Description Usage Arguments Details Value Author(s) References See Also Examples
fechner
provides the Fechnerian scaling computations. It is
the main function of this package.
1 2 |
X |
a required square matrix or data frame of numeric data.
No |
format |
an optional character string giving the data format
that is used. This must be one of |
compute.all |
an optional logical. The default value
|
check.computation |
an optional logical. If |
The format
argument specifies the data format that is used.
"probability.different"
and "percent.same"
are for
datasets in the probability-different and percent-same formats, and
in the latter case, the data are automatically transformed prior to
the analysis using the transformation (100 - X) / 100.
"general"
is to be used for datasets that are properly in the
general data format. Note that for "percent.same"
, the data
must satisfy regular maximality, for "probability.different"
and "general"
, regular minimality (otherwise function
fechner
produces respective messages). In particular, data
in the general format may possibly need to be transformed manually
prior to calling the function fechner
.
If compute.all = TRUE
and check.computation = TRUE
,
the performed check computes the difference ‘overall
Fechnerian distance of the first kind minus overall Fechnerian
distance of the second kind’. By theory, this difference is zero.
The function fechner
calculates that difference and checks
for equality of these Fechnerian distances up to machine precision
(see ‘Value’). fechner
calls
check.regular
, which in turn calls
check.data
. In particular, the specified data format
and regular minimality/maximality are checked, and the rows and
columns of the canonical representation matrix (see
check.regular
) are canonically relabeled based on the
labeling provided by check.data
.
The function fechner
returns an object of the class
fechner
(see ‘Value’), for which plot
,
print
, and summary
methods are provided;
plot.fechner
, print.fechner
, and
summary.fechner
, respectively. Moreover, objects of
the class fechner
are set the specific named attribute
computation
, which is assumed to have the value short
or long
indicating whether short computation
(compute.all = FALSE
) or long computation
(compute.all = TRUE
) was performed, respectively.
If the arguments X
, format
, compute.all
, and
check.computation
are of required types, fechner
returns a named list, of the class fechner
and with the
attribute computation
, which consists of 6 or 18
components, depending on whether short computation
(computation
is then set short
) or long computation
(computation
is then set long
) was performed,
respectively.
The short computation list contains the following first 6 components, the long computation list the subsequent ones:
points.of.subjective.equality |
a data frame giving the
permutation of the columns of |
canonical.representation |
a matrix giving the representation
of |
overall.Fechnerian.distances |
a matrix of the overall Fechnerian distances (of the first kind); by theory, invariant from observation area. |
geodesic.loops |
a data frame of the geodesic loops of the first kind; must be read from left to right for the first kind, and from right to left for the second kind. |
graph.lengths.of.geodesic.loops |
a matrix of the graph-theoretic (edge/link based) lengths of the geodesic loops (of the first kind). |
S.index |
a matrix of the generalized ‘Shepardian’ dissimilarity (or S-index) values. An S-index value is defined as the psychometric length of the loop between a row stimulus and a column stimulus containing only these two stimuli. (last component of short computation list) |
points.of.subjective.equality |
the same as in case of short computation; see above. (first component of long computation list) |
canonical.representation |
the same as in case of short computation; see above. |
psychometric.increments.1 |
a matrix of the psychometric increments of the first kind. |
psychometric.increments.2 |
a matrix of the psychometric increments of the second kind. |
oriented.Fechnerian.distances.1 |
a matrix of the oriented Fechnerian distances of the first kind. |
overall.Fechnerian.distances.1 |
a matrix of the overall Fechnerian distances of the first kind. |
oriented.Fechnerian.distances.2 |
a matrix of the oriented Fechnerian distances of the second kind. |
overall.Fechnerian.distances.2 |
a matrix of the overall Fechnerian distances of the second kind. |
check |
if |
geodesic.chains.1 |
a data frame of the geodesic chains of the first kind. |
geodesic.loops.1 |
a data frame of the geodesic loops of the first kind. |
graph.lengths.of.geodesic.chains.1 |
a matrix of the graph-theoretic (edge/link based) lengths of the geodesic chains of the first kind. |
graph.lengths.of.geodesic.loops.1 |
a matrix of the graph-theoretic (edge/link based) lengths of the geodesic loops of the first kind. |
geodesic.chains.2 |
a data frame of the geodesic chains of the second kind. |
geodesic.loops.2 |
a data frame of the geodesic loops of the second kind. |
graph.lengths.of.geodesic.chains.2 |
a matrix of the graph-theoretic (edge/link based) lengths of the geodesic chains of the second kind. |
graph.lengths.of.geodesic.loops.2 |
a matrix of the graph-theoretic (edge/link based) lengths of the geodesic loops of the second kind. |
S.index |
the same as in case of short computation; see above. (last component of long computation list) |
Thomas Kiefer, Ali Uenlue. Based on original MATLAB source by Ehtibar N. Dzhafarov.
Dzhafarov, E. N. and Colonius, H. (2006) Reconstructing distances among objects from their discriminability. Psychometrika, 71, 365–386.
Dzhafarov, E. N. and Colonius, H. (2007) Dissimilarity cumulation theory and subjective metrics. Journal of Mathematical Psychology, 51, 290–304.
Uenlue, A. and Kiefer, T. and Dzhafarov, E. N. (2009) Fechnerian scaling in R: The package fechner. Journal of Statistical Software, 31(6), 1–24. URL http://www.jstatsoft.org/v31/i06/.
check.data
for checking data format;
check.regular
for checking regular
minimality/maximality; plot.fechner
, the S3 method for
plotting objects of the class fechner
;
print.fechner
, the S3 method for printing objects of
the class fechner
; summary.fechner
, the S3
method for summarizing objects of the class fechner
, which
creates objects of the class summary.fechner
;
print.summary.fechner
, the S3 method for printing
objects of the class summary.fechner
. See also
fechner-package
for general information about this
package.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 | ##
## (1) examples based on dataset \link{morse}
##
## dataset \link{morse} satisfies regular maximality in canonical form
morse
check.regular(morse, type = "percent.same")
## a self-contained 10-code subspace consisting of the codes for the
## letter B and the digits 0, 1, 2, 4, \ldots, 9
indices <- which(is.element(names(morse), c("B", c(0, 1, 2, 4:9))))
f.scal.morse <- fechner(morse, format = "percent.same")
f.scal.morse$geodesic.loops[indices, indices]
morse.subspace <- morse[indices, indices]
check.regular(morse.subspace, type = "percent.same")
## since the subspace is self-contained, results must be the same
f.scal.subspace.mo <- fechner(morse.subspace, format = "percent.same")
identical(f.scal.morse$geodesic.loops[indices, indices],
f.scal.subspace.mo$geodesic.loops)
identical(f.scal.morse$overall.Fechnerian.distances[indices, indices],
f.scal.subspace.mo$overall.Fechnerian.distances)
## Fechnerian scaling analysis using short computation
f.scal.subspace.mo
str(f.scal.subspace.mo)
attributes(f.scal.subspace.mo)
## for instance, the S-index
f.scal.subspace.mo$S.index
## Fechnerian scaling analysis using long computation
f.scal.subspace.long.mo <- fechner(morse.subspace,
format = "percent.same",
compute.all = TRUE,
check.computation = TRUE)
f.scal.subspace.long.mo
str(f.scal.subspace.long.mo)
attributes(f.scal.subspace.long.mo)
## for instance, the geodesic chains of the first kind
f.scal.subspace.long.mo$geodesic.chains.1
## check whether the overall Fechnerian distance of the first kind is
## equal to the overall Fechnerian distance of the second kind
## the difference, by theory a zero matrix
f.scal.subspace.long.mo$check[1]
## or, up to machine precision
f.scal.subspace.long.mo$check[2]
