Exclude",]))

## Number of statements to be excluded is equal to 3

cat("Statements ",
  rownames(likert.df.results[likert.df.results$Classification=="Exclude",]),
  " should be excluded\n")

## Statements  30 33 34  should be excluded

######################################
# CONDUCTING STATEMENT PAIRWISE CORRELATIONS
# ASSUMPTION 1 : AT LEAST ORDINAL MEASURES
# ASSUMPTION 2 : MONOTONIC RELATIONSHIP BETWEEN VARIABLES
######################################
likert.df.results.include <- likert.df.results[likert.df.results$Classification=="Include",]
dim(likert.df.results.include)

## [1] 42  7

likert.df.results.include$Statements

##  [1] S_1  S_2  S_3  S_4  S_5  S_6  S_7  S_8  S_9  S_10 S_11 S_12 S_13 S_14
## [15] S_15 S_16 S_17 S_18 S_19 S_20 S_21 S_22 S_23 S_24 S_25 S_26 S_27 S_28
## [29] S_29 S_31 S_32 S_35 S_36 S_37 S_38 S_39 S_40 S_41 S_42 S_43 S_44 S_45
## 45 Levels: S_1 S_10 S_11 S_12 S_13 S_14 S_15 S_16 S_17 S_18 S_19 ... S_9

likert.df.s1s45 <- likert.df[,5:49]
likert.df.s1s45.include <- likert.df.s1s45[,names(likert.df.s1s45) %in% likert.df.results.include$Statements]
names(likert.df.s1s45.include)

##  [1] "S_1"  "S_2"  "S_3"  "S_4"  "S_5"  "S_6"  "S_7"  "S_8"  "S_9"  "S_10"
## [11] "S_11" "S_12" "S_13" "S_14" "S_15" "S_16" "S_17" "S_18" "S_19" "S_20"
## [21] "S_21" "S_22" "S_23" "S_24" "S_25" "S_26" "S_27" "S_28" "S_29" "S_31"
## [31] "S_32" "S_35" "S_36" "S_37" "S_38" "S_39" "S_40" "S_41" "S_42" "S_43"
## [41] "S_44" "S_45"

(spearmanrankcorr_values <- rcorr(as.matrix(likert.df.s1s45.include,type="spearman")))

