library(ggplot2)
library(dplyr)
library(broom)
library(ggpubr)
library(tidyverse)

The three indicators against efficiency and effectiveness, using a linear model as a fitting/interpolation function

## `geom_smooth()` using formula = 'y ~ x'

Statistical analysis of effectiveness against PEOU

mdl <- lm(PEOU ~ EFFECTIVENESS, data = data_neverlang)
summary(mdl)
## 
## Call:
## lm(formula = PEOU ~ EFFECTIVENESS, data = data_neverlang)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.41298 -0.22307 -0.01554  0.36464  1.04696 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept)     3.4227     1.1128   3.076   0.0152 *
## EFFECTIVENESS   0.3204     1.3820   0.232   0.8225  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7349 on 8 degrees of freedom
## Multiple R-squared:  0.006676,   Adjusted R-squared:  -0.1175 
## F-statistic: 0.05377 on 1 and 8 DF,  p-value: 0.8225

Statistical analysis of effectiveness against PU

mdl <- lm(PU ~ EFFECTIVENESS, data = data_neverlang)
summary(mdl)
## 
## Call:
## lm(formula = PU ~ EFFECTIVENESS, data = data_neverlang)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.69946 -0.11462 -0.05646  0.16244  0.72708 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    4.04175    0.59196   6.828 0.000134 ***
## EFFECTIVENESS  0.01962    0.73512   0.027 0.979356    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3909 on 8 degrees of freedom
## Multiple R-squared:  8.907e-05,  Adjusted R-squared:  -0.1249 
## F-statistic: 0.0007127 on 1 and 8 DF,  p-value: 0.9794

Statistical analysis of effectiveness against ITU

mdl <- lm(ITU ~ EFFECTIVENESS, data = data_neverlang)
summary(mdl)
## 
## Call:
## lm(formula = ITU ~ EFFECTIVENESS, data = data_neverlang)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.02970 -0.16247 -0.03488  0.33356  0.77762 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)   
## (Intercept)     3.1236     0.8441   3.701  0.00604 **
## EFFECTIVENESS   0.5414     1.0482   0.517  0.61945   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5574 on 8 degrees of freedom
## Multiple R-squared:  0.03228,    Adjusted R-squared:  -0.08869 
## F-statistic: 0.2668 on 1 and 8 DF,  p-value: 0.6194
## `geom_smooth()` using formula = 'y ~ x'

Statistical analysis of efficiency against PEOU

mdl <- lm(PEOU ~  EFFICIENCY, data = data_neverlang)
summary(mdl)
## 
## Call:
## lm(formula = PEOU ~ EFFICIENCY, data = data_neverlang)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.7582 -0.3380 -0.1332  0.4405  0.8481 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.5774     0.4077  11.227 3.55e-06 ***
## EFFICIENCY  -23.1375     9.4278  -2.454   0.0397 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.557 on 8 degrees of freedom
## Multiple R-squared:  0.4295, Adjusted R-squared:  0.3582 
## F-statistic: 6.023 on 1 and 8 DF,  p-value: 0.03968

Statistical analysis of efficiency against PU

mdl <- lm(PU ~  EFFICIENCY, data = data_neverlang)
summary(mdl)
## 
## Call:
## lm(formula = PU ~ EFFICIENCY, data = data_neverlang)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.25950 -0.16254 -0.06558  0.05527  0.74050 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.5137     0.2233  20.211 3.75e-08 ***
## EFFICIENCY  -11.7043     5.1644  -2.266   0.0532 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3051 on 8 degrees of freedom
## Multiple R-squared:  0.391,  Adjusted R-squared:  0.3149 
## F-statistic: 5.136 on 1 and 8 DF,  p-value: 0.05319

Statistical analysis of efficiency against ITU

mdl <- lm(ITU ~ EFFICIENCY, data = data_neverlang)
summary(mdl)
## 
## Call:
## lm(formula = ITU ~ EFFICIENCY, data = data_neverlang)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.53331 -0.30444 -0.09617  0.22681  0.84169 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    4.201      0.327  12.847 1.27e-06 ***
## EFFICIENCY   -16.691      7.562  -2.207   0.0583 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4467 on 8 degrees of freedom
## Multiple R-squared:  0.3785, Adjusted R-squared:  0.3008 
## F-statistic: 4.872 on 1 and 8 DF,  p-value: 0.05834

Boxplot of the three variables: PEOU, PU, ITU

Test of significance against average value 3

wilcox.test(data_neverlang$PEOU, mu = 3, alternative = "greater")
## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  data_neverlang$PEOU
## V = 49, p-value = 0.01588
## alternative hypothesis: true location is greater than 3
wilcox.test(data_neverlang$PU, mu = 3, alternative = "greater")
## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  data_neverlang$PU
## V = 55, p-value = 0.002881
## alternative hypothesis: true location is greater than 3
wilcox.test(data_neverlang$ITU, mu = 3, alternative = "greater")
## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  data_neverlang$ITU
## V = 42, p-value = 0.01188
## alternative hypothesis: true location is greater than 3

Relation between efficiency and effectiveness with linear model

## `geom_smooth()` using formula = 'y ~ x'

Statistical analysis of effectiveness against efficiency

mdl <- lm(EFFECTIVENESS ~ EFFICIENCY, data = data_neverlang)
summary(mdl)
## 
## Call:
## lm(formula = EFFECTIVENESS ~ EFFICIENCY, data = data_neverlang)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.34241 -0.03197  0.01415  0.12222  0.17192 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.6436     0.1255   5.127   0.0009 ***
## EFFICIENCY    3.6891     2.9031   1.271   0.2395    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1715 on 8 degrees of freedom
## Multiple R-squared:  0.1679, Adjusted R-squared:  0.06394 
## F-statistic: 1.615 on 1 and 8 DF,  p-value: 0.2395

Relation between PCU and effectiveness lm

## `geom_smooth()` using formula = 'y ~ x'

Statistical analysis of effectiveness against PCU

mdl <- lm(EFFECTIVENESS ~ PCU, data = data_neverlang)
summary(mdl)
## 
## Call:
## lm(formula = EFFECTIVENESS ~ PCU, data = data_neverlang)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.29353 -0.06159  0.02917  0.07492  0.19081 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   0.1111     0.3053   0.364   0.7254  
## PCU           0.8696     0.3880   2.241   0.0553 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1474 on 8 degrees of freedom
## Multiple R-squared:  0.3858, Adjusted R-squared:  0.309 
## F-statistic: 5.024 on 1 and 8 DF,  p-value: 0.0553

Relation between PCU and efficiency lm

## `geom_smooth()` using formula = 'y ~ x'

Statistical analysis of efficiency against PCU

mdl <- lm(EFFICIENCY ~ PCU, data = data_neverlang)
summary(mdl)
## 
## Call:
## lm(formula = EFFICIENCY ~ PCU, data = data_neverlang)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.021523 -0.010164 -0.002435  0.006315  0.040627 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.01674    0.03841  -0.436    0.674
## PCU          0.07167    0.04881   1.468    0.180
## 
## Residual standard error: 0.01854 on 8 degrees of freedom
## Multiple R-squared:  0.2123, Adjusted R-squared:  0.1138 
## F-statistic: 2.156 on 1 and 8 DF,  p-value: 0.1802