## plot of the S-index versus the overall Fechnerian distance
## for all (off-diagonal) pairs of stimuli
plot(f.scal.subspace.long.mo)
## for all (off-diagonal) pairs of stimuli with geodesic loops
## containing at least 3 links
plot(f.scal.subspace.long.mo, level = 3)
## corresponding summaries, including Pearson correlation and C-index
summary(f.scal.subspace.long.mo)
## in particular, accessing detailed summary through assignment
detailed.summary.mo <- summary(f.scal.subspace.long.mo, level = 3)
str(detailed.summary.mo)
##
## (2) examples based on dataset \link{wish}
##
## dataset \link{wish} satisfies regular minimality in canonical form
wish
check.regular(wish, type = "probability.different")
## a self-contained 10-code subspace consisting of S, U, W, X,
## 0, 1, \ldots, 5
indices <- which(is.element(names(wish), c("S", "U", "W", "X", 0:5)))
f.scal.wish <- fechner(wish, format = "probability.different")
f.scal.wish$geodesic.loops[indices, indices]
wish.subspace <- wish[indices, indices]
check.regular(wish.subspace, type = "probability.different")
## since the subspace is self-contained, results must be the same
f.scal.subspace.wi <- fechner(wish.subspace,
format = "probability.different")
identical(f.scal.wish$geodesic.loops[indices, indices],
f.scal.subspace.wi$geodesic.loops)
identical(f.scal.wish$overall.Fechnerian.distances[indices, indices],
f.scal.subspace.wi$overall.Fechnerian.distances)
## dataset \link{wish} transformed to percent-same format
check.data(100 - (wish * 100), format = "percent.same")
## Fechnerian scaling analysis using short computation
f.scal.subspace.wi
str(f.scal.subspace.wi)
attributes(f.scal.subspace.wi)
## for instance, the graph-theoretic lengths of geodesic loops
f.scal.subspace.wi$graph.lengths.of.geodesic.loops
## Fechnerian scaling analysis using long computation
f.scal.subspace.long.wi <- fechner(wish.subspace,
format = "probability.different",
compute.all = TRUE,
check.computation = TRUE)
f.scal.subspace.long.wi
str(f.scal.subspace.long.wi)
attributes(f.scal.subspace.long.wi)
## for instance, the oriented Fechnerian distances of the first kind
f.scal.subspace.long.wi$oriented.Fechnerian.distances.1
## or, graph-theoretic lengths of chains and loops
identical(f.scal.subspace.long.wi$graph.lengths.of.geodesic.chains.1 +
t(f.scal.subspace.long.wi$graph.lengths.of.geodesic.chains.1),
f.scal.subspace.long.wi$graph.lengths.of.geodesic.loops.1)
## overall Fechnerian distances are not monotonically related to
## discrimination probabilities; however, there is a strong positive
## correlation
cor(as.vector(f.scal.wish$overall.Fechnerian.distances),
as.vector(as.matrix(wish)))
## check whether the overall Fechnerian distance of the first kind is
## equal to the overall Fechnerian distance of the second kind
## the difference, by theory a zero matrix
f.scal.subspace.long.wi$check[1]
## or, up to machine precision
f.scal.subspace.long.wi$check[2]
## plot of the S-index versus the overall Fechnerian distance
## for all (off-diagonal) pairs of stimuli
plot(f.scal.subspace.long.wi)
## for all (off-diagonal) pairs of stimuli with geodesic loops
## containing at least 5 links
plot(f.scal.subspace.long.wi, level = 5)
## corresponding summaries, including Pearson correlation and C-index
summary(f.scal.subspace.long.wi)
## in particular, accessing detailed summary through assignment
detailed.summary.wi <- summary(f.scal.subspace.long.wi, level = 5)
str(detailed.summary.wi)
|
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A 92 4 6 13 3 14 10 13 46 5 22 3 25 34 6 6 9 35 23 6 37 13 17 12 7 3
B 5 84 37 31 5 28 17 21 5 19 34 40 6 10 12 22 25 16 18 2 18 34 8 83 30 42
C 4 38 87 17 4 29 13 7 11 19 24 35 14 3 9 51 34 24 14 6 6 11 14 32 82 38
D 8 62 17 88 7 23 40 36 9 13 81 56 8 7 9 27 9 45 29 6 17 20 27 40 15 33
E 6 13 14 6 97 2 4 4 17 1 5 6 4 4 5 1 5 10 7 67 3 3 2 5 6 5
F 4 51 33 19 2 90 10 29 5 33 16 50 7 6 10 42 12 35 14 2 21 27 25 19 27 13
G 9 18 27 38 1 14 90 6 5 22 33 16 14 13 62 52 23 21 5 3 15 14 32 21 23 39
H 3 45 23 25 9 32 8 87 10 10 9 29 5 8 8 14 8 17 37 4 36 59 9 33 14 11
I 64 7 7 13 10 8 6 12 93 3 5 16 13 30 7 3 5 19 35 16 10 5 8 2 5 7
J 7 9 38 9 2 24 18 5 4 85 22 31 8 3 21 63 47 11 2 7 9 9 9 22 32 28
K 5 24 38 73 1 17 25 11 5 27 91 33 10 12 31 14 31 22 2 2 23 17 33 63 16 18
L 2 69 43 45 10 24 12 26 9 30 27 86 6 2 9 37 36 28 12 5 16 19 20 31 25 59
M 24 12 5 14 7 17 29 8 8 11 23 8 96 62 11 10 15 20 7 9 13 4 21 9 18 8
N 31 4 13 30 8 12 10 16 13 3 16 8 59 93 5 9 5 28 12 10 16 4 12 4 16 11
O 7 7 20 6 5 9 76 7 2 39 26 10 4 8 86 37 35 10 3 4 11 14 25 35 27 27
P 5 22 33 12 5 36 22 12 3 78 14 46 5 6 21 83 43 23 9 4 12 19 19 19 41 30
Q 8 20 38 11 4 15 10 5 2 27 23 26 7 6 22 51 91 11 2 3 6 14 12 37 50 63
R 13 14 16 23 5 34 26 15 7 12 21 33 14 12 12 29 8 87 16 2 23 23 62 14 12 13
S 17 24 5 30 11 26 5 59 16 3 13 10 5 17 6 6 3 18 96 9 56 24 12 10 6 7
T 13 10 1 5 46 3 6 6 14 6 14 7 6 5 6 11 4 4 7 96 8 5 4 2 2 6
U 14 29 12 32 4 32 11 34 21 7 44 32 11 13 6 20 12 40 51 6 93 57 34 17 9 11
V 5 17 24 16 9 29 6 39 5 11 26 43 4 1 9 17 10 17 11 6 32 92 17 57 35 10
W 9 21 30 22 9 36 25 15 4 25 29 18 15 6 26 20 25 61 12 4 19 20 86 22 25 22
X 7 64 45 19 3 28 11 6 1 35 50 42 10 8 24 32 61 10 12 3 12 17 21 91 48 26
Y 9 23 62 15 4 26 22 9 1 30 12 14 5 6 14 30 52 5 7 4 6 13 21 44 86 23
Z 3 46 45 18 2 22 17 10 7 23 21 51 11 2 15 59 72 14 4 3 9 11 12 36 42 87
1 2 5 10 3 3 5 13 4 2 29 5 14 9 7 14 30 28 9 4 2 3 12 14 17 19 22
2 7 14 22 5 4 20 13 3 25 26 9 14 2 3 17 37 28 6 5 3 6 10 11 17 30 13
3 3 8 21 5 4 32 6 12 2 23 6 13 5 2 5 37 19 9 7 6 4 16 6 22 25 12
4 6 19 19 12 8 25 14 16 7 21 13 19 3 3 2 17 29 11 9 3 17 55 8 37 24 3
5 8 45 15 14 2 45 4 67 7 14 4 41 2 0 4 13 7 9 27 2 14 45 7 45 10 10
6 7 80 30 17 4 23 4 14 2 11 11 27 6 2 7 16 30 11 14 3 12 30 9 58 38 39
7 6 33 22 14 5 25 6 4 6 24 13 32 7 6 7 36 39 12 6 2 3 13 9 30 30 50
8 3 23 40 6 3 15 15 6 2 33 10 14 3 6 14 12 45 2 6 4 6 7 5 24 35 50
9 3 14 23 3 1 6 14 5 2 30 6 7 16 11 10 31 32 5 6 7 6 3 8 11 21 24
0 9 3 11 2 5 7 14 4 5 30 8 3 2 3 25 21 29 2 3 4 5 3 2 12 15 20
1 2 3 4 5 6 7 8 9 0
A 2 7 5 5 8 6 5 6 2 3
B 12 17 14 40 32 74 43 17 4 4
C 13 15 31 14 10 30 28 24 18 12
D 3 9 6 11 9 19 8 10 5 6
E 4 3 5 3 5 2 4 2 3 3
F 8 16 47 25 26 24 21 5 5 5
G 15 14 5 10 4 10 17 23 20 11
H 3 9 15 43 70 35 17 4 3 3
I 2 5 8 9 6 8 5 2 4 5
J 67 66 33 15 7 11 28 29 26 23
K 5 9 17 8 8 18 14 13 5 6
L 12 13 17 15 26 29 36 16 7 3
M 5 7 6 6 5 7 11 7 10 4
N 5 2 3 4 4 6 2 2 10 2
O 19 17 7 7 6 18 14 11 20 12
P 34 44 24 11 15 17 24 23 25 13
Q 34 32 17 12 9 27 40 58 37 24
R 7 10 13 4 7 12 7 9 1 2
S 8 2 2 15 28 9 5 5 5 2
T 5 5 3 3 3 8 7 6 14 6
U 6 6 16 34 10 9 9 7 4 3
V 10 14 28 79 44 36 25 10 1 5
W 10 22 19 16 5 9 11 6 3 7
X 12 20 24 27 16 57 29 16 17 6
Y 26 44 40 15 11 26 22 33 23 16
Z 16 21 27 9 10 25 66 47 15 15
1 84 63 13 8 10 8 19 32 57 55
2 62 89 54 20 5 14 20 21 16 11
3 18 64 86 31 23 41 16 17 8 10
4 5 26 44 89 42 44 32 10 3 3
5 14 10 30 69 90 42 24 10 6 5
6 15 14 26 24 17 88 69 14 5 14
7 22 29 18 15 12 61 85 70 20 13
8 42 29 16 16 9 30 60 89 61 26
9 57 39 9 12 4 11 42 56 91 78
0 50 26 9 11 5 22 17 52 81 94
$canonical.representation
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A 92 4 6 13 3 14 10 13 46 5 22 3 25 34 6 6 9 35 23 6 37 13 17 12 7 3
B 5 84 37 31 5 28 17 21 5 19 34 40 6 10 12 22 25 16 18 2 18 34 8 83 30 42
C 4 38 87 17 4 29 13 7 11 19 24 35 14 3 9 51 34 24 14 6 6 11 14 32 82 38
D 8 62 17 88 7 23 40 36 9 13 81 56 8 7 9 27 9 45 29 6 17 20 27 40 15 33
E 6 13 14 6 97 2 4 4 17 1 5 6 4 4 5 1 5 10 7 67 3 3 2 5 6 5
F 4 51 33 19 2 90 10 29 5 33 16 50 7 6 10 42 12 35 14 2 21 27 25 19 27 13
G 9 18 27 38 1 14 90 6 5 22 33 16 14 13 62 52 23 21 5 3 15 14 32 21 23 39
H 3 45 23 25 9 32 8 87 10 10 9 29 5 8 8 14 8 17 37 4 36 59 9 33 14 11
I 64 7 7 13 10 8 6 12 93 3 5 16 13 30 7 3 5 19 35 16 10 5 8 2 5 7
J 7 9 38 9 2 24 18 5 4 85 22 31 8 3 21 63 47 11 2 7 9 9 9 22 32 28
K 5 24 38 73 1 17 25 11 5 27 91 33 10 12 31 14 31 22 2 2 23 17 33 63 16 18
L 2 69 43 45 10 24 12 26 9 30 27 86 6 2 9 37 36 28 12 5 16 19 20 31 25 59
M 24 12 5 14 7 17 29 8 8 11 23 8 96 62 11 10 15 20 7 9 13 4 21 9 18 8
N 31 4 13 30 8 12 10 16 13 3 16 8 59 93 5 9 5 28 12 10 16 4 12 4 16 11
O 7 7 20 6 5 9 76 7 2 39 26 10 4 8 86 37 35 10 3 4 11 14 25 35 27 27
P 5 22 33 12 5 36 22 12 3 78 14 46 5 6 21 83 43 23 9 4 12 19 19 19 41 30
Q 8 20 38 11 4 15 10 5 2 27 23 26 7 6 22 51 91 11 2 3 6 14 12 37 50 63
