College admission over subscription, does the type of school matter?
Nai Zexin
6 Aug 2019
Our Problem Statement
In the US, college admission is very much different from Singapore as much more weight and consideration is placed on the student’s extra curicular activities. Through this data set from the National Centre for Education Statistics, colleges from throughout the US had provided the different matricses used for admission.
library(tidyverse)## ── Attaching packages ──────────────────────────────────────────────────────────────────────── tidyverse 1.2.1 ──## ✔ ggplot2 3.2.0 ✔ purrr 0.2.5
## ✔ tibble 1.4.2 ✔ dplyr 0.7.7
## ✔ tidyr 0.8.1 ✔ stringr 1.3.1
## ✔ readr 1.1.1 ✔ forcats 0.3.0## Warning: package 'ggplot2' was built under R version 3.5.2## ── Conflicts ─────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()Import - Part 1 : Streaming the Colleges
Different types of colleges attract different students. Therefore, for further analysis, the colleges were split into 3 different streams. According to Prepscholar, the top 75th percentile of ACT scores were students who scored above 25. The bottom 25th percentile were students who scored below 16. Thus the colleges were spilt into three different streams according to those scores.
https://blog.prepscholar.com/historical-act-percentiles-2014-2013-2012-2011
Group 1 will be called “Normal” being the schools where the ACT score submitted at the 25th percentile is below 16. Group 2 will be called “Express” being the schools where the ACT score submitted at the 25th percentile is above 16 but the ACT score submitted at the 75th percentile is below 25. Group 3 will be called “Special” being the schools where the ACT score submitted at the 25th percentil is above 25.
adm2017 <- read.csv("adm2017.csv")