##       S_1  S_2  S_3  S_4  S_5  S_6  S_7  S_8  S_9 S_10 S_11 S_12 S_13 S_14
## S_1  1.00 0.85 0.76 0.65 0.78 0.80 0.74 0.78 0.51 0.61 0.79 0.78 0.56 0.67
## S_2  0.85 1.00 0.82 0.68 0.88 0.85 0.81 0.83 0.54 0.66 0.80 0.82 0.65 0.72
## S_3  0.76 0.82 1.00 0.67 0.82 0.80 0.74 0.75 0.47 0.57 0.70 0.78 0.65 0.73
## S_4  0.65 0.68 0.67 1.00 0.73 0.71 0.65 0.71 0.39 0.62 0.72 0.69 0.46 0.68
## S_5  0.78 0.88 0.82 0.73 1.00 0.84 0.79 0.79 0.55 0.64 0.83 0.84 0.68 0.79
## S_6  0.80 0.85 0.80 0.71 0.84 1.00 0.81 0.84 0.46 0.63 0.81 0.87 0.61 0.80
## S_7  0.74 0.81 0.74 0.65 0.79 0.81 1.00 0.86 0.48 0.70 0.82 0.83 0.76 0.80
## S_8  0.78 0.83 0.75 0.71 0.79 0.84 0.86 1.00 0.51 0.72 0.83 0.82 0.74 0.75
## S_9  0.51 0.54 0.47 0.39 0.55 0.46 0.48 0.51 1.00 0.49 0.55 0.57 0.38 0.39
## S_10 0.61 0.66 0.57 0.62 0.64 0.63 0.70 0.72 0.49 1.00 0.78 0.59 0.45 0.62
## S_11 0.79 0.80 0.70 0.72 0.83 0.81 0.82 0.83 0.55 0.78 1.00 0.81 0.62 0.81
## S_12 0.78 0.82 0.78 0.69 0.84 0.87 0.83 0.82 0.57 0.59 0.81 1.00 0.74 0.81
## S_13 0.56 0.65 0.65 0.46 0.68 0.61 0.76 0.74 0.38 0.45 0.62 0.74 1.00 0.73
## S_14 0.67 0.72 0.73 0.68 0.79 0.80 0.80 0.75 0.39 0.62 0.81 0.81 0.73 1.00
## S_15 0.74 0.69 0.68 0.68 0.74 0.75 0.70 0.76 0.44 0.58 0.74 0.77 0.63 0.75
## S_16 0.70 0.75 0.67 0.66 0.72 0.76 0.64 0.69 0.45 0.56 0.74 0.73 0.48 0.63
## S_17 0.68 0.70 0.72 0.75 0.72 0.67 0.72 0.72 0.52 0.66 0.70 0.70 0.55 0.68
## S_18 0.70 0.75 0.74 0.72 0.76 0.74 0.74 0.80 0.45 0.67 0.77 0.72 0.63 0.72
## S_19 0.72 0.80 0.72 0.60 0.74 0.70 0.74 0.74 0.52 0.59 0.72 0.73 0.63 0.63
## S_20 0.62 0.78 0.75 0.67 0.73 0.66 0.72 0.77 0.46 0.56 0.73 0.76 0.76 0.73
## S_21 0.72 0.78 0.72 0.70 0.82 0.82 0.83 0.84 0.49 0.64 0.80 0.84 0.76 0.81
## S_22 0.65 0.79 0.72 0.64 0.76 0.78 0.70 0.79 0.43 0.56 0.72 0.78 0.71 0.65
## S_23 0.80 0.84 0.71 0.66 0.82 0.84 0.78 0.82 0.54 0.68 0.84 0.82 0.60 0.72
## S_24 0.75 0.75 0.64 0.65 0.74 0.83 0.79 0.84 0.40 0.62 0.84 0.79 0.67 0.78
## S_25 0.64 0.75 0.65 0.61 0.81 0.73 0.73 0.75 0.50 0.55 0.69 0.80 0.68 0.65
## S_26 0.71 0.78 0.68 0.69 0.79 0.81 0.74 0.78 0.38 0.56 0.71 0.80 0.68 0.74
## S_27 0.64 0.72 0.68 0.59 0.77 0.70 0.69 0.70 0.45 0.54 0.62 0.75 0.64 0.64
## S_28 0.59 0.68 0.70 0.70 0.63 0.60 0.63 0.71 0.42 0.63 0.65 0.61 0.53 0.66
## S_29 0.65 0.78 0.67 0.65 0.82 0.78 0.73 0.75 0.42 0.57 0.72 0.78 0.67 0.78
## S_31 0.46 0.52 0.43 0.44 0.53 0.54 0.49 0.51 0.28 0.35 0.46 0.55 0.45 0.49
## S_32 0.64 0.71 0.65 0.67 0.65 0.66 0.69 0.77 0.43 0.63 0.70 0.63 0.51 0.54
## S_35 0.61 0.76 0.64 0.54 0.76 0.75 0.65 0.65 0.49 0.49 0.65 0.72 0.63 0.69
## S_36 0.69 0.81 0.75 0.72 0.81 0.77 0.80 0.77 0.47 0.69 0.81 0.82 0.65 0.82
## S_37 0.71 0.78 0.75 0.54 0.74 0.77 0.73 0.73 0.52 0.53 0.68 0.74 0.67 0.66
## S_38 0.72 0.74 0.72 0.71 0.75 0.81 0.85 0.84 0.39 0.62 0.81 0.80 0.73 0.82
## S_39 0.76 0.83 0.71 0.68 0.80 0.81 0.76 0.76 0.51 0.56 0.77 0.78 0.62 0.74
## S_40 0.56 0.55 0.45 0.51 0.60 0.53 0.55 0.52 0.52 0.43 0.56 0.57 0.43 0.55
## S_41 0.71 0.81 0.72 0.72 0.84 0.81 0.79 0.82 0.51 0.64 0.82 0.87 0.67 0.80
## S_42 0.71 0.79 0.77 0.66 0.84 0.82 0.83 0.83 0.51 0.65 0.81 0.89 0.75 0.87
## S_43 0.70 0.71 0.67 0.65 0.73 0.69 0.73 0.70 0.49 0.58 0.73 0.76 0.53 0.69
## S_44 0.53 0.55 0.57 0.45 0.63 0.69 0.70 0.58 0.34 0.42 0.54 0.71 0.62 0.68
## S_45 0.77 0.74 0.66 0.71 0.72 0.70 0.79 0.83 0.45 0.67 0.84 0.73 0.66 0.75
##      S_15 S_16 S_17 S_18 S_19 S_20 S_21 S_22 S_23 S_24 S_25 S_26 S_27 S_28
## S_1  0.74 0.70 0.68 0.70 0.72 0.62 0.72 0.65 0.80 0.75 0.64 0.71 0.64 0.59
## S_2  0.69 0.75 0.70 0.75 0.80 0.78 0.78 0.79 0.84 0.75 0.75 0.78 0.72 0.68
## S_3  0.68 0.67 0.72 0.74 0.72 0.75 0.72 0.72 0.71 0.64 0.65 0.68 