R 13 14 16 23 5 34 26 15 7 12 21 33 14 12 12 29 8 87 16 2 23 23 62 14 12 13
S 17 24 5 30 11 26 5 59 16 3 13 10 5 17 6 6 3 18 96 9 56 24 12 10 6 7
T 13 10 1 5 46 3 6 6 14 6 14 7 6 5 6 11 4 4 7 96 8 5 4 2 2 6
U 14 29 12 32 4 32 11 34 21 7 44 32 11 13 6 20 12 40 51 6 93 57 34 17 9 11
V 5 17 24 16 9 29 6 39 5 11 26 43 4 1 9 17 10 17 11 6 32 92 17 57 35 10
W 9 21 30 22 9 36 25 15 4 25 29 18 15 6 26 20 25 61 12 4 19 20 86 22 25 22
X 7 64 45 19 3 28 11 6 1 35 50 42 10 8 24 32 61 10 12 3 12 17 21 91 48 26
Y 9 23 62 15 4 26 22 9 1 30 12 14 5 6 14 30 52 5 7 4 6 13 21 44 86 23
Z 3 46 45 18 2 22 17 10 7 23 21 51 11 2 15 59 72 14 4 3 9 11 12 36 42 87
1 2 5 10 3 3 5 13 4 2 29 5 14 9 7 14 30 28 9 4 2 3 12 14 17 19 22
2 7 14 22 5 4 20 13 3 25 26 9 14 2 3 17 37 28 6 5 3 6 10 11 17 30 13
3 3 8 21 5 4 32 6 12 2 23 6 13 5 2 5 37 19 9 7 6 4 16 6 22 25 12
4 6 19 19 12 8 25 14 16 7 21 13 19 3 3 2 17 29 11 9 3 17 55 8 37 24 3
5 8 45 15 14 2 45 4 67 7 14 4 41 2 0 4 13 7 9 27 2 14 45 7 45 10 10
6 7 80 30 17 4 23 4 14 2 11 11 27 6 2 7 16 30 11 14 3 12 30 9 58 38 39
7 6 33 22 14 5 25 6 4 6 24 13 32 7 6 7 36 39 12 6 2 3 13 9 30 30 50
8 3 23 40 6 3 15 15 6 2 33 10 14 3 6 14 12 45 2 6 4 6 7 5 24 35 50
9 3 14 23 3 1 6 14 5 2 30 6 7 16 11 10 31 32 5 6 7 6 3 8 11 21 24
0 9 3 11 2 5 7 14 4 5 30 8 3 2 3 25 21 29 2 3 4 5 3 2 12 15 20
1 2 3 4 5 6 7 8 9 0
A 2 7 5 5 8 6 5 6 2 3
B 12 17 14 40 32 74 43 17 4 4
C 13 15 31 14 10 30 28 24 18 12
D 3 9 6 11 9 19 8 10 5 6
E 4 3 5 3 5 2 4 2 3 3
F 8 16 47 25 26 24 21 5 5 5
G 15 14 5 10 4 10 17 23 20 11
H 3 9 15 43 70 35 17 4 3 3
I 2 5 8 9 6 8 5 2 4 5
J 67 66 33 15 7 11 28 29 26 23
K 5 9 17 8 8 18 14 13 5 6
L 12 13 17 15 26 29 36 16 7 3
M 5 7 6 6 5 7 11 7 10 4
N 5 2 3 4 4 6 2 2 10 2
O 19 17 7 7 6 18 14 11 20 12
P 34 44 24 11 15 17 24 23 25 13
Q 34 32 17 12 9 27 40 58 37 24
R 7 10 13 4 7 12 7 9 1 2
S 8 2 2 15 28 9 5 5 5 2
T 5 5 3 3 3 8 7 6 14 6
U 6 6 16 34 10 9 9 7 4 3
V 10 14 28 79 44 36 25 10 1 5
W 10 22 19 16 5 9 11 6 3 7
X 12 20 24 27 16 57 29 16 17 6
Y 26 44 40 15 11 26 22 33 23 16
Z 16 21 27 9 10 25 66 47 15 15
1 84 63 13 8 10 8 19 32 57 55
2 62 89 54 20 5 14 20 21 16 11
3 18 64 86 31 23 41 16 17 8 10
4 5 26 44 89 42 44 32 10 3 3
5 14 10 30 69 90 42 24 10 6 5
6 15 14 26 24 17 88 69 14 5 14
7 22 29 18 15 12 61 85 70 20 13
8 42 29 16 16 9 30 60 89 61 26
9 57 39 9 12 4 11 42 56 91 78
0 50 26 9 11 5 22 17 52 81 94
$canonical.transformation
observation.area.1 observation.area.2 common.label
1 A A A
2 B B B
3 C C C
4 D D D
5 E E E
6 F F F
7 G G G
8 H H H
9 I I I
10 J J J
11 K K K
12 L L L
13 M M M
14 N N N
15 O O O
16 P P P
17 Q Q Q
18 R R R
19 S S S
20 T T T
21 U U U
22 V V V
23 W W W
24 X X X
25 Y Y Y
26 Z Z Z
27 1 1 1
28 2 2 2
29 3 3 3
30 4 4 4
31 5 5 5
32 6 6 6
33 7 7 7
34 8 8 8
35 9 9 9
36 0 0 0
$check
[1] "regular maximality"
$in.canonical.form
[1] TRUE
B 1 2 4 5 6 7 8 9 0
B B B1B B2B B46B B5B B6B B676B B67876B B6789B B06B
1 1B1 1 121 141 151 161 1781 181 191 101
2 2B2 212 2 242 252 262 272 282 2192 21092
4 46B4 414 424 4 454 46B4 474 4784 494 404
5 5B5 515 525 545 5 56B5 575 585 595 505
6 6B6 616 626 6B46 6B56 6 676 67876 678976 606
7 76B67 7817 727 747 757 767 7 787 7897 789097
8 876B678 818 828 8478 858 87678 878 8 898 8908
9 9B6789 919 9219 949 959 976789 9789 989 9 909
0 06B0 010 09210 040 050 060 097890 0890 090 0
$canonical.representation
B 1 2 4 5 6 7 8 9 0
B 84 12 17 40 32 74 43 17 4 4
1 5 84 63 8 10 8 19 32 57 55
2 14 62 89 20 5 14 20 21 16 11
4 19 5 26 89 42 44 32 10 3 3
5 45 14 10 69 90 42 24 10 6 5
6 80 15 14 24 17 88 69 14 5 14
7 33 22 29 15 12 61 85 70 20 13
8 23 42 29 16 9 30 60 89 61 26
9 14 57 39 12 4 11 42 56 91 78
0 3 50 26 11 5 22 17 52 81 94
$canonical.transformation
observation.area.1 observation.area.2 common.label
1 B B B
2 1 1 1
3 2 2 2
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9
10 0 0 0
$check
[1] "regular maximality"
$in.canonical.form
[1] TRUE
[1] TRUE
[1] TRUE
overall Fechnerian distances:
B 1 2 4 5 6 7 8 9 0
B 0.00 1.51 1.42 0.97 0.97 0.18 0.61 1.05 1.49 1.60
1 1.51 0.00 0.48 1.60 1.50 1.49 1.27 0.99 0.61 0.73
2 1.42 0.48 0.00 1.32 1.64 1.49 1.25 1.28 1.06 1.21
4 0.97 1.60 1.32 0.00 0.68 0.97 1.27 1.45 1.65 1.69
5 0.97 1.50 1.64 0.68 0.00 1.08 1.39 1.60 1.71 1.74
6 0.18 1.49 1.49 0.97 1.08 0.00 0.43 0.87 1.35 1.46
7 0.61 1.27 1.25 1.27 1.39 0.43 0.00 0.44 0.92 1.18
8 1.05 0.99 1.28 1.45 1.60 0.87 0.44 0.00 0.63 0.83
9 1.49 0.61 1.06 1.65 1.71 1.35 0.92 0.63 0.00 0.26
0 1.60 0.73 1.21 1.69 1.74 1.46 1.18 0.83 0.26 0.00
geodesic loops:
B 1 2 4 5 6 7 8 9 0
B B B1B B2B B46B B5B B6B B676B B67876B B6789B B06B
1 1B1 1 121 141 151 161 1781 181 191 101
2 2B2 212 2 242 252 262 272 282 2192 21092
4 46B4 414 424 4 454 46B4 474 4784 494 404
5 5B5 515 525 545 5 56B5 575 585 595 505
6 6B6 616 626 6B46 6B56 6 676 67876 678976 606
7 76B67 7817 727 747 757 767 7 787 7897 789097
8 876B678 818 828 8478 858 87678 878 8 898 8908
9 9B6789 919 9219 949 959 976789 9789 989 9 909
0 06B0 010 09210 040 050 060 097890 0890 090 0
List of 6
$ points.of.subjective.equality :'data.frame': 10 obs. of 3 variables:
..$ observation.area.1: chr [1:10] "B" "1" "2" "4" ...
..$ observation.area.2: chr [1:10] "B" "1" "2" "4" ...
..$ common.label : chr [1:10] "B" "1" "2" "4" ...
$ canonical.representation : num [1:10, 1:10] 0.16 0.95 0.86 0.81 0.55 0.2 0.67 0.77 0.86 0.97 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ overall.Fechnerian.distances : num [1:10, 1:10] 0 1.51 1.42 0.97 0.97 0.18 0.61 1.05 1.49 1.6 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ geodesic.loops :'data.frame': 10 obs. of 10 variables:
..$ B: chr [1:10] "B" "1B1" "2B2" "46B4" ...
..$ 1: chr [1:10] "B1B" "1" "212" "414" ...
..$ 2: chr [1:10] "B2B" "121" "2" "424" ...
..$ 4: chr [1:10] "B46B" "141" "242" "4" ...
..$ 5: chr [1:10] "B5B" "151" "252" "454" ...
..$ 6: chr [1:10] "B6B" "161" "262" "46B4" ...
..$ 7: chr [1:10] "B676B" "1781" "272" "474" ...
..$ 8: chr [1:10] "B67876B" "181" "282" "4784" ...
..$ 9: chr [1:10] "B6789B" "191" "2192" "494" ...
..$ 0: chr [1:10] "B06B" "101" "21092" "404" ...
$ graph.lengths.of.geodesic.loops: num [1:10, 1:10] 0 2 2 3 2 2 4 6 5 3 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ S.index : num [1:10, 1:10] 0 1.51 1.42 1.14 0.97 0.18 0.93 1.33 1.57 1.71 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
- attr(*, "computation")= chr "short"
- attr(*, "class")= chr "fechner"
$names
[1] "points.of.subjective.equality" "canonical.representation"
[3] "overall.Fechnerian.distances" "geodesic.loops"
[5] "graph.lengths.of.geodesic.loops" "S.index"
$computation
[1] "short"
$class
[1] "fechner"
B 1 2 4 5 6 7 8 9 0
B 0.00 1.51 1.42 1.14 0.97 0.18 0.93 1.33 1.57 1.71
1 1.51 0.00 0.48 1.60 1.50 1.49 1.28 0.99 0.61 0.73
2 1.42 0.48 0.00 1.32 1.64 1.49 1.25 1.28 1.25 1.46
4 1.14 1.60 1.32 0.00 0.68 1.09 1.27 1.52 1.65 1.69
5 0.97 1.50 1.64 0.68 0.00 1.19 1.39 1.60 1.71 1.74
6 0.18 1.49 1.49 1.09 1.19 0.00 0.43 1.33 1.63 1.46
7 0.93 1.28 1.25 1.27 1.39 0.43 0.00 0.44 1.14 1.49
8 1.33 0.99 1.28 1.52 1.60 1.33 0.44 0.00 0.63 1.05
9 1.57 0.61 1.25 1.65 1.71 1.63 1.14 0.63 0.00 0.26
0 1.71 0.73 1.46 1.69 1.74 1.46 1.49 1.05 0.26 0.00
overall Fechnerian distances:
B 1 2 4 5 6 7 8 9 0
B 0.00 1.51 1.42 0.97 0.97 0.18 0.61 1.05 1.49 1.60
1 1.51 0.00 0.48 1.60 1.50 1.49 1.27 0.99 0.61 0.73
2 1.42 0.48 0.00 1.32 1.64 1.49 1.25 1.28 1.06 1.21
4 0.97 1.60 1.32 0.00 0.68 0.97 1.27 1.45 1.65 1.69
5 0.97 1.50 1.64 0.68 0.00 1.08 1.39 1.60 1.71 1.74
6 0.18 1.49 1.49 0.97 1.08 0.00 0.43 0.87 1.35 1.46
7 0.61 1.27 1.25 1.27 1.39 0.43 0.00 0.44 0.92 1.18
8 1.05 0.99 1.28 1.45 1.60 0.87 0.44 0.00 0.63 0.83
9 1.49 0.61 1.06 1.65 1.71 1.35 0.92 0.63 0.00 0.26
0 1.60 0.73 1.21 1.69 1.74 1.46 1.18 0.83 0.26 0.00
geodesic loops:
B 1 2 4 5 6 7 8 9 0
B B B1B B2B B46B B5B B6B B676B B67876B B6789B B06B
1 1B1 1 121 141 151 161 1781 181 191 101
2 2B2 212 2 242 252 262 272 282 2192 21092
4 46B4 414 424 4 454 46B4 474 4784 494 404
5 5B5 515 525 545 5 56B5 575 585 595 505
6 6B6 616 626 6B46 6B56 6 676 67876 678976 606
7 76B67 7817 727 747 757 767 7 787 7897 789097
8 876B678 818 828 8478 858 87678 878 8 898 8908
9 9B6789 919 9219 949 959 976789 9789 989 9 909
0 06B0 010 09210 040 050 060 097890 0890 090 0
List of 18
$ points.of.subjective.equality :'data.frame': 10 obs. of 3 variables:
..$ observation.area.1: chr [1:10] "B" "1" "2" "4" ...