glimpse(adm2017)## Observations: 2,075
## Variables: 68
## $ UNITID <int> 100654, 100663, 100706, 100724, 100751, 100830, 10085...
## $ ADMCON1 <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 2, 1, 1, 1,...
## $ ADMCON2 <int> 2, 3, 2, 3, 2, 2, 2, 1, 2, 3, 2, 3, 3, 2, 3, 3, 2, 2,...
## $ ADMCON3 <int> 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
## $ ADMCON4 <int> 2, 1, 1, 3, 1, 3, 1, 3, 3, 3, 2, 3, 3, 2, 2, 1, 2, 2,...
## $ ADMCON5 <int> 3, 3, 3, 3, 3, 3, 2, 1, 2, 3, 2, 1, 3, 2, 3, 3, 3, 3,...
## $ ADMCON6 <int> 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3,...
## $ ADMCON7 <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,...
## $ ADMCON8 <int> 1, 3, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1,...
## $ ADMCON9 <int> 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3,...
## $ XAPPLCN <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R,...
## $ APPLCN <int> 8610, 7555, 4454, 6842, 38129, 2474, 18072, 2559, 233...
## $ XAPPLCNM <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R,...
## $ APPLCNM <int> 3066, 2729, 2466, 2136, 14705, 841, 7841, 1098, 878, ...
## $ XAPPLCNW <fct> R, R, R, R, R, R, R, R, R, R, R, Z, R, R, R, R, R, R,...
## $ APPLCNW <int> 5544, 4826, 1988, 4515, 23424, 1633, 10231, 1461, 145...
## $ XADMSSN <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R,...
## $ ADMSSN <int> 7772, 6936, 3618, 6696, 20321, 2042, 15168, 1583, 119...
## $ XADMSSNM <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R,...
## $ ADMSSNM <int> 2704, 2487, 2082, 2071, 7992, 715, 6576, 726, 484, 34...
## $ XADMSSNW <fct> R, R, R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R,...
## $ ADMSSNW <int> 5068, 4449, 1536, 4438, 12329, 1327, 8592, 857, 707, ...
## $ XENRLT <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R,...
## $ ENRLT <int> 1294, 2299, 1352, 967, 7407, 673, 4836, 349, 333, 51,...
## $ XENRLM <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R,...
## $ ENRLM <int> 518, 861, 867, 357, 3167, 276, 2261, 183, 162, 28, 15...
## $ XENRLW <fct> R, R, R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R,...
## $ ENRLW <int> 776, 1438, 485, 610, 4240, 397, 2575, 166, 171, 23, 1...
## $ XENRLFT <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R,...
## $ ENRLFT <int> 1288, 2228, 1341, 951, 7385, 648, 4771, 349, 311, 8, ...
## $ XENRLFTM <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, A, R, R, R, R,...
## $ ENRLFTM <int> 515, 833, 860, 349, 3157, 265, 2216, 183, 153, 1, 155...
## $ XENRLFTW <fct> R, R, R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R,...
## $ ENRLFTW <int> 773, 1395, 481, 602, 4228, 383, 2555, 166, 158, 7, 13...
## $ XENRLPT <fct> R, R, R, R, R, R, R, A, R, R, R, R, R, R, R, A, R, R,...
## $ ENRLPT <int> 6, 71, 11, 16, 22, 25, 65, NA, 22, 43, 0, 0, 32, 1, 1...
## $ XENRLPTM <fct> R, R, R, R, R, R, R, A, R, R, R, R, R, A, R, A, R, R,...
## $ ENRLPTM <int> 3, 28, 7, 8, 10, 11, 45, NA, 9, 27, 0, 0, 12, NA, 0, ...
## $ XENRLPTW <fct> R, R, R, R, R, R, R, A, R, R, R, A, R, R, R, A, R, R,...
## $ ENRLPTW <int> 3, 43, 4, 8, 12, 14, 20, NA, 13, 16, 0, NA, 20, 1, 1,...
## $ XSATNUM <fct> R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R, R,...
## $ SATNUM <int> 21, 15, 29, 173, 1397, 26, 572, 65, 36, NA, 63, 0, 26...
## $ XSATPCT <fct> R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R, R,...
## $ SATPCT <int> 1, 1, 2, 18, 19, 4, 12, 18, 11, NA, 21, 0, 2, 2, 4, 3...
## $ XACTNUM <fct> R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R, R,...
## $ ACTNUM <int> 1270, 2093, 1292, 826, 5981, 563, 4215, 296, 266, NA,...
## $ XACTPCT <fct> R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R, R,...
## $ ACTPCT <int> 88, 94, 96, 85, 81, 84, 87, 83, 80, NA, 92, 100, 90, ...
## $ XSATVR25 <fct> R, R, R, R, R, R, R, R, R, A, R, A, R, A, R, R, R, R,...
## $ SATVR25 <int> 365, 440, 550, 380, 530, 490, 570, 520, 460, NA, 490,...
## $ XSATVR75 <fct> R, R, R, R, R, R, R, R, R, A, R, A, R, A, R, R, R, R,...
## $ SATVR75 <int> 485, 630, 660, 485, 640, 565, 650, 630, 590, NA, 595,...
## $ XSATMT25 <fct> R, R, R, R, R, R, R, R, R, A, R, A, R, A, R, R, R, R,...
## $ SATMT25 <int> 360, 550, 530, 375, 520, 475, 560, 510, 460, NA, 500,...
## $ XSATMT75 <fct> R, R, R, R, R, R, R, R, R, A, R, A, R, A, R, R, R, R,...
## $ SATMT75 <int> 495, 740, 670, 481, 640, 545, 660, 630, 560, NA, 580,...
## $ XACTCM25 <fct> R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R, R,...
## $ ACTCM25 <int> 16, 21, 25, 16, 23, 19, 24, 23, 18, NA, 19, 19, 19, 1...