0.68 0.70
## S_4  0.68 0.66 0.75 0.72 0.60 0.67 0.70 0.64 0.66 0.65 0.61 0.69 0.59 0.70
## S_5  0.74 0.72 0.72 0.76 0.74 0.73 0.82 0.76 0.82 0.74 0.81 0.79 0.77 0.63
## S_6  0.75 0.76 0.67 0.74 0.70 0.66 0.82 0.78 0.84 0.83 0.73 0.81 0.70 0.60
## S_7  0.70 0.64 0.72 0.74 0.74 0.72 0.83 0.70 0.78 0.79 0.73 0.74 0.69 0.63
## S_8  0.76 0.69 0.72 0.80 0.74 0.77 0.84 0.79 0.82 0.84 0.75 0.78 0.70 0.71
## S_9  0.44 0.45 0.52 0.45 0.52 0.46 0.49 0.43 0.54 0.40 0.50 0.38 0.45 0.42
## S_10 0.58 0.56 0.66 0.67 0.59 0.56 0.64 0.56 0.68 0.62 0.55 0.56 0.54 0.63
## S_11 0.74 0.74 0.70 0.77 0.72 0.73 0.80 0.72 0.84 0.84 0.69 0.71 0.62 0.65
## S_12 0.77 0.73 0.70 0.72 0.73 0.76 0.84 0.78 0.82 0.79 0.80 0.80 0.75 0.61
## S_13 0.63 0.48 0.55 0.63 0.63 0.76 0.76 0.71 0.60 0.67 0.68 0.68 0.64 0.53
## S_14 0.75 0.63 0.68 0.72 0.63 0.73 0.81 0.65 0.72 0.78 0.65 0.74 0.64 0.66
## S_15 1.00 0.68 0.67 0.70 0.68 0.63 0.74 0.64 0.64 0.74 0.75 0.88 0.73 0.69
## S_16 0.68 1.00 0.60 0.65 0.77 0.63 0.67 0.67 0.72 0.69 0.59 0.75 0.71 0.61
## S_17 0.67 0.60 1.00 0.86 0.72 0.71 0.65 0.57 0.68 0.57 0.60 0.65 0.56 0.75
## S_18 0.70 0.65 0.86 1.00 0.76 0.77 0.71 0.65 0.71 0.67 0.66 0.70 0.59 0.73
## S_19 0.68 0.77 0.72 0.76 1.00 0.75 0.72 0.67 0.79 0.65 0.68 0.69 0.70 0.72
## S_20 0.63 0.63 0.71 0.77 0.75 1.00 0.78 0.77 0.70 0.66 0.59 0.65 0.56 0.72
## S_21 0.74 0.67 0.65 0.71 0.72 0.78 1.00 0.77 0.73 0.82 0.69 0.74 0.69 0.60
## S_22 0.64 0.67 0.57 0.65 0.67 0.77 0.77 1.00 0.76 0.74 0.69 0.77 0.66 0.54
## S_23 0.64 0.72 0.68 0.71 0.79 0.70 0.73 0.76 1.00 0.78 0.70 0.71 0.70 0.65
## S_24 0.74 0.69 0.57 0.67 0.65 0.66 0.82 0.74 0.78 1.00 0.71 0.74 0.59 0.57
## S_25 0.75 0.59 0.60 0.66 0.68 0.59 0.69 0.69 0.70 0.71 1.00 0.82 0.79 0.59
## S_26 0.88 0.75 0.65 0.70 0.69 0.65 0.74 0.77 0.71 0.74 0.82 1.00 0.82 0.61
## S_27 0.73 0.71 0.56 0.59 0.70 0.56 0.69 0.66 0.70 0.59 0.79 0.82 1.00 0.52
## S_28 0.69 0.61 0.75 0.73 0.72 0.72 0.60 0.54 0.65 0.57 0.59 0.61 0.52 1.00
## S_29 0.78 0.74 0.67 0.69 0.75 0.71 0.78 0.70 0.74 0.75 0.76 0.84 0.75 0.71
## S_31 0.58 0.55 0.36 0.42 0.56 0.39 0.49 0.46 0.47 0.46 0.65 0.63 0.65 0.42
## S_32 0.51 0.54 0.74 0.73 0.64 0.71 0.66 0.67 0.71 0.62 0.51 0.55 0.47 0.71
## S_35 0.71 0.72 0.48 0.54 0.65 0.60 0.71 0.65 0.65 0.68 0.76 0.79 0.75 0.54
## S_36 0.79 0.72 0.72 0.74 0.75 0.76 0.81 0.72 0.71 0.77 0.81 0.80 0.71 0.74
## S_37 0.79 0.71 0.59 0.61 0.80 0.64 0.71 0.59 0.71 0.70 0.73 0.72 0.74 0.63
## S_38 0.73 0.65 0.73 0.78 0.69 0.72 0.82 0.73 0.70 0.83 0.72 0.76 0.64 0.58
## S_39 0.77 0.78 0.61 0.66 0.74 0.67 0.82 0.70 0.71 0.75 0.70 0.81 0.78 0.58
## S_40 0.62 0.49 0.50 0.48 0.53 0.40 0.52 0.48 0.51 0.47 0.61 0.63 0.56 0.48
## S_41 0.78 0.72 0.71 0.75 0.72 0.75 0.82 0.79 0.76 0.74 0.79 0.84 0.78 0.62
## S_42 0.80 0.72 0.75 0.79 0.79 0.75 0.82 0.72 0.80 0.76 0.83 0.81 0.79 0.72
## S_43 0.60 0.61 0.68 0.61 0.67 0.62 0.72 0.67 0.74 0.64 0.59 0.64 0.63 0.55
## S_44 0.59 0.54 0.48 0.43 0.47 0.40 0.66 0.58 0.60 0.67 0.66 0.68 0.64 0.38
## S_45 0.69 0.68 0.74 0.77 0.67 0.75 0.81 0.70 0.72 0.75 0.57 0.70 0.53 0.66
##      S_29 S_31 S_32 S_35 S_36 S_37 S_38 S_39 S_40 S_41 S_42 S_43 S_44 S_45
## S_1  0.65 0.46 0.64 0.61 0.69 0.71 0.72 0.76 0.56 0.71 0.71 0.70 0.53 0.77
## S_2  0.78 0.52 0.71 0.76 0.81 0.78 0.74 0.83 0.55 0.81 0.79 0.71 0.55 0.74
## S_3  0.67 0.43 0.65 0.64 0.75 0.75 0.72 0.71 0.45 0.72 0.77 0.67 0.57 0.66
## S_4  0.65 0.44 0.67 0.54 0.72 0.54 0.71 0.68 0.51 0.72 0.66 0.65 0.45 0.71
## S_5  0.82 0.53 0.65 0.76 0.81 0.74 0.75 0.80 0.60 0.84 0.84 0.73 0.63 0.72
## S_6  0.78 0.54 0.66 0.75 0.77 0.77 0.81 0.81 0.53 0.81 0.82 0.69 0.69 0.70
## S_7  0.73 0.49 0.69 0.65 0.80 0.73 0.85 0.76 0.55 0.79 