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Author*Unverified author*
R Software Modulerwasp_pairs.wasp
Title produced by softwareKendall tau Correlation Matrix
Date of computationFri, 11 Dec 2020 17:53:49 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2020/Dec/11/t1607705773j0nia71zu2uiyae.htm/, Retrieved Tue, 23 Apr 2024 07:28:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319315, Retrieved Tue, 23 Apr 2024 07:28:27 +0000
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Original text written by user:
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Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Kendall tau Correlation Matrix] [] [2020-12-11 16:53:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
6	4	7	7	7	7
15	5	13	14	13	11
9	6	6	9	9	6
13	7	11	12	11	12
1	1	1	1	1	1
5	8	4	6	5	5
10	9	15	11	15	15
4	10	5	3	4	4
7	11	8	4	6	10
3	2	2	5	3	2
14	12	14	15	14	9
2	3	3	2	2	3
11	13	10	10	10	13
12	14	12	13	12	8
8	15	9	8	8	14




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319315&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319315&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center







Correlations for all pairs of data series (method=kendall)
ahpdextopsisprometheepapricabaseline
ahp10.3710.7710.8670.8480.581
dex0.37110.4480.3140.3710.486
topsis0.7710.44810.7520.8860.695
promethee0.8670.3140.75210.8670.486
paprica0.8480.3710.8860.86710.619
baseline0.5810.4860.6950.4860.6191

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series (method=kendall) \tabularnewline
  & ahp & dex & topsis & promethee & paprica & baseline \tabularnewline
ahp & 1 & 0.371 & 0.771 & 0.867 & 0.848 & 0.581 \tabularnewline
dex & 0.371 & 1 & 0.448 & 0.314 & 0.371 & 0.486 \tabularnewline
topsis & 0.771 & 0.448 & 1 & 0.752 & 0.886 & 0.695 \tabularnewline
promethee & 0.867 & 0.314 & 0.752 & 1 & 0.867 & 0.486 \tabularnewline
paprica & 0.848 & 0.371 & 0.886 & 0.867 & 1 & 0.619 \tabularnewline
baseline & 0.581 & 0.486 & 0.695 & 0.486 & 0.619 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319315&T=1

[TABLE]
[ROW][C]Correlations for all pairs of data series (method=kendall)[/C][/ROW]
[ROW][C] [/C][C]ahp[/C][C]dex[/C][C]topsis[/C][C]promethee[/C][C]paprica[/C][C]baseline[/C][/ROW]
[ROW][C]ahp[/C][C]1[/C][C]0.371[/C][C]0.771[/C][C]0.867[/C][C]0.848[/C][C]0.581[/C][/ROW]
[ROW][C]dex[/C][C]0.371[/C][C]1[/C][C]0.448[/C][C]0.314[/C][C]0.371[/C][C]0.486[/C][/ROW]
[ROW][C]topsis[/C][C]0.771[/C][C]0.448[/C][C]1[/C][C]0.752[/C][C]0.886[/C][C]0.695[/C][/ROW]
[ROW][C]promethee[/C][C]0.867[/C][C]0.314[/C][C]0.752[/C][C]1[/C][C]0.867[/C][C]0.486[/C][/ROW]
[ROW][C]paprica[/C][C]0.848[/C][C]0.371[/C][C]0.886[/C][C]0.867[/C][C]1[/C][C]0.619[/C][/ROW]
[ROW][C]baseline[/C][C]0.581[/C][C]0.486[/C][C]0.695[/C][C]0.486[/C][C]0.619[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319315&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Correlations for all pairs of data series (method=kendall)
ahpdextopsisprometheepapricabaseline
ahp10.3710.7710.8670.8480.581
dex0.37110.4480.3140.3710.486
topsis0.7710.44810.7520.8860.695
promethee0.8670.3140.75210.8670.486
paprica0.8480.3710.8860.86710.619
baseline0.5810.4860.6950.4860.6191