## $ XACTCM75 <fct> R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R, R,...
## $ ACTCM75 <int> 19, 28, 31, 20, 32, 24, 30, 29, 22, NA, 24, 21, 26, 2...
## $ XACTEN25 <fct> R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R, R,...
## $ ACTEN25 <int> 14, 22, 25, 15, 23, 19, 24, 23, 17, NA, 18, 15, 20, 1...
## $ XACTEN75 <fct> R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R, R,...
## $ ACTEN75 <int> 20, 31, 33, 19, 33, 24, 32, 31, 23, NA, 24, 20, 27, 2...
## $ XACTMT25 <fct> R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R, R,...
## $ ACTMT25 <int> 15, 21, 24, 14, 21, 17, 23, 22, 16, NA, 17, 18, 18, 1...
## $ XACTMT75 <fct> R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R, R,...
## $ ACTMT75 <int> 18, 26, 29, 19, 29, 22, 28, 27, 22, NA, 24, 19, 25, 2...admACTR <- adm2017[adm2017$ADMCON7==1,]
admACTR$ACTstream <- 1
admACTR$ACTstream[admACTR$ACTCM25 >= 16 & admACTR$ACTCM75 >= 25] <- 2
admACTR$ACTstream[admACTR$ACTCM25 >= 25] <- 3
glimpse(admACTR)## Observations: 1,212
## Variables: 69
## $ UNITID <int> 100654, 100663, 100706, 100724, 100751, 100830, 1008...
## $ ADMCON1 <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1...
## $ ADMCON2 <int> 2, 3, 2, 3, 2, 2, 2, 1, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3...
## $ ADMCON3 <int> 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1...
## $ ADMCON4 <int> 2, 1, 1, 3, 1, 3, 1, 3, 3, 2, 3, 3, 2, 2, 1, 2, 2, 2...
## $ ADMCON5 <int> 3, 3, 3, 3, 3, 3, 2, 1, 2, 2, 1, 3, 2, 3, 3, 3, 3, 3...
## $ ADMCON6 <int> 2, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3...
## $ ADMCON7 <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1...
## $ ADMCON8 <int> 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1...
## $ ADMCON9 <int> 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3...
## $ XAPPLCN <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ APPLCN <int> 8610, 7555, 4454, 6842, 38129, 2474, 18072, 2559, 23...
## $ XAPPLCNM <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ APPLCNM <int> 3066, 2729, 2466, 2136, 14705, 841, 7841, 1098, 878,...
## $ XAPPLCNW <fct> R, R, R, R, R, R, R, R, R, R, Z, R, R, R, R, R, R, R...
## $ APPLCNW <int> 5544, 4826, 1988, 4515, 23424, 1633, 10231, 1461, 14...
## $ XADMSSN <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ADMSSN <int> 7772, 6936, 3618, 6696, 20321, 2042, 15168, 1583, 11...
## $ XADMSSNM <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ADMSSNM <int> 2704, 2487, 2082, 2071, 7992, 715, 6576, 726, 484, 5...
## $ XADMSSNW <fct> R, R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R...
## $ ADMSSNW <int> 5068, 4449, 1536, 4438, 12329, 1327, 8592, 857, 707,...
## $ XENRLT <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ENRLT <int> 1294, 2299, 1352, 967, 7407, 673, 4836, 349, 333, 29...
## $ XENRLM <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ENRLM <int> 518, 861, 867, 357, 3167, 276, 2261, 183, 162, 155, ...
## $ XENRLW <fct> R, R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R...
## $ ENRLW <int> 776, 1438, 485, 610, 4240, 397, 2575, 166, 171, 139,...
## $ XENRLFT <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ENRLFT <int> 1288, 2228, 1341, 951, 7385, 648, 4771, 349, 311, 29...
## $ XENRLFTM <fct> R, R, R, R, R, R, R, R, R, R, R, R, A, R, R, R, R, R...
## $ ENRLFTM <int> 515, 833, 860, 349, 3157, 265, 2216, 183, 153, 155, ...
## $ XENRLFTW <fct> R, R, R, R, R, R, R, R, R, R, A, R, R, R, R, R, R, R...
## $ ENRLFTW <int> 773, 1395, 481, 602, 4228, 383, 2555, 166, 158, 139,...
## $ XENRLPT <fct> R, R, R, R, R, R, R, A, R, R, R, R, R, R, A, R, R, R...
## $ ENRLPT <int> 6, 71, 11, 16, 22, 25, 65, NA, 22, 0, 0, 32, 1, 1, N...
## $ XENRLPTM <fct> R, R, R, R, R, R, R, A, R, R, R, R, A, R, A, R, R, R...
## $ ENRLPTM <int> 3, 28, 7, 8, 10, 11, 45, NA, 9, 0, 0, 12, NA, 0, NA,...
## $ XENRLPTW <fct> R, R, R, R, R, R, R, A, R, R, A, R, R, R, A, R, R, R...
## $ ENRLPTW <int> 3, 43, 4, 8, 12, 14, 20, NA, 13, 0, NA, 20, 1, 1, NA...
## $ XSATNUM <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ SATNUM <int> 21, 15, 29, 173, 1397, 26, 572, 65, 36, 63, 0, 26, 1...
## $ XSATPCT <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ SATPCT <int> 1, 1, 2, 18, 19, 4, 12, 18, 11, 21, 0, 2, 2, 4, 32, ...
## $ XACTNUM <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ACTNUM <int> 1270, 2093, 1292, 826, 5981, 563, 4215, 296, 266, 26...
## $ XACTPCT <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ACTPCT <int> 88, 94, 96, 85, 81, 84, 87, 83, 80, 92, 100, 90, 98,...