0.83 0.73 0.70 0.79
## S_8  0.75 0.51 0.77 0.65 0.77 0.73 0.84 0.76 0.52 0.82 0.83 0.70 0.58 0.83
## S_9  0.42 0.28 0.43 0.49 0.47 0.52 0.39 0.51 0.52 0.51 0.51 0.49 0.34 0.45
## S_10 0.57 0.35 0.63 0.49 0.69 0.53 0.62 0.56 0.43 0.64 0.65 0.58 0.42 0.67
## S_11 0.72 0.46 0.70 0.65 0.81 0.68 0.81 0.77 0.56 0.82 0.81 0.73 0.54 0.84
## S_12 0.78 0.55 0.63 0.72 0.82 0.74 0.80 0.78 0.57 0.87 0.89 0.76 0.71 0.73
## S_13 0.67 0.45 0.51 0.63 0.65 0.67 0.73 0.62 0.43 0.67 0.75 0.53 0.62 0.66
## S_14 0.78 0.49 0.54 0.69 0.82 0.66 0.82 0.74 0.55 0.80 0.87 0.69 0.68 0.75
## S_15 0.78 0.58 0.51 0.71 0.79 0.79 0.73 0.77 0.62 0.78 0.80 0.60 0.59 0.69
## S_16 0.74 0.55 0.54 0.72 0.72 0.71 0.65 0.78 0.49 0.72 0.72 0.61 0.54 0.68
## S_17 0.67 0.36 0.74 0.48 0.72 0.59 0.73 0.61 0.50 0.71 0.75 0.68 0.48 0.74
## S_18 0.69 0.42 0.73 0.54 0.74 0.61 0.78 0.66 0.48 0.75 0.79 0.61 0.43 0.77
## S_19 0.75 0.56 0.64 0.65 0.75 0.80 0.69 0.74 0.53 0.72 0.79 0.67 0.47 0.67
## S_20 0.71 0.39 0.71 0.60 0.76 0.64 0.72 0.67 0.40 0.75 0.75 0.62 0.40 0.75
## S_21 0.78 0.49 0.66 0.71 0.81 0.71 0.82 0.82 0.52 0.82 0.82 0.72 0.66 0.81
## S_22 0.70 0.46 0.67 0.65 0.72 0.59 0.73 0.70 0.48 0.79 0.72 0.67 0.58 0.70
## S_23 0.74 0.47 0.71 0.65 0.71 0.71 0.70 0.71 0.51 0.76 0.80 0.74 0.60 0.72
## S_24 0.75 0.46 0.62 0.68 0.77 0.70 0.83 0.75 0.47 0.74 0.76 0.64 0.67 0.75
## S_25 0.76 0.65 0.51 0.76 0.81 0.73 0.72 0.70 0.61 0.79 0.83 0.59 0.66 0.57
## S_26 0.84 0.63 0.55 0.79 0.80 0.72 0.76 0.81 0.63 0.84 0.81 0.64 0.68 0.70
## S_27 0.75 0.65 0.47 0.75 0.71 0.74 0.64 0.78 0.56 0.78 0.79 0.63 0.64 0.53
## S_28 0.71 0.42 0.71 0.54 0.74 0.63 0.58 0.58 0.48 0.62 0.72 0.55 0.38 0.66
## S_29 1.00 0.60 0.60 0.78 0.85 0.77 0.76 0.84 0.64 0.84 0.86 0.64 0.63 0.63
## S_31 0.60 1.00 0.22 0.65 0.57 0.58 0.55 0.60 0.49 0.57 0.63 0.42 0.42 0.38
## S_32 0.60 0.22 1.00 0.43 0.60 0.50 0.64 0.57 0.32 0.63 0.62 0.65 0.37 0.72
## S_35 0.78 0.65 0.43 1.00 0.73 0.79 0.65 0.83 0.59 0.72 0.76 0.53 0.62 0.54
## S_36 0.85 0.57 0.60 0.73 1.00 0.72 0.82 0.80 0.64 0.88 0.87 0.67 0.63 0.72
## S_37 0.77 0.58 0.50 0.79 0.72 1.00 0.67 0.81 0.48 0.69 0.78 0.56 0.60 0.55
## S_38 0.76 0.55 0.64 0.65 0.82 0.67 1.00 0.78 0.57 0.80 0.81 0.70 0.65 0.80
## S_39 0.84 0.60 0.57 0.83 0.80 0.81 0.78 1.00 0.63 0.83 0.78 0.69 0.59 0.72
## S_40 0.64 0.49 0.32 0.59 0.64 0.48 0.57 0.63 1.00 0.67 0.59 0.52 0.40 0.50
## S_41 0.84 0.57 0.63 0.72 0.88 0.69 0.80 0.83 0.67 1.00 0.89 0.78 0.62 0.73
## S_42 0.86 0.63 0.62 0.76 0.87 0.78 0.81 0.78 0.59 0.89 1.00 0.76 0.70 0.74
## S_43 0.64 0.42 0.65 0.53 0.67 0.56 0.70 0.69 0.52 0.78 0.76 1.00 0.59 0.74
## S_44 0.63 0.42 0.37 0.62 0.63 0.60 0.65 0.59 0.40 0.62 0.70 0.59 1.00 0.53
## S_45 0.63 0.38 0.72 0.54 0.72 0.55 0.80 0.72 0.50 0.73 0.74 0.74 0.53 1.00
## 
## n= 60 
## 
## 
## P
##      S_1    S_2    S_3    S_4    S_5    S_6    S_7    S_8    S_9    S_10  
## S_1         0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_2  0.0000        0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_3  0.0000 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000
## S_4  0.0000 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000 0.0019 0.0000
## S_5  0.0000 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000
## S_6  0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000 0.0002 0.0000
## S_7  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000
## S_8  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000
## S_9  0.0000 0.0000 0.0001 0.0019 0.0000 0.0002 0.0000 0.0000        0.0000
## S_10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000       
## S_11 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_12 