..$ observation.area.2: chr [1:10] "B" "1" "2" "4" ...
..$ common.label : chr [1:10] "B" "1" "2" "4" ...
$ canonical.representation : num [1:10, 1:10] 0.16 0.95 0.86 0.81 0.55 0.2 0.67 0.77 0.86 0.97 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ psychometric.increments.1 : num [1:10, 1:10] 0 0.79 0.75 0.7 0.45 0.08 0.52 0.66 0.77 0.91 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ psychometric.increments.2 : num [1:10, 1:10] 0 0.72 0.72 0.49 0.58 0.14 0.42 0.72 0.87 0.9 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ oriented.Fechnerian.distances.1 : num [1:10, 1:10] 0 0.79 0.75 0.53 0.45 0.08 0.32 0.61 0.77 0.8 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ overall.Fechnerian.distances.1 : num [1:10, 1:10] 0 1.51 1.42 0.97 0.97 0.18 0.61 1.05 1.49 1.6 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ oriented.Fechnerian.distances.2 : num [1:10, 1:10] 0 0.72 0.72 0.49 0.58 0.14 0.3 0.49 0.79 0.9 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ overall.Fechnerian.distances.2 : num [1:10, 1:10] 0 1.51 1.42 0.97 0.97 0.18 0.61 1.05 1.49 1.6 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ check :List of 2
..$ difference : num [1:10, 1:10] 0.00 0.00 0.00 -1.11e-16 0.00 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. .. ..$ : chr [1:10] "B" "1" "2" "4" ...
..$ are.nearly.equal: logi TRUE
$ geodesic.chains.1 :'data.frame': 10 obs. of 10 variables:
..$ B: chr [1:10] "B" "1B" "2B" "46B" ...
..$ 1: chr [1:10] "B1" "1" "21" "41" ...
..$ 2: chr [1:10] "B2" "12" "2" "42" ...
..$ 4: chr [1:10] "B4" "14" "24" "4" ...
..$ 5: chr [1:10] "B5" "15" "25" "45" ...
..$ 6: chr [1:10] "B6" "16" "26" "46" ...
..$ 7: chr [1:10] "B67" "17" "27" "47" ...
..$ 8: chr [1:10] "B678" "18" "28" "478" ...
..$ 9: chr [1:10] "B6789" "19" "219" "49" ...
..$ 0: chr [1:10] "B0" "10" "210" "40" ...
$ geodesic.loops.1 :'data.frame': 10 obs. of 10 variables:
..$ B: chr [1:10] "B" "1B1" "2B2" "46B4" ...
..$ 1: chr [1:10] "B1B" "1" "212" "414" ...
..$ 2: chr [1:10] "B2B" "121" "2" "424" ...
..$ 4: chr [1:10] "B46B" "141" "242" "4" ...
..$ 5: chr [1:10] "B5B" "151" "252" "454" ...
..$ 6: chr [1:10] "B6B" "161" "262" "46B4" ...
..$ 7: chr [1:10] "B676B" "1781" "272" "474" ...
..$ 8: chr [1:10] "B67876B" "181" "282" "4784" ...
..$ 9: chr [1:10] "B6789B" "191" "2192" "494" ...
..$ 0: chr [1:10] "B06B" "101" "21092" "404" ...
$ graph.lengths.of.geodesic.chains.1: num [1:10, 1:10] 0 1 1 2 1 1 2 3 1 2 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ graph.lengths.of.geodesic.loops.1 : num [1:10, 1:10] 0 2 2 3 2 2 4 6 5 3 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ geodesic.chains.2 :'data.frame': 10 obs. of 10 variables:
..$ B: chr [1:10] "B" "1B" "2B" "4B" ...
..$ 1: chr [1:10] "B1" "1" "21" "41" ...
..$ 2: chr [1:10] "B2" "12" "2" "42" ...
..$ 4: chr [1:10] "B64" "14" "24" "4" ...
..$ 5: chr [1:10] "B5" "15" "25" "45" ...
..$ 6: chr [1:10] "B6" "16" "26" "4B6" ...
..$ 7: chr [1:10] "B67" "187" "27" "47" ...
..$ 8: chr [1:10] "B678" "18" "28" "48" ...
..$ 9: chr [1:10] "B9" "19" "29" "49" ...
..$ 0: chr [1:10] "B60" "10" "210" "40" ...
$ geodesic.loops.2 :'data.frame': 10 obs. of 10 variables:
..$ B: chr [1:10] "B" "1B1" "2B2" "4B64" ...
..$ 1: chr [1:10] "B1B" "1" "212" "414" ...
..$ 2: chr [1:10] "B2B" "121" "2" "424" ...
..$ 4: chr [1:10] "B64B" "141" "242" "4" ...
..$ 5: chr [1:10] "B5B" "151" "252" "454" ...
..$ 6: chr [1:10] "B6B" "161" "262" "4B64" ...
..$ 7: chr [1:10] "B676B" "1871" "272" "474" ...
..$ 8: chr [1:10] "B67876B" "181" "282" "4874" ...
..$ 9: chr [1:10] "B9876B" "191" "2912" "494" ...
..$ 0: chr [1:10] "B60B" "101" "21012" "404" ...
$ graph.lengths.of.geodesic.chains.2: num [1:10, 1:10] 0 1 1 1 1 1 2 3 4 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ graph.lengths.of.geodesic.loops.2 : num [1:10, 1:10] 0 2 2 3 2 2 4 6 5 3 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
$ S.index : num [1:10, 1:10] 0 1.51 1.42 1.14 0.97 0.18 0.93 1.33 1.57 1.71 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
.. ..$ : chr [1:10] "B" "1" "2" "4" ...
- attr(*, "computation")= chr "long"
- attr(*, "class")= chr "fechner"
$names
[1] "points.of.subjective.equality" "canonical.representation"
[3] "psychometric.increments.1" "psychometric.increments.2"
[5] "oriented.Fechnerian.distances.1" "overall.Fechnerian.distances.1"
[7] "oriented.Fechnerian.distances.2" "overall.Fechnerian.distances.2"
[9] "check" "geodesic.chains.1"
[11] "geodesic.loops.1" "graph.lengths.of.geodesic.chains.1"
[13] "graph.lengths.of.geodesic.loops.1" "geodesic.chains.2"
[15] "geodesic.loops.2" "graph.lengths.of.geodesic.chains.2"
[17] "graph.lengths.of.geodesic.loops.2" "S.index"
$computation
[1] "long"
$class
[1] "fechner"
B 1 2 4 5 6 7 8 9 0
B B B1 B2 B4 B5 B6 B67 B678 B6789 B0
1 1B 1 12 14 15 16 17 18 19 10
2 2B 21 2 24 25 26 27 28 219 210
4 46B 41 42 4 45 46 47 478 49 40
5 5B 51 52 54 5 56 57 58 59 50
6 6B 61 62 6B4 6B5 6 67 678 6789 60
7 76B 781 72 74 75 76 7 78 789 7890
8 876B 81 82 84 85 876 87 8 89 890
9 9B 91 92 94 95 976 97 98 9 90
0 06B 01 092 04 05 06 097 08 09 0
$difference
B 1 2 4 5 6 7 8 9
B 0.000000e+00 0 0 -1.110223e-16 0 0 0.000000e+00 2.220446e-16 2.220446e-16
1 0.000000e+00 0 0 0.000000e+00 0 0 0.000000e+00 0.000000e+00 0.000000e+00
2 0.000000e+00 0 0 0.000000e+00 0 0 0.000000e+00 0.000000e+00 0.000000e+00
4 -1.110223e-16 0 0 0.000000e+00 0 0 0.000000e+00 2.220446e-16 0.000000e+00
5 0.000000e+00 0 0 0.000000e+00 0 0 0.000000e+00 0.000000e+00 0.000000e+00
6 0.000000e+00 0 0 0.000000e+00 0 0 0.000000e+00 0.000000e+00 0.000000e+00
7 0.000000e+00 0 0 0.000000e+00 0 0 0.000000e+00 5.551115e-17 1.110223e-16
8 2.220446e-16 0 0 2.220446e-16 0 0 5.551115e-17 0.000000e+00 -1.110223e-16
9 2.220446e-16 0 0 0.000000e+00 0 0 1.110223e-16 -1.110223e-16 0.000000e+00
0 0.000000e+00 0 0 0.000000e+00 0 0 0.000000e+00 0.000000e+00 0.000000e+00
0
B 0
1 0
2 0
4 0
5 0
6 0
7 0
8 0
9 0
0 0
$are.nearly.equal
[1] TRUE
number of stimuli pairs used for comparison: 45
summary of corresponding S-index values:
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.180 0.990 1.320 1.212 1.510 1.740
summary of corresponding Fechnerian distance G values:
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.18 0.87 1.25 1.14 1.49 1.74
Pearson correlation: 0.9612372
C-index: 0.01198188
comparison level: 2
List of 4
$ pairs.used.for.comparison:'data.frame': 16 obs. of 3 variables:
..$ stimuli.pairs : chr [1:16] "B.4" "4.6" "5.6" "B.7" ...
..$ S.index : num [1:16] 1.14 1.09 1.19 0.93 1.28 1.33 1.52 1.33 1.57 1.25 ...
..$ Fechnerian.distance.G: num [1:16] 0.97 0.97 1.08 0.61 1.27 1.05 1.45 0.87 1.49 1.06 ...