Correlations for all pairs of data series with p-values
pairPearson rSpearman rhoKendall tau
ahp;dex0.51070.51070.3714
p-value(0.0517)(0.0543)(0.059)
ahp;topsis0.91070.91070.7714
p-value(0)(0)(0)
ahp;promethee0.96070.96070.8667
p-value(0)(0)(0)
ahp;paprica0.93570.93570.8476
p-value(0)(0)(0)
ahp;baseline0.74290.74290.581
p-value(0.0015)(0.0022)(0.0019)
dex;topsis0.59290.59290.4476
p-value(0.0198)(0.0223)(0.0208)
dex;promethee0.450.450.3143
p-value(0.0924)(0.0944)(0.1142)
dex;paprica0.51430.51430.3714
p-value(0.0498)(0.0524)(0.059)
dex;baseline0.64640.64640.4857
p-value(0.0092)(0.0111)(0.0114)
topsis;promethee0.88570.88570.7524
p-value(0)(0)(0)
topsis;paprica0.96790.96790.8857
p-value(0)(0)(0)
topsis;baseline0.84640.84640.6952
p-value(1e-04)(1e-04)(1e-04)
promethee;paprica0.94640.94640.8667
p-value(0)(0)(0)
promethee;baseline0.66430.66430.4857
p-value(0.0069)(0.0086)(0.0114)
paprica;baseline0.78930.78930.619
p-value(5e-04)(7e-04)(8e-04)

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series with p-values \tabularnewline
pair & Pearson r & Spearman rho & Kendall tau \tabularnewline
ahp;dex & 0.5107 & 0.5107 & 0.3714 \tabularnewline
p-value & (0.0517) & (0.0543) & (0.059) \tabularnewline
ahp;topsis & 0.9107 & 0.9107 & 0.7714 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
ahp;promethee & 0.9607 & 0.9607 & 0.8667 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
ahp;paprica & 0.9357 & 0.9357 & 0.8476 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
ahp;baseline & 0.7429 & 0.7429 & 0.581 \tabularnewline
p-value & (0.0015) & (0.0022) & (0.0019) \tabularnewline
dex;topsis & 0.5929 & 0.5929 & 0.4476 \tabularnewline
p-value & (0.0198) & (0.0223) & (0.0208) \tabularnewline
dex;promethee & 0.45 & 0.45 & 0.3143 \tabularnewline
p-value & (0.0924) & (0.0944) & (0.1142) \tabularnewline
dex;paprica & 0.5143 & 0.5143 & 0.3714 \tabularnewline
p-value & (0.0498) & (0.0524) & (0.059) \tabularnewline
dex;baseline & 0.6464 & 0.6464 & 0.4857 \tabularnewline
p-value & (0.0092) & (0.0111) & (0.0114) \tabularnewline
topsis;promethee & 0.8857 & 0.8857 & 0.7524 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
topsis;paprica & 0.9679 & 0.9679 & 0.8857 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
topsis;baseline & 0.8464 & 0.8464 & 0.6952 \tabularnewline
p-value & (1e-04) & (1e-04) & (1e-04) \tabularnewline
promethee;paprica & 0.9464 & 0.9464 & 0.8667 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
promethee;baseline & 0.6643 & 0.6643 & 0.4857 \tabularnewline
p-value & (0.0069) & (0.0086) & (0.0114) \tabularnewline
paprica;baseline & 0.7893 & 0.7893 & 0.619 \tabularnewline
p-value & (5e-04) & (7e-04) & (8e-04) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319315&T=2