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_13 0.0000 0.0000 0.0000 0.0002 0.0000 0.0000 0.0000 0.0000 0.0028 0.0003
## S_14 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0023 0.0000
## S_15 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0000
## S_16 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0000
## S_17 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_18 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0000
## S_19 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_20 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0000
## S_21 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0006 0.0000
## S_23 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_24 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0016 0.0000
## S_25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_26 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0027 0.0000
## S_27 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0000
## S_28 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0000
## S_29 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0000
## S_31 0.0002 0.0000 0.0005 0.0004 0.0000 0.0000 0.0000 0.0000 0.0329 0.0055
## S_32 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0006 0.0000
## S_35 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_36 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0000
## S_37 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_38 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0021 0.0000
## S_39 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_40 0.0000 0.0000 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005
## S_41 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_42 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_43 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_44 0.0000 0.0000 0.0000 0.0003 0.0000 0.0000 0.0000 0.0000 0.0087 0.0009
## S_45 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0000
##      S_11   S_12   S_13   S_14   S_15   S_16   S_17   S_18   S_19   S_20  
## S_1  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_2  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_3  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_4  0.0000 0.0000 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_5  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_6  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_7  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_8  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_9  0.0000 0.0000 0.0028 0.0023 0.0004 0.0003 0.0000 0.0003 0.0000 0.0002
## S_10 0.0000 0.0000 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_11        0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_12 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_13 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_14 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_15 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000
## S_16 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000
## S_17 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000
## S_18 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000
## S_19 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000
## S_20 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000       
## S_21 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_23 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_24 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_26 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_27 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_28 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_29 