$ Pearson.correlation : num 0.902
$ C.index : num 0.0338
$ comparison.level : num 3
- attr(*, "class")= chr "summary.fechner"
A B C D E F G H I J K L M N O
A 0.03 0.06 0.19 0.34 0.84 0.69 0.96 0.97 0.21 0.82 0.72 0.89 0.99 0.96 0.98
B 0.37 0.02 0.94 0.26 0.09 0.27 0.77 0.84 0.43 0.39 0.51 0.79 0.87 0.91 0.94
C 0.73 0.27 0.06 0.50 0.28 0.38 0.49 0.78 0.58 0.48 0.36 0.51 0.70 0.89 0.84
D 0.53 0.25 0.31 0.04 0.67 0.06 0.33 0.91 0.57 0.87 0.60 0.66 0.89 0.74 0.81
E 0.97 0.60 0.36 0.58 0.06 0.24 0.32 0.30 0.80 0.49 0.27 0.60 0.31 0.51 0.46
F 0.93 0.56 0.67 0.31 0.31 0.05 0.30 0.33 0.81 0.63 0.60 0.44 0.74 0.26 0.73
G 0.99 0.92 0.51 0.50 0.22 0.25 0.07 0.18 0.92 0.86 0.52 0.20 0.77 0.47 0.10
H 0.98 0.90 0.81 0.96 0.69 0.49 0.24 0.03 1.00 0.96 0.88 0.84 0.80 0.50 0.18
I 0.56 0.46 0.38 0.44 0.68 0.59 0.81 0.96 0.06 0.16 0.38 0.46 0.62 0.78 0.93
J 0.97 0.61 0.56 0.85 0.34 0.39 0.71 0.81 0.37 0.06 0.61 0.48 0.23 0.52 0.86
K 0.95 0.84 0.52 0.85 0.41 0.81 0.55 0.72 0.69 0.62 0.05 0.53 0.14 0.64 0.47
L 0.94 0.86 0.80 0.54 0.74 0.49 0.31 0.57 0.53 0.61 0.57 0.06 0.65 0.21 0.27
M 0.98 0.86 0.76 0.91 0.38 0.61 0.73 0.41 0.93 0.46 0.31 0.63 0.06 0.36 0.44
N 0.99 0.97 0.95 0.93 0.78 0.46 0.63 0.44 0.86 0.81 0.77 0.32 0.52 0.02 0.53
O 0.99 0.95 0.90 0.94 0.70 0.72 0.29 0.27 0.92 0.93 0.54 0.43 0.56 0.58 0.07
P 1.00 0.99 0.96 0.97 0.79 0.92 0.65 0.20 1.00 0.96 0.93 0.76 0.45 0.67 0.42
Q 0.58 0.62 0.50 0.52 0.77 0.78 0.81 0.94 0.31 0.47 0.69 0.67 0.91 0.97 0.95
R 0.96 0.91 0.70 0.82 0.58 0.48 0.65 0.71 0.70 0.71 0.86 0.79 0.70 0.78 0.95
S 0.95 0.95 0.57 0.92 0.78 0.76 0.62 0.80 0.90 0.83 0.60 0.69 0.72 0.69 0.76
T 0.99 0.96 0.94 0.74 0.91 0.53 0.69 0.95 0.81 0.64 0.79 0.49 0.94 0.81 0.79
U 0.99 0.98 0.85 0.98 0.68 0.88 0.63 0.50 0.96 0.84 0.79 0.92 0.64 0.71 0.47
V 0.98 0.96 0.94 0.89 0.86 0.39 0.82 0.73 0.98 0.74 0.87 0.78 0.87 0.72 0.83
W 0.99 0.93 0.97 0.95 0.93 0.71 0.57 0.86 0.99 0.95 0.96 0.73 0.87 0.84 0.63
X 1.00 1.00 0.97 1.00 0.92 0.82 0.81 0.36 0.98 0.97 0.91 0.93 0.83 0.78 0.80
Y 0.98 0.95 0.96 0.98 0.94 0.95 0.94 0.88 0.72 0.83 0.85 0.72 0.93 0.93 0.77
Z 1.00 0.99 0.96 0.94 0.88 0.83 0.78 0.74 0.96 0.86 0.80 0.87 0.81 0.71 0.65
0 0.98 0.99 0.90 0.98 0.84 0.93 0.80 0.83 0.97 0.94 0.51 0.77 0.79 0.83 0.61
1 0.99 0.97 0.93 0.94 0.87 0.95 0.72 0.67 0.99 0.95 0.93 0.72 0.94 0.81 0.78
2 1.00 0.98 0.97 0.98 0.94 0.94 0.78 0.67 0.99 0.97 0.86 0.94 0.62 0.91 0.58
3 0.99 0.99 1.00 0.98 0.98 0.93 0.95 0.68 0.99 0.95 0.98 0.90 0.89 0.73 0.72
4 0.99 0.99 0.99 0.99 0.94 0.94 0.74 0.82 0.98 0.97 0.93 0.99 0.92 0.89 0.41
5 1.00 0.98 1.00 0.99 1.00 0.99 0.93 0.91 0.98 0.99 1.00 0.98 0.94 0.95 0.65
P Q R S T U V W X Y Z 0 1 2 3
A 0.99 0.56 0.89 0.95 0.99 1.00 0.98 0.99 0.98 0.98 0.98 1.00 1.00 1.00 0.99
B 1.00 0.56 0.65 0.94 0.96 0.96 0.93 0.97 0.99 0.97 1.00 0.97 0.97 0.95 0.99
C 1.00 0.77 0.78 0.67 0.78 0.86 0.88 0.88 0.96 0.93 0.93 0.88 0.91 0.99 0.95
D 0.98 0.75 0.84 0.83 0.70 1.00 0.95 0.97 0.94 0.97 0.98 1.00 0.93 0.97 0.98
E 0.69 0.78 0.67 0.75 0.83 0.69 0.81 0.88 0.95 0.91 0.81 0.81 0.89 0.94 0.91
F 0.84 0.92 0.73 0.68 0.53 0.83 0.54 0.89 0.94 0.97 0.94 0.95 0.84 0.94 0.94
G 0.67 0.96 0.89 0.53 0.63 0.60 0.73 0.78 0.62 0.90 0.82 0.81 0.62 0.87 0.86
H 0.48 0.95 0.89 0.75 0.91 0.62 0.69 0.77 0.43 0.89 0.69 0.92 0.67 0.69 0.72
I 1.00 0.31 0.57 0.73 0.61 0.90 0.79 0.94 0.99 0.75 0.89 0.97 0.83 1.00 1.00
J 0.93 0.70 0.55 0.78 0.76 0.79 0.66 0.91 0.86 0.80 0.73 0.97 0.92 0.96 0.85
K 0.88 0.81 0.75 0.67 0.76 0.67 0.81 0.79 0.93 0.90 0.86 0.73 0.68 0.89 0.98
L 0.65 0.91 0.82 0.66 0.58 0.85 0.63 0.67 0.84 0.81 0.83 0.81 0.49 0.95 0.66
M 0.59 0.95 0.79 0.81 0.81 0.56 0.71 0.81 0.66 0.96 0.78 0.94 0.87 0.86 0.81
N 0.28 0.97 0.85 0.86 0.75 0.86 0.67 0.59 0.63 0.99 0.94 0.94 0.69 0.85 0.63
O 0.29 0.99 0.90 0.73 0.96 0.64 0.77 0.41 0.50 0.95 0.89 0.68 0.46 0.79 0.56
P 0.06 0.98 0.94 0.93 0.97 0.81 0.86 0.75 0.40 0.98 0.85 0.89 0.69 0.53 0.59
Q 0.99 0.06 0.09 0.41 0.46 0.84 0.55 0.97 0.95 0.59 0.87 0.88 0.73 0.98 0.97
R 0.95 0.44 0.06 0.47 0.43 0.36 0.33 0.77 0.88 0.83 0.66 0.81 0.85 0.82 0.84
S 0.95 0.71 0.47 0.06 0.48 0.16 0.57 0.38 0.45 0.73 0.63 0.35 0.73 0.81 0.70
T 0.96 0.70 0.64 0.65 0.06 0.84 0.07 0.53 0.80 0.84 0.95 0.93 0.40 0.99 0.85
U 0.66 0.86 0.49 0.28 0.81 0.06 0.69 0.44 0.24 0.85 0.40 0.59 0.56 0.49 0.51
V 0.91 0.83 0.44 0.87 0.20 0.87 0.03 0.21 0.32 0.97 0.91 0.92 0.54 0.94 0.33
W 0.58 0.95 0.89 0.44 0.32 0.42 0.43 0.04 0.11 0.96 0.88 0.78 0.40 0.79 0.55
X 0.48 0.99 0.90 0.64 0.72 0.71 0.50 0.26 0.03 0.98 0.85 0.86 0.51 0.73 0.27
Y 0.92 0.56 0.45 0.43 0.81 0.72 0.88 0.81 0.85 0.04 0.22 0.41 0.53 0.92 0.65
Z 0.74 0.96 0.48 0.50 0.88 0.41 0.74 0.81 0.56 0.55 0.03 0.45 0.72 0.33 0.36
0 0.70 0.96 0.83 0.34 0.79 0.55 0.94 0.56 0.46 0.69 0.71 0.06 0.52 0.39 0.69
1 0.75 0.97 0.75 0.84 0.33 0.75 0.48 0.22 0.33 0.74 0.58 0.70 0.03 0.69 0.17
2 0.46 0.97 0.95 0.81 0.92 0.44 0.88 0.62 0.31 0.75 0.54 0.45 0.50 0.07 0.41
3 0.66 0.96 0.92 0.94 0.72 0.85 0.25 0.44 0.17 0.94 0.58 0.85 0.19 0.84 0.02
4 0.53 1.00 0.97 0.89 0.93 0.73 0.92 0.26 0.20 0.95 0.78 0.65 0.38 0.67 0.45
5 0.36 0.97 0.99 1.00 0.99 0.94 0.97 0.74 0.11 0.94 0.91 0.83 0.95 0.58 0.67
4 5
A 0.97 0.98
B 1.00 0.98
C 0.98 0.91
D 0.96 1.00
E 0.94 1.00
F 0.99 0.99
G 0.89 0.94
H 0.86 0.91
I 0.98 0.98
J 0.95 0.97
K 0.94 0.99
L 0.91 1.00
M 0.97 0.89
N 0.82 0.93
O 0.43 0.81
P 0.43 0.44
Q 0.98 1.00
R 0.98 0.97
S 0.89 0.97
T 0.95 0.99
U 0.71 0.69
V 0.88 0.98
W 0.48 0.83
X 0.31 0.44
Y 0.64 0.97
Z 0.87 0.87
0 0.39 0.95
1 0.40 0.97
2 0.35 0.26
3 0.63 0.47
4 0.03 0.49
5 0.25 0.03
$canonical.representation
A B C D E F G H I J K L M N O
A 0.03 0.06 0.19 0.34 0.84 0.69 0.96 0.97 0.21 0.82 0.72 0.89 0.99 0.96 0.98
B 0.37 0.02 0.94 0.26 0.09 0.27 0.77 0.84 0.43 0.39 0.51 0.79 0.87 0.91 0.94
C 0.73 0.27 0.06 0.50 0.28 0.38 0.49 0.78 0.58 0.48 0.36 0.51 0.70 0.89 0.84
D 0.53 0.25 0.31 0.04 0.67 0.06 0.33 0.91 0.57 0.87 0.60 0.66 0.89 0.74 0.81
E 0.97 0.60 0.36 0.58 0.06 0.24 0.32 0.30 0.80 0.49 0.27 0.60 0.31 0.51 0.46
