mito_ben
Emre Toros
06/06/2021
library(tidyverse)## -- Attaching packages --------------------------------------- tidyverse 1.3.0 --## v ggplot2 3.3.3.9000 v purrr 0.3.4
## v tibble 3.0.6 v dplyr 1.0.4
## v tidyr 1.1.2 v stringr 1.4.0
## v readr 1.4.0 v forcats 0.5.0## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(benford.analysis)## Warning: package 'benford.analysis' was built under R version 4.0.5library(readxl)
ben <- read_excel("ben_final.xlsx")#positive
fd_pos1<- benford(ben$pos,number.of.digits = 1)
fd_pos1##
## Benford object:
##
## Data: ben$pos
## Number of observations used = 36013
## Number of obs. for second order = 1077
## First digits analysed = 1
##
## Mantissa:
##
## Statistic Value
## Mean 0.468
## Var 0.079
## Ex.Kurtosis -1.068
## Skewness 0.056
##
##
## The 5 largest deviations:
##
## digits absolute.diff
## 1 2 1567.43
## 2 1 1399.99
## 3 3 581.58
## 4 9 242.86
## 5 8 218.16
##
## Stats:
##
## Pearson's Chi-squared test
##
## data: ben$pos
## X-squared = 747.29, df = 8, p-value < 2.2e-16
##
##
## Mantissa Arc Test
##
## data: ben$pos
## L2 = 0.0041113, df = 2, p-value < 2.2e-16
##
## Mean Absolute Deviation (MAD): 0.01407166
## MAD Conformity - Nigrini (2012): Marginally acceptable conformity
## Distortion Factor: -14.64946
##
## Remember: Real data will never conform perfectly to Benford's Law. You should not focus on p-values!plot(fd_pos1)
fd_pos2<- benford(ben$pos,number.of.digits = 2)
fd_pos2##
## Benford object:
##
## Data: ben$pos
## Number of observations used = 36013
## Number of obs. for second order = 1077
## First digits analysed = 2
##
## Mantissa:
##
## Statistic Value
## Mean 0.468
## Var 0.079
## Ex.Kurtosis -1.068
## Skewness 0.056
##
##
## The 5 largest deviations:
##
## digits absolute.diff
## 1 20 3755.91
## 2 30 2409.16
## 3 40 1687.80
## 4 50 1403.28
## 5 60 1078.48
##
## Stats:
##
## Pearson's Chi-squared test
##
## data: ben$pos
## X-squared = 66341, df = 89, p-value < 2.2e-16
##
##
## Mantissa Arc Test
##
## data: ben$pos
## L2 = 0.0041113, df = 2, p-value < 2.2e-16
##
## Mean Absolute Deviation (MAD): 0.008474712
## MAD Conformity - Nigrini (2012): Nonconformity
## Distortion Factor: -14.64946
##
## Remember: Real data will never conform perfectly to Benford's Law. You should not focus on p-values!plot(fd_pos2)
#negative
fd_neg1<- benford(ben$neg,number.of.digits = 1)
fd_neg1##
## Benford object:
##
## Data: ben$neg
## Number of observations used = 20709
## Number of obs. for second order = 171
## First digits analysed = 1
##
## Mantissa:
##
## Statistic Value
## Mean 0.33
## Var 0.09
## Ex.Kurtosis -1.06
## Skewness 0.41
##
##
## The 5 largest deviations:
##
## digits absolute.diff
## 1 1 2180.97
## 2 2 735.33
## 3 8 538.32
## 4 7 517.96
## 5 6 502.40
##
## Stats:
##
## Pearson's Chi-squared test
##
## data: ben$neg
## X-squared = 2037.8, df = 8, p-value < 2.2e-16
##
##
## Mantissa Arc Test
##
## data: ben$neg
## L2 = 0.029807, df = 2, p-value < 2.2e-16
##
## Mean Absolute Deviation (MAD): 0.03129392
## MAD Conformity - Nigrini (2012): Nonconformity
## Distortion Factor: -35.13094
##
## Remember: Real data will never conform perfectly to Benford's Law. You should not focus on p-values!plot(fd_neg1)
fd_neg2<- benford(ben$neg,number.of.digits = 2)
fd_neg2##
## Benford object:
##
## Data: ben$neg
## Number of observations used = 20709
## Number of obs. for second order = 171
## First digits analysed = 2
##
## Mantissa:
##
## Statistic Value
## Mean 0.33
## Var 0.09
## Ex.Kurtosis -1.06
## Skewness 0.41
##
##
## The 5 largest deviations:
##
## digits absolute.diff
## 1 10 5892.80
## 2 20 3308.19
## 3 30 1936.09
## 4 40 1283.92
## 5 50 905.90
##
## Stats:
##
## Pearson's Chi-squared test
##
## data: ben$neg
## X-squared = 110163, df = 89, p-value < 2.2e-16
##
##
## Mantissa Arc Test
##
## data: ben$neg
## L2 = 0.029807, df = 2, p-value < 2.2e-16
##
## Mean Absolute Deviation (MAD): 0.01628231
## MAD Conformity - Nigrini (2012): Nonconformity
## Distortion Factor: -35.13094
##
## Remember: Real data will never conform perfectly to Benford's Law. You should not focus on p-values!plot(fd_neg2)
#notr