## $ XSATVR25 <fct> R, R, R, R, R, R, R, R, R, R, A, R, A, R, R, R, R, R...
## $ SATVR25 <int> 365, 440, 550, 380, 530, 490, 570, 520, 460, 490, NA...
## $ XSATVR75 <fct> R, R, R, R, R, R, R, R, R, R, A, R, A, R, R, R, R, R...
## $ SATVR75 <int> 485, 630, 660, 485, 640, 565, 650, 630, 590, 595, NA...
## $ XSATMT25 <fct> R, R, R, R, R, R, R, R, R, R, A, R, A, R, R, R, R, R...
## $ SATMT25 <int> 360, 550, 530, 375, 520, 475, 560, 510, 460, 500, NA...
## $ XSATMT75 <fct> R, R, R, R, R, R, R, R, R, R, A, R, A, R, R, R, R, R...
## $ SATMT75 <int> 495, 740, 670, 481, 640, 545, 660, 630, 560, 580, NA...
## $ XACTCM25 <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ACTCM25 <int> 16, 21, 25, 16, 23, 19, 24, 23, 18, 19, 19, 19, 18, ...
## $ XACTCM75 <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ACTCM75 <int> 19, 28, 31, 20, 32, 24, 30, 29, 22, 24, 21, 26, 25, ...
## $ XACTEN25 <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ACTEN25 <int> 14, 22, 25, 15, 23, 19, 24, 23, 17, 18, 15, 20, 18, ...
## $ XACTEN75 <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ACTEN75 <int> 20, 31, 33, 19, 33, 24, 32, 31, 23, 24, 20, 27, 26, ...
## $ XACTMT25 <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ACTMT25 <int> 15, 21, 24, 14, 21, 17, 23, 22, 16, 17, 18, 18, 16, ...
## $ XACTMT75 <fct> R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R, R...
## $ ACTMT75 <int> 18, 26, 29, 19, 29, 22, 28, 27, 22, 24, 19, 25, 23, ...
## $ ACTstream <dbl> 1, 2, 3, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2...From the three different streams, then see how oversubscription is affecting the colleges for admission. A boxplot will be created to show the oversubscription rate by stream. Therefore leading us into the next part of the project where the different admission conditions are taken into consideration.
admACTR <- admACTR[admACTR$ADMSSN!=0,]
admACTR$OverSub <- admACTR$APPLCN/admACTR$ADMSSN
admACTR$ACTstream <- factor(admACTR$ACTstream,
levels = c(1, 2, 3),
labels = c("Normal", "Express", "Special"))
boxplot(OverSub ~ ACTstream, data=admACTR,
notch=TRUE,
varwidth=TRUE,
col="cyan3",
main="Enrollment Rate by School Type",
ylim = c(0,10),
xlab="School Type by ACT Score",
ylab="Rate of Oversubscription",
outline=FALSE)
Tidy & Transform
- filter out unnecessary data rows
- remove “,” in the value fields and change them to numeric fields
- remove all null values
- rename the field of both files for ease of reading and joining purpose
Model
Although all the admission conditions are categorical, a linear regression was first ran to figure out the admission conditions that are significant. Using the ACT scores above were part of admission condition 7.
adm2017$ADMCON1_R <- 0
adm2017$ADMCON2_R <- 0
adm2017$ADMCON3_R <- 0
adm2017$ADMCON4_R <- 0
adm2017$ADMCON5_R <- 0
adm2017$ADMCON6_R <- 0
adm2017$ADMCON7_R <- 0
adm2017$ADMCON8_R <- 0
adm2017$ADMCON9_R <- 0
adm2017$ADMCON1_R[adm2017$ADMCON1 == 1] <- 1
adm2017$ADMCON2_R[adm2017$ADMCON2 == 1] <- 1
adm2017$ADMCON3_R[adm2017$ADMCON3 == 1] <- 1
adm2017$ADMCON4_R[adm2017$ADMCON4 == 1] <- 1
adm2017$ADMCON5_R[adm2017$ADMCON5 == 1] <- 1
adm2017$ADMCON6_R[adm2017$ADMCON6 == 1] <- 1
adm2017$ADMCON7_R[adm2017$ADMCON7 == 1] <- 1
adm2017$ADMCON8_R[adm2017$ADMCON8 == 1] <- 1
adm2017$ADMCON9_R[adm2017$ADMCON9 == 1] <- 1
adm2017 <- adm2017[adm2017$ADMSSN!=0,]
adm2017$OverSub <- adm2017$APPLCN/adm2017$ADMSSN
adm2017 <- adm2017[!(is.na(adm2017$OverSub)),]
model1 <- lm(OverSub ~ ADMCON1_R + ADMCON2_R + ADMCON3_R + ADMCON4_R
+ ADMCON5_R + ADMCON6_R + ADMCON7_R + ADMCON8_R +
ADMCON9_R, adm2017)From the model summary, admission conditions 1, 5, 7 and 8 are significant. To further test this however, an ANOVA test should be ran as it is the more accurate modelling for catergorical variables.