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_31 0.0002 0.0000 0.0003 0.0000 0.0000 0.0000 0.0047 0.0008 0.0000 0.0021
## S_32 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_35 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000
## S_36 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_37 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_38 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_39 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_40 0.0000 0.0000 0.0006 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0014
## S_41 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_42 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_43 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_44 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0006 0.0001 0.0013
## S_45 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
##      S_21   S_22   S_23   S_24   S_25   S_26   S_27   S_28   S_29   S_31  
## S_1  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002
## S_2  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_3  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005
## S_4  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004
## S_5  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_6  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_7  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_8  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_9  0.0000 0.0006 0.0000 0.0016 0.0000 0.0027 0.0003 0.0010 0.0010 0.0329
## S_10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0055
## S_11 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002
## S_12 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_13 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003
## S_14 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_15 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_16 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_17 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0047
## S_18 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0008
## S_19 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_20 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0021
## S_21        0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_22 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002
## S_23 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001
## S_24 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000 0.0002
## S_25 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000
## S_26 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000
## S_27 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000
## S_28 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0010
## S_29 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000
## S_31 0.0000 0.0002 0.0001 0.0002 0.0000 0.0000 0.0000 0.0010 0.0000       
## S_32 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0929
## S_35 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_36 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_37 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_38 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_39 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_40 0.0000 0.0001 0.0000 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_41 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_42 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_43 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0009
## S_44 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0024 0.0000 0.0008
## S_45 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0031
##      S_32   S_35   S_36   S_37   S_38   S_39   S_40   S_41   