F 0.93 0.56 0.67 0.31 0.31 0.05 0.30 0.33 0.81 0.63 0.60 0.44 0.74 0.26 0.73
G 0.99 0.92 0.51 0.50 0.22 0.25 0.07 0.18 0.92 0.86 0.52 0.20 0.77 0.47 0.10
H 0.98 0.90 0.81 0.96 0.69 0.49 0.24 0.03 1.00 0.96 0.88 0.84 0.80 0.50 0.18
I 0.56 0.46 0.38 0.44 0.68 0.59 0.81 0.96 0.06 0.16 0.38 0.46 0.62 0.78 0.93
J 0.97 0.61 0.56 0.85 0.34 0.39 0.71 0.81 0.37 0.06 0.61 0.48 0.23 0.52 0.86
K 0.95 0.84 0.52 0.85 0.41 0.81 0.55 0.72 0.69 0.62 0.05 0.53 0.14 0.64 0.47
L 0.94 0.86 0.80 0.54 0.74 0.49 0.31 0.57 0.53 0.61 0.57 0.06 0.65 0.21 0.27
M 0.98 0.86 0.76 0.91 0.38 0.61 0.73 0.41 0.93 0.46 0.31 0.63 0.06 0.36 0.44
N 0.99 0.97 0.95 0.93 0.78 0.46 0.63 0.44 0.86 0.81 0.77 0.32 0.52 0.02 0.53
O 0.99 0.95 0.90 0.94 0.70 0.72 0.29 0.27 0.92 0.93 0.54 0.43 0.56 0.58 0.07
P 1.00 0.99 0.96 0.97 0.79 0.92 0.65 0.20 1.00 0.96 0.93 0.76 0.45 0.67 0.42
Q 0.58 0.62 0.50 0.52 0.77 0.78 0.81 0.94 0.31 0.47 0.69 0.67 0.91 0.97 0.95
R 0.96 0.91 0.70 0.82 0.58 0.48 0.65 0.71 0.70 0.71 0.86 0.79 0.70 0.78 0.95
S 0.95 0.95 0.57 0.92 0.78 0.76 0.62 0.80 0.90 0.83 0.60 0.69 0.72 0.69 0.76
T 0.99 0.96 0.94 0.74 0.91 0.53 0.69 0.95 0.81 0.64 0.79 0.49 0.94 0.81 0.79
U 0.99 0.98 0.85 0.98 0.68 0.88 0.63 0.50 0.96 0.84 0.79 0.92 0.64 0.71 0.47
V 0.98 0.96 0.94 0.89 0.86 0.39 0.82 0.73 0.98 0.74 0.87 0.78 0.87 0.72 0.83
W 0.99 0.93 0.97 0.95 0.93 0.71 0.57 0.86 0.99 0.95 0.96 0.73 0.87 0.84 0.63
X 1.00 1.00 0.97 1.00 0.92 0.82 0.81 0.36 0.98 0.97 0.91 0.93 0.83 0.78 0.80
Y 0.98 0.95 0.96 0.98 0.94 0.95 0.94 0.88 0.72 0.83 0.85 0.72 0.93 0.93 0.77
Z 1.00 0.99 0.96 0.94 0.88 0.83 0.78 0.74 0.96 0.86 0.80 0.87 0.81 0.71 0.65
0 0.98 0.99 0.90 0.98 0.84 0.93 0.80 0.83 0.97 0.94 0.51 0.77 0.79 0.83 0.61
1 0.99 0.97 0.93 0.94 0.87 0.95 0.72 0.67 0.99 0.95 0.93 0.72 0.94 0.81 0.78
2 1.00 0.98 0.97 0.98 0.94 0.94 0.78 0.67 0.99 0.97 0.86 0.94 0.62 0.91 0.58
3 0.99 0.99 1.00 0.98 0.98 0.93 0.95 0.68 0.99 0.95 0.98 0.90 0.89 0.73 0.72
4 0.99 0.99 0.99 0.99 0.94 0.94 0.74 0.82 0.98 0.97 0.93 0.99 0.92 0.89 0.41
5 1.00 0.98 1.00 0.99 1.00 0.99 0.93 0.91 0.98 0.99 1.00 0.98 0.94 0.95 0.65
P Q R S T U V W X Y Z 0 1 2 3
A 0.99 0.56 0.89 0.95 0.99 1.00 0.98 0.99 0.98 0.98 0.98 1.00 1.00 1.00 0.99
B 1.00 0.56 0.65 0.94 0.96 0.96 0.93 0.97 0.99 0.97 1.00 0.97 0.97 0.95 0.99
C 1.00 0.77 0.78 0.67 0.78 0.86 0.88 0.88 0.96 0.93 0.93 0.88 0.91 0.99 0.95
D 0.98 0.75 0.84 0.83 0.70 1.00 0.95 0.97 0.94 0.97 0.98 1.00 0.93 0.97 0.98
E 0.69 0.78 0.67 0.75 0.83 0.69 0.81 0.88 0.95 0.91 0.81 0.81 0.89 0.94 0.91
F 0.84 0.92 0.73 0.68 0.53 0.83 0.54 0.89 0.94 0.97 0.94 0.95 0.84 0.94 0.94
G 0.67 0.96 0.89 0.53 0.63 0.60 0.73 0.78 0.62 0.90 0.82 0.81 0.62 0.87 0.86
H 0.48 0.95 0.89 0.75 0.91 0.62 0.69 0.77 0.43 0.89 0.69 0.92 0.67 0.69 0.72
I 1.00 0.31 0.57 0.73 0.61 0.90 0.79 0.94 0.99 0.75 0.89 0.97 0.83 1.00 1.00
J 0.93 0.70 0.55 0.78 0.76 0.79 0.66 0.91 0.86 0.80 0.73 0.97 0.92 0.96 0.85
K 0.88 0.81 0.75 0.67 0.76 0.67 0.81 0.79 0.93 0.90 0.86 0.73 0.68 0.89 0.98
L 0.65 0.91 0.82 0.66 0.58 0.85 0.63 0.67 0.84 0.81 0.83 0.81 0.49 0.95 0.66
M 0.59 0.95 0.79 0.81 0.81 0.56 0.71 0.81 0.66 0.96 0.78 0.94 0.87 0.86 0.81
N 0.28 0.97 0.85 0.86 0.75 0.86 0.67 0.59 0.63 0.99 0.94 0.94 0.69 0.85 0.63
O 0.29 0.99 0.90 0.73 0.96 0.64 0.77 0.41 0.50 0.95 0.89 0.68 0.46 0.79 0.56
P 0.06 0.98 0.94 0.93 0.97 0.81 0.86 0.75 0.40 0.98 0.85 0.89 0.69 0.53 0.59
Q 0.99 0.06 0.09 0.41 0.46 0.84 0.55 0.97 0.95 0.59 0.87 0.88 0.73 0.98 0.97
R 0.95 0.44 0.06 0.47 0.43 0.36 0.33 0.77 0.88 0.83 0.66 0.81 0.85 0.82 0.84
S 0.95 0.71 0.47 0.06 0.48 0.16 0.57 0.38 0.45 0.73 0.63 0.35 0.73 0.81 0.70
T 0.96 0.70 0.64 0.65 0.06 0.84 0.07 0.53 0.80 0.84 0.95 0.93 0.40 0.99 0.85
U 0.66 0.86 0.49 0.28 0.81 0.06 0.69 0.44 0.24 0.85 0.40 0.59 0.56 0.49 0.51
V 0.91 0.83 0.44 0.87 0.20 0.87 0.03 0.21 0.32 0.97 0.91 0.92 0.54 0.94 0.33
W 0.58 0.95 0.89 0.44 0.32 0.42 0.43 0.04 0.11 0.96 0.88 0.78 0.40 0.79 0.55
X 0.48 0.99 0.90 0.64 0.72 0.71 0.50 0.26 0.03 0.98 0.85 0.86 0.51 0.73 0.27
Y 0.92 0.56 0.45 0.43 0.81 0.72 0.88 0.81 0.85 0.04 0.22 0.41 0.53 0.92 0.65
Z 0.74 0.96 0.48 0.50 0.88 0.41 0.74 0.81 0.56 0.55 0.03 0.45 0.72 0.33 0.36
0 0.70 0.96 0.83 0.34 0.79 0.55 0.94 0.56 0.46 0.69 0.71 0.06 0.52 0.39 0.69
1 0.75 0.97 0.75 0.84 0.33 0.75 0.48 0.22 0.33 0.74 0.58 0.70 0.03 0.69 0.17
2 0.46 0.97 0.95 0.81 0.92 0.44 0.88 0.62 0.31 0.75 0.54 0.45 0.50 0.07 0.41
3 0.66 0.96 0.92 0.94 0.72 0.85 0.25 0.44 0.17 0.94 0.58 0.85 0.19 0.84 0.02
4 0.53 1.00 0.97 0.89 0.93 0.73 0.92 0.26 0.20 0.95 0.78 0.65 0.38 0.67 0.45
5 0.36 0.97 0.99 1.00 0.99 0.94 0.97 0.74 0.11 0.94 0.91 0.83 0.95 0.58 0.67
4 5
A 0.97 0.98
B 1.00 0.98
C 0.98 0.91
D 0.96 1.00
E 0.94 1.00
F 0.99 0.99
G 0.89 0.94
H 0.86 0.91
I 0.98 0.98
J 0.95 0.97
K 0.94 0.99
L 0.91 1.00
M 0.97 0.89
N 0.82 0.93
O 0.43 0.81
P 0.43 0.44
Q 0.98 1.00
R 0.98 0.97
S 0.89 0.97
T 0.95 0.99
U 0.71 0.69
V 0.88 0.98
W 0.48 0.83
X 0.31 0.44
Y 0.64 0.97
Z 0.87 0.87
0 0.39 0.95
1 0.40 0.97
2 0.35 0.26
3 0.63 0.47
4 0.03 0.49
5 0.25 0.03
$canonical.transformation
observation.area.1 observation.area.2 common.label
1 A A A
2 B B B
3 C C C
4 D D D
5 E E E
6 F F F
7 G G G
8 H H H
9 I I I
10 J J J
11 K K K
12 L L L
13 M M M
14 N N N
15 O O O
16 P P P
17 Q Q Q
18 R R R
19 S S S
20 T T T
21 U U U
22 V V V
23 W W W
24 X X X
25 Y Y Y
26 Z Z Z
27 0 0 0
28 1 1 1
29 2 2 2
30 3 3 3
31 4 4 4
32 5 5 5
$check
[1] "regular minimality"
$in.canonical.form
[1] TRUE
S U W X 0 1 2 3 4 5
S S SUS SWS SUXS S0S SU1WS SU2US SUX3XS SUX4WS SUX5XS
U USU U UWU UXWU US0SU U1WU U2U UX31WU UX4WU UX5XWU
W WSW WUW W WXW WS0W W1W W2XW WX31W WX4W WX5XW
X XSUX XWUX XWX X X0X X31WX X2X X3X X4X X5X
0 0S0 0SUS0 0WS0 0X0 0 010 020 0130 040 0250
1 1WSU1 1WU1 1W1 1WX31 101 1 121 131 141 135X31
2 2USU2 2U2 2XW2 2X2 202 212 2 232 242 252
3 3XSUX3 31WUX3 31WX3 3X3 3013 313 323 3 3X4X3 35X3
4 4WSUX4 4WUX4 4WX4 4X4 404 414 424 4X3X4 4 454
5 5XSUX5 5XWUX5 5XWX5 5X5 5025 5X3135 525 5X35 545 5