[TABLE]
[ROW][C]Correlations for all pairs of data series with p-values[/C][/ROW]
[ROW][C]pair[/C][C]Pearson r[/C][C]Spearman rho[/C][C]Kendall tau[/C][/ROW]
[ROW][C]ahp;dex[/C][C]0.5107[/C][C]0.5107[/C][C]0.3714[/C][/ROW]
[ROW][C]p-value[/C][C](0.0517)[/C][C](0.0543)[/C][C](0.059)[/C][/ROW]
[ROW][C]ahp;topsis[/C][C]0.9107[/C][C]0.9107[/C][C]0.7714[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]ahp;promethee[/C][C]0.9607[/C][C]0.9607[/C][C]0.8667[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]ahp;paprica[/C][C]0.9357[/C][C]0.9357[/C][C]0.8476[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]ahp;baseline[/C][C]0.7429[/C][C]0.7429[/C][C]0.581[/C][/ROW]
[ROW][C]p-value[/C][C](0.0015)[/C][C](0.0022)[/C][C](0.0019)[/C][/ROW]
[ROW][C]dex;topsis[/C][C]0.5929[/C][C]0.5929[/C][C]0.4476[/C][/ROW]
[ROW][C]p-value[/C][C](0.0198)[/C][C](0.0223)[/C][C](0.0208)[/C][/ROW]
[ROW][C]dex;promethee[/C][C]0.45[/C][C]0.45[/C][C]0.3143[/C][/ROW]
[ROW][C]p-value[/C][C](0.0924)[/C][C](0.0944)[/C][C](0.1142)[/C][/ROW]
[ROW][C]dex;paprica[/C][C]0.5143[/C][C]0.5143[/C][C]0.3714[/C][/ROW]
[ROW][C]p-value[/C][C](0.0498)[/C][C](0.0524)[/C][C](0.059)[/C][/ROW]
[ROW][C]dex;baseline[/C][C]0.6464[/C][C]0.6464[/C][C]0.4857[/C][/ROW]
[ROW][C]p-value[/C][C](0.0092)[/C][C](0.0111)[/C][C](0.0114)[/C][/ROW]
[ROW][C]topsis;promethee[/C][C]0.8857[/C][C]0.8857[/C][C]0.7524[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]topsis;paprica[/C][C]0.9679[/C][C]0.9679[/C][C]0.8857[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]topsis;baseline[/C][C]0.8464[/C][C]0.8464[/C][C]0.6952[/C][/ROW]
[ROW][C]p-value[/C][C](1e-04)[/C][C](1e-04)[/C][C](1e-04)[/C][/ROW]
[ROW][C]promethee;paprica[/C][C]0.9464[/C][C]0.9464[/C][C]0.8667[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]promethee;baseline[/C][C]0.6643[/C][C]0.6643[/C][C]0.4857[/C][/ROW]
[ROW][C]p-value[/C][C](0.0069)[/C][C](0.0086)[/C][C](0.0114)[/C][/ROW]
[ROW][C]paprica;baseline[/C][C]0.7893[/C][C]0.7893[/C][C]0.619[/C][/ROW]
[ROW][C]p-value[/C][C](5e-04)[/C][C](7e-04)[/C][C](8e-04)[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319315&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319315&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Correlations for all pairs of data series with p-values
pairPearson rSpearman rhoKendall tau
ahp;dex0.51070.51070.3714
p-value(0.0517)(0.0543)(0.059)
ahp;topsis0.91070.91070.7714
p-value(0)(0)(0)
ahp;promethee0.96070.96070.8667
p-value(0)(0)(0)
ahp;paprica0.93570.93570.8476
p-value(0)(0)(0)
ahp;baseline0.74290.74290.581
p-value(0.0015)(0.0022)(0.0019)
dex;topsis0.59290.59290.4476
p-value(0.0198)(0.0223)(0.0208)
dex;promethee0.450.450.3143
p-value(0.0924)(0.0944)(0.1142)
dex;paprica0.51430.51430.3714
p-value(0.0498)(0.0524)(0.059)
dex;baseline0.64640.64640.4857
p-value(0.0092)(0.0111)(0.0114)
topsis;promethee0.88570.88570.7524
p-value(0)(0)(0)
topsis;paprica0.96790.96790.8857
p-value(0)(0)(0)
topsis;baseline0.84640.84640.6952
p-value(1e-04)(1e-04)(1e-04)
promethee;paprica0.94640.94640.8667
p-value(0)(0)(0)
promethee;baseline0.66430.66430.4857
p-value(0.0069)(0.0086)(0.0114)
paprica;baseline0.78930.78930.619
p-value(5e-04)(7e-04)(8e-04)