S_42   S_43  
## S_1  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_2  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_3  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0000 0.0000 0.0000
## S_4  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_5  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_6  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_7  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_8  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_9  0.0006 0.0000 0.0002 0.0000 0.0021 0.0000 0.0000 0.0000 0.0000 0.0000
## S_10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0000 0.0000 0.0000
## S_11 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_12 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_13 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0006 0.0000 0.0000 0.0000
## S_14 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_15 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_16 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_17 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_18 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_19 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_20 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0014 0.0000 0.0000 0.0000
## S_21 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000
## S_23 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_24 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0000 0.0000 0.0000
## S_25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_26 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_27 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_28 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_29 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_31 0.0929 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0009
## S_32        0.0005 0.0000 0.0000 0.0000 0.0000 0.0119 0.0000 0.0000 0.0000
## S_35 0.0005        0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_36 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## S_37 0.0000 0.0000 0.0000        0.0000 0.0000 0.0001 0.0000 0.0000 0.0000
## S_38 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000 0.0000
## S_39 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000 0.0000 0.0000
## S_40 0.0119 0.0000 0.0000 0.0001 0.0000 0.0000        0.0000 0.0000 0.0000
## S_41 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0000
## S_42 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000        0.0000
## S_43 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000       
## S_44 0.0036 0.0000 0.0000 0.0000 0.0000 0.0000 0.0018 0.0000 0.0000 0.0000
## S_45 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
##      S_44   S_45  
## S_1  0.0000 0.0000
## S_2  0.0000 0.0000
## S_3  0.0000 0.0000
## S_4  0.0003 0.0000
## S_5  0.0000 0.0000
## S_6  0.0000 0.0000
## S_7  0.0000 0.0000
## S_8  0.0000 0.0000
## S_9  0.0087 0.0003
## S_10 0.0009 0.0000
## S_11 0.0000 0.0000
## S_12 0.0000 0.0000
## S_13 0.0000 0.0000
## S_14 0.0000 0.0000
## S_15 0.0000 0.0000
## S_16 0.0000 0.0000
## S_17 0.0001 0.0000
## S_18 0.0006 0.0000
## S_19 0.0001 0.0000
## S_20 0.0013 0.0000
## S_21 0.0000 0.0000
## S_22 0.0000 0.0000
## S_23 0.0000 0.0000
## S_24 0.0000 0.0000
## S_25 0.0000 0.0000
## S_26 0.0000 0.0000
## S_27 0.0000 0.0000
## S_28 0.0024 0.0000
## S_29 0.0000 0.0000
## S_31 0.0008 0.0031
## S_32 0.0036 0.0000
## S_35 0.0000 0.0000
## S_36 0.0000 0.0000
## S_37 0.0000 0.0000
## S_38 0.0000 0.0000
## S_39 0.0000 0.0000
## S_40 0.0018 0.0000
## S_41 0.0000 0.0000
## S_42 0.0000 0.0000
## S_43 0.0000 0.0000
## S_44        0.0000
## S_45 0.0000