$canonical.representation
S U W X 0 1 2 3 4 5
S 0.06 0.16 0.38 0.45 0.35 0.73 0.81 0.70 0.89 0.97
U 0.28 0.06 0.44 0.24 0.59 0.56 0.49 0.51 0.71 0.69
W 0.44 0.42 0.04 0.11 0.78 0.40 0.79 0.55 0.48 0.83
X 0.64 0.71 0.26 0.03 0.86 0.51 0.73 0.27 0.31 0.44
0 0.34 0.55 0.56 0.46 0.06 0.52 0.39 0.69 0.39 0.95
1 0.84 0.75 0.22 0.33 0.70 0.03 0.69 0.17 0.40 0.97
2 0.81 0.44 0.62 0.31 0.45 0.50 0.07 0.41 0.35 0.26
3 0.94 0.85 0.44 0.17 0.85 0.19 0.84 0.02 0.63 0.47
4 0.89 0.73 0.26 0.20 0.65 0.38 0.67 0.45 0.03 0.49
5 1.00 0.94 0.74 0.11 0.83 0.95 0.58 0.67 0.25 0.03
$canonical.transformation
observation.area.1 observation.area.2 common.label
1 S S S
2 U U U
3 W W W
4 X X X
5 0 0 0
6 1 1 1
7 2 2 2
8 3 3 3
9 4 4 4
10 5 5 5
$check
[1] "regular minimality"
$in.canonical.form
[1] TRUE
[1] TRUE
[1] TRUE
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A 97 94 81 66 16 31 4 3 79 18 28 11 1 4 2 1 44 11 5 1 0 2 1 2 2 2
B 63 98 6 74 91 73 23 16 57 61 49 21 13 9 6 0 44 35 6 4 4 7 3 1 3 0
C 27 73 94 50 72 62 51 22 42 52 64 49 30 11 16 0 23 22 33 22 14 12 12 4 7 7
D 47 75 69 96 33 94 67 9 43 13 40 34 11 26 19 2 25 16 17 30 0 5 3 6 3 2
E 3 40 64 42 94 76 68 70 20 51 73 40 69 49 54 31 22 33 25 17 31 19 12 5 9 19
F 7 44 33 69 69 95 70 67 19 37 40 56 26 74 27 16 8 27 32 47 17 46 11 6 3 6
G 1 8 49 50 78 75 93 82 8 14 48 80 23 53 90 33 4 11 47 37 40 27 22 38 10 18
H 2 10 19 4 31 51 76 97 0 4 12 16 20 50 82 52 5 11 25 9 38 31 23 57 11 31
I 44 54 62 56 32 41 19 4 94 84 62 54 38 22 7 0 69 43 27 39 10 21 6 1 25 11
J 3 39 44 15 66 61 29 19 63 94 39 52 77 48 14 7 30 45 22 24 21 34 9 14 20 27
K 5 16 48 15 59 19 45 28 31 38 95 47 86 36 53 12 19 25 33 24 33 19 21 7 10 14
L 6 14 20 46 26 51 69 43 47 39 43 94 35 79 73 35 9 18 34 42 15 37 33 16 19 17
M 2 14 24 9 62 39 27 59 7 54 69 37 94 64 56 41 5 21 19 19 44 29 19 34 4 22
N 1 3 5 7 22 54 37 56 14 19 23 68 48 98 47 72 3 15 14 25 14 33 41 37 1 6
O 1 5 10 6 30 28 71 73 8 7 46 57 44 42 93 71 1 10 27 4 36 23 59 50 5 11
P 0 1 4 3 21 8 35 80 0 4 7 24 55 33 58 94 2 6 7 3 19 14 25 60 2 15
Q 42 38 50 48 23 22 19 6 69 53 31 33 9 3 5 1 94 91 59 54 16 45 3 5 41 13
R 4 9 30 18 42 52 35 29 30 29 14 21 30 22 5 5 56 94 53 57 64 67 23 12 17 34
S 5 5 43 8 22 24 38 20 10 17 40 31 28 31 24 5 29 53 94 52 84 43 62 55 27 37
T 1 4 6 26 9 47 31 5 19 36 21 51 6 19 21 4 30 36 35 94 16 93 47 20 16 5
U 1 2 15 2 32 12 37 50 4 16 21 8 36 29 53 34 14 51 72 19 94 31 56 76 15 60
V 2 4 6 11 14 61 18 27 2 26 13 22 13 28 17 9 17 56 13 80 13 97 79 68 3 9
W 1 7 3 5 7 29 43 14 1 5 4 27 13 16 37 42 5 11 56 68 58 57 96 89 4 12
X 0 0 3 0 8 18 19 64 2 3 9 7 17 22 20 52 1 10 36 28 29 50 74 97 2 15
Y 2 5 4 2 6 5 6 12 28 17 15 28 7 7 23 8 44 55 57 19 28 12 19 15 96 78
Z 0 1 4 6 12 17 22 26 4 14 20 13 19 29 35 26 4 52 50 12 59 26 19 44 45 97
0 2 1 10 2 16 7 20 17 3 6 49 23 21 17 39 30 4 17 66 21 45 6 44 54 31 29
1 1 3 7 6 13 5 28 33 1 5 7 28 6 19 22 25 3 25 16 67 25 52 78 67 26 42
2 0 2 3 2 6 6 22 33 1 3 14 6 38 9 42 54 3 5 19 8 56 12 38 69 25 46
3 1 1 0 2 2 7 5 32 1 5 2 10 11 27 28 34 4 8 6 28 15 75 56 83 6 42
4 1 1 1 1 6 6 26 18 2 3 7 1 8 11 59 47 0 3 11 7 27 8 74 80 5 22
5 0 2 0 1 0 1 7 9 2 1 0 2 6 5 35 64 3 1 0 1 6 3 26 89 6 9
0 1 2 3 4 5
A 0 0 0 1 3 2
B 3 3 5 1 0 2
C 12 9 1 5 2 9
D 0 7 3 2 4 0
E 19 11 6 9 6 0
F 5 16 6 6 1 1
G 19 38 13 14 11 6
H 8 33 31 28 14 9
I 3 17 0 0 2 2
J 3 8 4 15 5 3
K 27 32 11 2 6 1
L 19 51 5 34 9 0
M 6 13 14 19 3 11
N 6 31 15 37 18 7
O 32 54 21 44 57 19
P 11 31 47 41 57 56
Q 12 27 2 3 2 0
R 19 15 18 16 2 3
S 65 27 19 30 11 3
T 7 60 1 15 5 1
U 41 44 51 49 29 31
V 8 46 6 67 12 2
W 22 60 21 45 52 17
X 14 49 27 73 69 56
Y 59 47 8 35 36 3
Z 55 28 67 64 13 13
0 94 48 61 31 61 5
1 30 97 31 83 60 3
2 55 50 93 59 65 74
3 15 81 16 98 37 53
4 35 62 33 55 97 51
5 17 5 42 33 75 97
overall Fechnerian distances:
S U W X 0 1 2 3 4 5
S 0.00 0.32 0.72 0.89 0.57 1.19 1.12 1.28 1.19 1.38
U 0.32 0.00 0.76 0.79 0.89 1.07 0.80 1.16 1.07 1.28
W 0.72 0.76 0.00 0.30 1.19 0.55 1.22 0.67 0.58 0.79
X 0.89 0.79 0.30 0.00 1.23 0.67 0.94 0.39 0.45 0.49
0 0.57 0.89 1.19 1.23 0.00 1.13 0.71 1.43 0.95 1.32
1 1.19 1.07 0.55 0.67 1.13 0.00 1.09 0.31 0.72 1.08
2 1.12 0.80 1.22 0.94 0.71 1.09 0.00 1.16 0.92 0.74
3 1.28 1.16 0.67 0.39 1.43 0.31 1.16 0.00 0.84 0.77
4 1.19 1.07 0.58 0.45 0.95 0.72 0.92 0.84 0.00 0.68
5 1.38 1.28 0.79 0.49 1.32 1.08 0.74 0.77 0.68 0.00
geodesic loops:
S U W X 0 1 2 3 4 5
S S SUS SWS SUXS S0S SU1WS SU2US SUX3XS SUX4WS SUX5XS
U USU U UWU UXWU US0SU U1WU U2U UX31WU UX4WU UX5XWU
W WSW WUW W WXW WS0W W1W W2XW WX31W WX4W WX5XW
X XSUX XWUX XWX X X0X X31WX X2X X3X X4X X5X
0 0S0 0SUS0 0WS0 0X0 0 010 020 0130 040 0250
1 1WSU1 1WU1 1W1 1WX31 101 1 121 131 141 135X31
2 2USU2 2U2 2XW2 2X2 202 212 2 232 242 252
3 3XSUX3 31WUX3 31WX3 3X3 3013 313 323 3 3X4X3 35X3
4 4WSUX4 4WUX4 4WX4 4X4 404 414 424 4X3X4 4 454
5 5XSUX5 5XWUX5 5XWX5 5X5 5025 5X3135 525 5X35 545 5
List of 6
$ points.of.subjective.equality :'data.frame': 10 obs. of 3 variables:
..$ observation.area.1: chr [1:10] "S" "U" "W" "X" ...
..$ observation.area.2: chr [1:10] "S" "U" "W" "X" ...
..$ common.label : chr [1:10] "S" "U" "W" "X" ...
$ canonical.representation : num [1:10, 1:10] 0.06 0.28 0.44 0.64 0.34 0.84 0.81 0.94 0.89 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ overall.Fechnerian.distances : num [1:10, 1:10] 0 0.32 0.72 0.89 0.57 1.19 1.12 1.28 1.19 1.38 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ geodesic.loops :'data.frame': 10 obs. of 10 variables:
..$ S: chr [1:10] "S" "USU" "WSW" "XSUX" ...
..$ U: chr [1:10] "SUS" "U" "WUW" "XWUX" ...
..$ W: chr [1:10] "SWS" "UWU" "W" "XWX" ...
..$ X: chr [1:10] "SUXS" "UXWU" "WXW" "X" ...
..$ 0: chr [1:10] "S0S" "US0SU" "WS0W" "X0X" ...
..$ 1: chr [1:10] "SU1WS" "U1WU" "W1W" "X31WX" ...
..$ 2: chr [1:10] "SU2US" "U2U" "W2XW" "X2X" ...
..$ 3: chr [1:10] "SUX3XS" "UX31WU" "WX31W" "X3X" ...
..$ 4: chr [1:10] "SUX4WS" "UX4WU" "WX4W" "X4X" ...
..$ 5: chr [1:10] "SUX5XS" "UX5XWU" "WX5XW" "X5X" ...