Meta Analysis of Correlation Tests
Number of significant by total number of Correlations
Type I errorPearson rSpearman rhoKendall tau
0.010.730.670.6
0.020.80.730.73
0.030.80.80.8
0.040.80.80.8
0.050.870.80.8
0.060.930.930.93
0.070.930.930.93
0.080.930.930.93
0.090.930.930.93
0.1110.93

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Correlation Tests \tabularnewline
Number of significant by total number of Correlations \tabularnewline
Type I error & Pearson r & Spearman rho & Kendall tau \tabularnewline
0.01 & 0.73 & 0.67 & 0.6 \tabularnewline
0.02 & 0.8 & 0.73 & 0.73 \tabularnewline
0.03 & 0.8 & 0.8 & 0.8 \tabularnewline
0.04 & 0.8 & 0.8 & 0.8 \tabularnewline
0.05 & 0.87 & 0.8 & 0.8 \tabularnewline
0.06 & 0.93 & 0.93 & 0.93 \tabularnewline
0.07 & 0.93 & 0.93 & 0.93 \tabularnewline
0.08 & 0.93 & 0.93 & 0.93 \tabularnewline
0.09 & 0.93 & 0.93 & 0.93 \tabularnewline
0.1 & 1 & 1 & 0.93 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319315&T=3

[TABLE]
[ROW][C]Meta Analysis of Correlation Tests[/C][/ROW]
[ROW][C]Number of significant by total number of Correlations[/C][/ROW]
[ROW][C]Type I error[/C][C]Pearson r[/C][C]Spearman rho[/C][C]Kendall tau[/C][/ROW]
[ROW][C]0.01[/C][C]0.73[/C][C]0.67[/C][C]0.6[/C][/ROW]
[ROW][C]0.02[/C][C]0.8[/C][C]0.73[/C][C]0.73[/C][/ROW]
[ROW][C]0.03[/C][C]0.8[/C][C]0.8[/C][C]0.8[/C][/ROW]
[ROW][C]0.04[/C][C]0.8[/C][C]0.8[/C][C]0.8[/C][/ROW]
[ROW][C]0.05[/C][C]0.87[/C][C]0.8[/C][C]0.8[/C][/ROW]
[ROW][C]0.06[/C][C]0.93[/C][C]0.93[/C][C]0.93[/C][/ROW]
[ROW][C]0.07[/C][C]0.93[/C][C]0.93[/C][C]0.93[/C][/ROW]
[ROW][C]0.08[/C][C]0.93[/C][C]0.93[/C][C]0.93[/C][/ROW]
[ROW][C]0.09[/C][C]0.93[/C][C]0.93[/C][C]0.93[/C][/ROW]
[ROW][C]0.1[/C][C]1[/C][C]1[/C][C]0.93[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319315&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319315&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Meta Analysis of Correlation Tests
Number of significant by total number of Correlations
Type I errorPearson rSpearman rhoKendall tau
0.010.730.670.6
0.020.80.730.73
0.030.80.80.8
0.040.80.80.8
0.050.870.80.8
0.060.930.930.93
0.070.930.930.93
0.080.930.930.93
0.090.930.930.93
0.1110.93