######################################
# USING SPEARMAN'S RHO
######################################
cor.spearman <- cor.mtest(likert.df.s1s45.include,
                       method = "spearman",
                       conf.level = .95)

corrplot(cor(likert.df.s1s45.include,method = "spearman"), 
         method = "circle",
         type = "upper", 
         order = "original", 
         tl.col = "black", 
         tl.cex = 0.75,
         tl.srt = 90, 
         sig.level = 0.05, 
         p.mat = cor.spearman$p,
         insig = "blank")

######################################
# SPEARMAN CORRELATION TEST SUMMARY
######################################
cat("Number of statements which failed the Spearman test is equal to", 
    nrow(which(cor.spearman$p >= 0.05, arr.ind=TRUE)))

## Number of statements which failed the Spearman test is equal to 2

cat("Statements ",
    ifelse(which(cor.spearman$p >= 0.05, arr.ind=TRUE)>29 &
           which(cor.spearman$p >= 0.05, arr.ind=TRUE)<33,
           which(cor.spearman$p >= 0.05, arr.ind=TRUE)+1,
           which(cor.spearman$p >= 0.05, arr.ind=TRUE)+3),
    " failed the Spearman correlation significance test \n")

## Statements  32 31 31 32  failed the Spearman correlation significance test

######################################
# TRYING THE BASE KENDALL'S TAU FUNCTION
######################################
cor.kendall <- cor.mtest(likert.df.s1s45.include,
                       method = "kendall",
                       conf.level = .95)

corrplot(cor(likert.df.s1s45.include,method = "kendall"), 
         method = "circle",
         type = "upper", 
         order = "original", 
         tl.col = "black", 
         tl.cex = 0.75,
         tl.srt = 90, 
         sig.level = 0.05, 
         p.mat = cor.kendall$p,
         insig = "blank")

######################################
# TRYING THE BASE PEARSON'S R FUNCTION
######################################
cor.pearson <- cor.mtest(likert.df.s1s45.include,
                         method = "pearson",
                         conf.level = .95)

corrplot(cor(likert.df.s1s45.include,method = "pearson"), 
         method = "circle",
         type = "upper", 
         order = "original", 
         tl.col = "black", 
         tl.cex = 0.75,
         tl.srt = 90, 
         sig.level = 0.05, 
         p.mat = cor.pearson$p,
         insig = "blank")

######################################
# TRYING THE BASE CRONBACH'S ALPHA FUNCTION
######################################

######################################
# CRONBACH'S ALPHA FOR ALL 45 STATEMENTS
######################################
cronbach(likert.df.s1s45)

## $sample.size
## [1] 60
## 
## $number.of.items
## [1] 45
## 
## $alpha
## [1] 0.9858165

######################################
# CRONBACH'S ALPHA WITHOUT STATEMENTS 30,33,34
######################################
cronbach(likert.df.s1s45.include)

## $sample.size
## [1] 60
## 
## $number.of.items
## [1] 42
## 
## $alpha
## [1] 0.9885144

######################################
# CRONBACH'S ALPHA WITHOUT STATEMENTS 30,31,32,33,34
######################################
cronbach(likert.df.s1s45.include[,-(which(colnames(likert.df.s1s45.include) %in% c("S_31","S_32")))])

## $sample.size
## [1] 60
## 
## $number.of.items
## [1] 40
## 
## $alpha
## [1] 0.9886114