fd_ntr1<- benford(ben$notr,number.of.digits = 1)
fd_ntr1##
## Benford object:
##
## Data: ben$notr
## Number of observations used = 18775
## Number of obs. for second order = 216
## First digits analysed = 1
##
## Mantissa:
##
## Statistic Value
## Mean 0.327
## Var 0.093
## Ex.Kurtosis -1.052
## Skewness 0.453
##
##
## The 5 largest deviations:
##
## digits absolute.diff
## 1 1 2471.16
## 2 7 470.80
## 3 6 460.93
## 4 9 430.10
## 5 4 424.49
##
## Stats:
##
## Pearson's Chi-squared test
##
## data: ben$notr
## X-squared = 2149, df = 8, p-value < 2.2e-16
##
##
## Mantissa Arc Test
##
## data: ben$notr
## L2 = 0.042732, df = 2, p-value < 2.2e-16
##
## Mean Absolute Deviation (MAD): 0.03406478
## MAD Conformity - Nigrini (2012): Nonconformity
## Distortion Factor: -31.31379
##
## Remember: Real data will never conform perfectly to Benford's Law. You should not focus on p-values!plot(fd_ntr1)
fd_ntr2<- benford(ben$notr,number.of.digits = 2)
fd_ntr2##
## Benford object:
##
## Data: ben$notr
## Number of observations used = 18775
## Number of obs. for second order = 216
## First digits analysed = 2
##
## Mantissa:
##
## Statistic Value
## Mean 0.327
## Var 0.093
## Ex.Kurtosis -1.052
## Skewness 0.453
##
##
## The 5 largest deviations:
##
## digits absolute.diff
## 1 10 5447.85
## 2 20 2588.17
## 3 30 1462.64
## 4 40 995.66
## 5 50 741.53
##
## Stats:
##
## Pearson's Chi-squared test
##
## data: ben$notr
## X-squared = 87877, df = 89, p-value < 2.2e-16
##
##
## Mantissa Arc Test
##
## data: ben$notr
## L2 = 0.042732, df = 2, p-value < 2.2e-16
##
## Mean Absolute Deviation (MAD): 0.0152508
## MAD Conformity - Nigrini (2012): Nonconformity
## Distortion Factor: -31.31379
##
## Remember: Real data will never conform perfectly to Benford's Law. You should not focus on p-values!plot(fd_ntr2)
#total
fd_tot1<- benford(ben$total,number.of.digits = 1)
fd_tot1##
## Benford object:
##
## Data: ben$total
## Number of observations used = 37221
## Number of obs. for second order = 1141
## First digits analysed = 1
##
## Mantissa:
##
## Statistic Value
## Mean 0.489
## Var 0.072
## Ex.Kurtosis -1.050
## Skewness 0.075
##
##
## The 5 largest deviations:
##
## digits absolute.diff
## 1 1 2831.64
## 2 2 2159.71
## 3 3 809.66
## 4 4 351.91
## 5 9 184.14
##
## Stats:
##
## Pearson's Chi-squared test
##
## data: ben$total
## X-squared = 1651.9, df = 8, p-value < 2.2e-16
##
##
## Mantissa Arc Test
##
## data: ben$total
## L2 = 0.012481, df = 2, p-value < 2.2e-16
##
## Mean Absolute Deviation (MAD): 0.02034735
## MAD Conformity - Nigrini (2012): Nonconformity
## Distortion Factor: -14.46284
##
## Remember: Real data will never conform perfectly to Benford's Law. You should not focus on p-values!plot(fd_tot1)
fd_tot2<- benford(ben$total,number.of.digits = 2)
fd_tot2##
## Benford object:
##
## Data: ben$total
## Number of observations used = 37221
## Number of obs. for second order = 1141
## First digits analysed = 2
##
## Mantissa:
##
## Statistic Value
## Mean 0.489
## Var 0.072
## Ex.Kurtosis -1.050
## Skewness 0.075
##
##
## The 5 largest deviations:
##
## digits absolute.diff
## 1 20 4228.31
## 2 30 2701.96
## 3 40 1970.85
## 4 50 1439.89
## 5 60 1235.81
##
## Stats:
##
## Pearson's Chi-squared test
##
## data: ben$total
## X-squared = 77718, df = 89, p-value < 2.2e-16
##
##
## Mantissa Arc Test
##
## data: ben$total
## L2 = 0.012481, df = 2, p-value < 2.2e-16
##
## Mean Absolute Deviation (MAD): 0.008562129
## MAD Conformity - Nigrini (2012): Nonconformity
## Distortion Factor: -14.46284
##
## Remember: Real data will never conform perfectly to Benford's Law. You should not focus on p-values!plot(fd_tot2)