Parameters (Session):
par1 = kendall ;
Parameters (R input):
par1 = kendall ;
R code (references can be found in the software module):
par1 <- 'kendall'
panel.tau <- function(x, y, digits=2, prefix='', cex.cor)
{
usr <- par('usr'); on.exit(par(usr))
par(usr = c(0, 1, 0, 1))
rr <- cor.test(x, y, method=par1)
r <- round(rr$p.value,2)
txt <- format(c(r, 0.123456789), digits=digits)[1]
txt <- paste(prefix, txt, sep='')
if(missing(cex.cor)) cex <- 0.5/strwidth(txt)
text(0.5, 0.5, txt, cex = cex)
}
panel.hist <- function(x, ...)
{
usr <- par('usr'); on.exit(par(usr))
par(usr = c(usr[1:2], 0, 1.5) )
h <- hist(x, plot = FALSE)
breaks <- h$breaks; nB <- length(breaks)
y <- h$counts; y <- y/max(y)
rect(breaks[-nB], 0, breaks[-1], y, col='grey', ...)
}
x <- na.omit(x)
y <- t(na.omit(t(y)))
bitmap(file='test1.png')
pairs(t(y),diag.panel=panel.hist, upper.panel=panel.smooth, lower.panel=panel.tau, main=main)
dev.off()
load(file='createtable')
n <- length(y[,1])
print(n)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,paste('Correlations for all pairs of data series (method=',par1,')',sep=''),n+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ',header=TRUE)
for (i in 1:n) {
a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)
}
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)
for (j in 1:n) {
r <- cor.test(y[i,],y[j,],method=par1)
a<-table.element(a,round(r$estimate,3))
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
ncorrs <- (n*n -n)/2
mycorrs <- array(0, dim=c(10,3))
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Correlations for all pairs of data series with p-values',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'pair',1,TRUE)
a<-table.element(a,'Pearson r',1,TRUE)
a<-table.element(a,'Spearman rho',1,TRUE)
a<-table.element(a,'Kendall tau',1,TRUE)
a<-table.row.end(a)
cor.test(y[1,],y[2,],method=par1)
for (i in 1:(n-1))
{
for (j in (i+1):n)
{
a<-table.row.start(a)
dum <- paste(dimnames(t(x))[[2]][i],';',dimnames(t(x))[[2]][j],sep='')
a<-table.element(a,dum,header=TRUE)
rp <- cor.test(y[i,],y[j,],method='pearson')
a<-table.element(a,round(rp$estimate,4))
rs <- cor.test(y[i,],y[j,],method='spearman')
a<-table.element(a,round(rs$estimate,4))
rk <- cor.test(y[i,],y[j,],method='kendall')
a<-table.element(a,round(rk$estimate,4))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=T)
a<-table.element(a,paste('(',round(rp$p.value,4),')',sep=''))
a<-table.element(a,paste('(',round(rs$p.value,4),')',sep=''))
a<-table.element(a,paste('(',round(rk$p.value,4),')',sep=''))
a<-table.row.end(a)
for (iii in 1:10) {
iiid100 <- iii / 100
if (rp$p.value < iiid100) mycorrs[iii, 1] = mycorrs[iii, 1] + 1
if (rs$p.value < iiid100) mycorrs[iii, 2] = mycorrs[iii, 2] + 1
if (rk$p.value < iiid100) mycorrs[iii, 3] = mycorrs[iii, 3] + 1
}
}
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Correlation Tests',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of significant by total number of Correlations',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Type I error',1,TRUE)
a<-table.element(a,'Pearson r',1,TRUE)
a<-table.element(a,'Spearman rho',1,TRUE)
a<-table.element(a,'Kendall tau',1,TRUE)
a<-table.row.end(a)
for (iii in 1:10) {
iiid100 <- iii / 100
a<-table.row.start(a)
a<-table.element(a,round(iiid100,2),header=T)
a<-table.element(a,round(mycorrs[iii,1]/ncorrs,2))
a<-table.element(a,round(mycorrs[iii,2]/ncorrs,2))
a<-table.element(a,round(mycorrs[iii,3]/ncorrs,2))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')