Visualize Part ANOVA test
#ANOVA test
adm2017$ADMCON[adm2017$ADMCON1 == 1] <- 1
adm2017$ADMCON[adm2017$ADMCON2 == 1] <- 2
adm2017$ADMCON[adm2017$ADMCON3 == 1] <- 3
adm2017$ADMCON[adm2017$ADMCON4 == 1] <- 4
adm2017$ADMCON[adm2017$ADMCON5 == 1] <- 5
adm2017$ADMCON[adm2017$ADMCON6 == 1] <- 6
adm2017$ADMCON[adm2017$ADMCON7 == 1] <- 7
adm2017$ADMCON[adm2017$ADMCON8 == 1] <- 8
adm2017$ADMCON[adm2017$ADMCON9 == 1] <- 9
adm2017$ADMCON<- as.factor(adm2017$ADMCON)
# aov() is a command for Analysis of Variance.
# It takes the form of outcome ~ predictor.
# Please put the name of the data after the data command.
# Please assign the results of the analysis of variance
# into an object named obj.aov.x1.
obj_aov_x1 <- aov(OverSub ~ ADMCON, data = adm2017)
summary(obj_aov_x1)## Df Sum Sq Mean Sq F value Pr(>F)
## ADMCON 7 111 15.863 4.041 0.000209 ***
## Residuals 2035 7989 3.926
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Post-Hoc Test
# For the post-hoc comparison,
# let’s use Tukey’s Honest Significant Difference (HSD) method.
# For each option, you input the factor
# that you wish to examine with the post-hoc comparison.
TukeyHSD(obj_aov_x1, which = 'ADMCON', ordered = FALSE)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = OverSub ~ ADMCON, data = adm2017)
##
## $ADMCON
## diff lwr upr p adj
## 3-1 0.9009707 -1.8723033 3.6742446 0.9765146
## 4-1 0.2229624 -2.9769263 3.4228510 0.9999991
## 5-1 0.3536599 -2.3936194 3.1009392 0.9999359
## 6-1 0.6981595 -2.0965881 3.4929071 0.9950821
## 7-1 1.2505081 -1.4699044 3.9709207 0.8599563
## 8-1 0.5680965 -2.1254501 3.2616431 0.9983100
## 9-1 0.4627971 -2.2526131 3.1782073 0.9995791
## 4-3 -0.6780083 -2.5421089 1.1860924 0.9561918
## 5-3 -0.5473108 -1.4322556 0.3376341 0.5673623
## 6-3 -0.2028112 -1.2256493 0.8200270 0.9988652
## 7-3 0.3495375 -0.4481018 1.1471768 0.8876895
## 8-3 -0.3328742 -1.0334290 0.3676807 0.8377436
## 9-3 -0.4381736 -1.2185815 0.3422344 0.6850436
## 5-4 0.1306975 -1.6945056 1.9559006 0.9999989
## 6-4 0.4751971 -1.4207029 2.3710971 0.9949797
## 7-4 1.0275457 -0.7569619 2.8120533 0.6561210
## 8-4 0.3451341 -1.3981433 2.0884115 0.9988764
## 9-4 0.2398347 -1.5370377 2.0167071 0.9999116
## 6-5 0.3444996 -0.6056019 1.2946011 0.9569148
## 7-5 0.8968482 0.1949056 1.5987908 0.0027596
## 8-5 0.2144366 -0.3748614 0.8037346 0.9560844
## 9-5 0.1091372 -0.5731615 0.7914359 0.9997238
## 7-6 0.5523486 -0.3170154 1.4217127 0.5318300
## 8-6 -0.1300630 -0.9113073 0.6511813 0.9996396
## 9-6 -0.2353624 -1.0889443 0.6182195 0.9910098
## 8-7 -0.6824116 -1.1300423 -0.2347809 0.0001076
## 9-7 -0.7877110 -1.3521866 -0.2232355 0.0006316
## 9-8 -0.1052994 -0.5214501 0.3108513 0.9946769# Since I have 9 groups here,
# it will be better if you present your results with a visual display.
plot (TukeyHSD(obj_aov_x1, which = 'ADMCON'), cex.axis = 0.5)