$ graph.lengths.of.geodesic.loops: num [1:10, 1:10] 0 2 2 3 2 4 4 5 5 5 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ S.index : num [1:10, 1:10] 0 0.32 0.72 1 0.57 1.48 1.49 1.56 1.69 1.88 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
- attr(*, "computation")= chr "short"
- attr(*, "class")= chr "fechner"
$names
[1] "points.of.subjective.equality" "canonical.representation"
[3] "overall.Fechnerian.distances" "geodesic.loops"
[5] "graph.lengths.of.geodesic.loops" "S.index"
$computation
[1] "short"
$class
[1] "fechner"
S U W X 0 1 2 3 4 5
S 0 2 2 3 2 4 4 5 5 5
U 2 0 2 3 4 3 2 5 4 5
W 2 2 0 2 3 2 3 4 3 4
X 3 3 2 0 2 4 2 2 2 2
0 2 4 3 2 0 2 2 3 2 3
1 4 3 2 4 2 0 2 2 2 5
2 4 2 3 2 2 2 0 2 2 2
3 5 5 4 2 3 2 2 0 4 3
4 5 4 3 2 2 2 2 4 0 2
5 5 5 4 2 3 5 2 3 2 0
overall Fechnerian distances:
S U W X 0 1 2 3 4 5
S 0.00 0.32 0.72 0.89 0.57 1.19 1.12 1.28 1.19 1.38
U 0.32 0.00 0.76 0.79 0.89 1.07 0.80 1.16 1.07 1.28
W 0.72 0.76 0.00 0.30 1.19 0.55 1.22 0.67 0.58 0.79
X 0.89 0.79 0.30 0.00 1.23 0.67 0.94 0.39 0.45 0.49
0 0.57 0.89 1.19 1.23 0.00 1.13 0.71 1.43 0.95 1.32
1 1.19 1.07 0.55 0.67 1.13 0.00 1.09 0.31 0.72 1.08
2 1.12 0.80 1.22 0.94 0.71 1.09 0.00 1.16 0.92 0.74
3 1.28 1.16 0.67 0.39 1.43 0.31 1.16 0.00 0.84 0.77
4 1.19 1.07 0.58 0.45 0.95 0.72 0.92 0.84 0.00 0.68
5 1.38 1.28 0.79 0.49 1.32 1.08 0.74 0.77 0.68 0.00
geodesic loops:
S U W X 0 1 2 3 4 5
S S SUS SWS SUXS S0S SU1WS SU2US SUX3XS SUX4WS SUX5XS
U USU U UWU UXWU US0SU U1WU U2U UX31WU UX4WU UX5XWU
W WSW WUW W WXW WS0W W1W W2XW WX31W WX4W WX5XW
X XSUX XWUX XWX X X0X X31WX X2X X3X X4X X5X
0 0S0 0SUS0 0WS0 0X0 0 010 020 0130 040 0250
1 1WSU1 1WU1 1W1 1WX31 101 1 121 131 141 135X31
2 2USU2 2U2 2XW2 2X2 202 212 2 232 242 252
3 3XSUX3 31WUX3 31WX3 3X3 3013 313 323 3 3X4X3 35X3
4 4WSUX4 4WUX4 4WX4 4X4 404 414 424 4X3X4 4 454
5 5XSUX5 5XWUX5 5XWX5 5X5 5025 5X3135 525 5X35 545 5
List of 18
$ points.of.subjective.equality :'data.frame': 10 obs. of 3 variables:
..$ observation.area.1: chr [1:10] "S" "U" "W" "X" ...
..$ observation.area.2: chr [1:10] "S" "U" "W" "X" ...
..$ common.label : chr [1:10] "S" "U" "W" "X" ...
$ canonical.representation : num [1:10, 1:10] 0.06 0.28 0.44 0.64 0.34 0.84 0.81 0.94 0.89 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ psychometric.increments.1 : num [1:10, 1:10] 0 0.22 0.4 0.61 0.28 0.81 0.74 0.92 0.86 0.97 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ psychometric.increments.2 : num [1:10, 1:10] 0 0.1 0.34 0.42 0.29 0.7 0.74 0.68 0.86 0.94 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ oriented.Fechnerian.distances.1 : num [1:10, 1:10] 0 0.22 0.4 0.61 0.28 0.59 0.59 0.76 0.63 0.69 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ overall.Fechnerian.distances.1 : num [1:10, 1:10] 0 0.32 0.72 0.89 0.57 1.19 1.12 1.28 1.19 1.38 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ oriented.Fechnerian.distances.2 : num [1:10, 1:10] 0 0.1 0.34 0.31 0.29 0.63 0.52 0.56 0.59 0.72 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ overall.Fechnerian.distances.2 : num [1:10, 1:10] 0 0.32 0.72 0.89 0.57 1.19 1.12 1.28 1.19 1.38 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ check :List of 2
..$ difference : num [1:10, 1:10] 0.00 0.00 0.00 -1.11e-16 0.00 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. .. ..$ : chr [1:10] "S" "U" "W" "X" ...
..$ are.nearly.equal: logi TRUE
$ geodesic.chains.1 :'data.frame': 10 obs. of 10 variables:
..$ S: chr [1:10] "S" "US" "WS" "XS" ...
..$ U: chr [1:10] "SU" "U" "WU" "XWU" ...
..$ W: chr [1:10] "SW" "UW" "W" "XW" ...
..$ X: chr [1:10] "SUX" "UX" "WX" "X" ...
..$ 0: chr [1:10] "S0" "US0" "WS0" "X0" ...
..$ 1: chr [1:10] "SU1" "U1" "W1" "X31" ...
..$ 2: chr [1:10] "SU2" "U2" "W2" "X2" ...
..$ 3: chr [1:10] "SUX3" "UX3" "WX3" "X3" ...
..$ 4: chr [1:10] "SUX4" "UX4" "WX4" "X4" ...
..$ 5: chr [1:10] "SUX5" "UX5" "WX5" "X5" ...
$ geodesic.loops.1 :'data.frame': 10 obs. of 10 variables:
..$ S: chr [1:10] "S" "USU" "WSW" "XSUX" ...
..$ U: chr [1:10] "SUS" "U" "WUW" "XWUX" ...
..$ W: chr [1:10] "SWS" "UWU" "W" "XWX" ...
..$ X: chr [1:10] "SUXS" "UXWU" "WXW" "X" ...
..$ 0: chr [1:10] "S0S" "US0SU" "WS0W" "X0X" ...
..$ 1: chr [1:10] "SU1WS" "U1WU" "W1W" "X31WX" ...
..$ 2: chr [1:10] "SU2US" "U2U" "W2XW" "X2X" ...
..$ 3: chr [1:10] "SUX3XS" "UX31WU" "WX31W" "X3X" ...
..$ 4: chr [1:10] "SUX4WS" "UX4WU" "WX4W" "X4X" ...
..$ 5: chr [1:10] "SUX5XS" "UX5XWU" "WX5XW" "X5X" ...
$ graph.lengths.of.geodesic.chains.1: num [1:10, 1:10] 0 1 1 1 1 2 2 2 2 2 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ graph.lengths.of.geodesic.loops.1 : num [1:10, 1:10] 0 2 2 3 2 4 4 5 5 5 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ geodesic.chains.2 :'data.frame': 10 obs. of 10 variables:
..$ S: chr [1:10] "S" "US" "WS" "XUS" ...
..$ U: chr [1:10] "SU" "U" "WU" "XU" ...
..$ W: chr [1:10] "SW" "UW" "W" "XW" ...
..$ X: chr [1:10] "SX" "UWX" "WX" "X" ...
..$ 0: chr [1:10] "S0" "US0" "W0" "X0" ...
..$ 1: chr [1:10] "SW1" "UW1" "W1" "XW1" ...
..$ 2: chr [1:10] "SU2" "U2" "WX2" "X2" ...
..$ 3: chr [1:10] "SW13" "UW13" "W13" "X3" ...
..$ 4: chr [1:10] "SW4" "UW4" "W4" "X4" ...
..$ 5: chr [1:10] "SX5" "UWX5" "WX5" "X5" ...
$ geodesic.loops.2 :'data.frame': 10 obs. of 10 variables:
..$ S: chr [1:10] "S" "USU" "WSW" "XUSX" ...
..$ U: chr [1:10] "SUS" "U" "WUW" "XUWX" ...
..$ W: chr [1:10] "SWS" "UWU" "W" "XWX" ...
..$ X: chr [1:10] "SXUS" "UWXU" "WXW" "X" ...
..$ 0: chr [1:10] "S0S" "US0SU" "W0SW" "X0X" ...
..$ 1: chr [1:10] "SW1US" "UW1U" "W1W" "XW13X" ...
..$ 2: chr [1:10] "SU2US" "U2U" "WX2W" "X2X" ...
..$ 3: chr [1:10] "SW13XUS" "UW13XU" "W13XW" "X3X" ...
..$ 4: chr [1:10] "SW4XUS" "UW4XU" "W4XW" "X4X" ...
..$ 5: chr [1:10] "SX5XUS" "UWX5XU" "WX5XW" "X5X" ...
$ graph.lengths.of.geodesic.chains.2: num [1:10, 1:10] 0 1 1 2 1 2 2 3 3 3 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ graph.lengths.of.geodesic.loops.2 : num [1:10, 1:10] 0 2 2 3 2 4 4 6 5 5 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
$ S.index : num [1:10, 1:10] 0 0.32 0.72 1 0.57 1.48 1.49 1.56 1.69 1.88 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
.. ..$ : chr [1:10] "S" "U" "W" "X" ...
- attr(*, "computation")= chr "long"
- attr(*, "class")= chr "fechner"
$names
[1] "points.of.subjective.equality" "canonical.representation"
[3] "psychometric.increments.1" "psychometric.increments.2"
[5] "oriented.Fechnerian.distances.1" "overall.Fechnerian.distances.1"
[7] "oriented.Fechnerian.distances.2" "overall.Fechnerian.distances.2"
[9] "check" "geodesic.chains.1"
[11] "geodesic.loops.1" "graph.lengths.of.geodesic.chains.1"
[13] "graph.lengths.of.geodesic.loops.1" "geodesic.chains.2"
[15] "geodesic.loops.2" "graph.lengths.of.geodesic.chains.2"
[17] "graph.lengths.of.geodesic.loops.2" "S.index"
$computation
[1] "long"
$class
[1] "fechner"
S U W X 0 1 2 3 4 5
S 0.00 0.10 0.32 0.28 0.29 0.60 0.53 0.52 0.56 0.69
U 0.22 0.00 0.38 0.18 0.51 0.50 0.43 0.42 0.46 0.59
W 0.40 0.38 0.00 0.07 0.69 0.36 0.75 0.31 0.35 0.48
X 0.61 0.61 0.23 0.00 0.83 0.41 0.70 0.24 0.28 0.41
0 0.28 0.38 0.50 0.40 0.00 0.46 0.33 0.60 0.33 0.52
1 0.59 0.57 0.19 0.26 0.67 0.00 0.66 0.14 0.37 0.59
2 0.59 0.37 0.47 0.24 0.38 0.43 0.00 0.34 0.28 0.19
3 0.76 0.74 0.36 0.15 0.83 0.17 0.82 0.00 0.43 0.45
4 0.63 0.61 0.23 0.17 0.62 0.35 0.64 0.41 0.00 0.46
5 0.69 0.69 0.31 0.08 0.80 0.49 0.55 0.32 0.22 0.00
[1] TRUE
[1] 0.8857489
$difference
S U W X 0 1
S 0.000000e+00 0.000000e+00 0.000000e+00 -1.110223e-16 0.000000e+00 0
U 0.000000e+00 0.000000e+00 0.000000e+00 1.110223e-16 0.000000e+00 0
W 0.000000e+00 0.000000e+00 0.000000e+00 5.551115e-17 0.000000e+00 0
X -1.110223e-16 1.110223e-16 5.551115e-17 0.000000e+00 0.000000e+00 0
0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0
1 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0
2 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0
3 0.000000e+00 0.000000e+00 1.110223e-16 0.000000e+00 0.000000e+00 0
4 0.000000e+00 2.220446e-16 0.000000e+00 0.000000e+00 -1.110223e-16 0
5 0.000000e+00 2.220446e-16 0.000000e+00 0.000000e+00 -2.220446e-16 0
2 3 4 5
S 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
U 0.000000e+00 0.000000e+00 2.220446e-16 2.220446e-16
W 0.000000e+00 1.110223e-16 0.000000e+00 0.000000e+00
X 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0 0.000000e+00 0.000000e+00 -1.110223e-16 -2.220446e-16
1 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2 0.000000e+00 0.000000e+00 -1.110223e-16 0.000000e+00
3 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4 -1.110223e-16 0.000000e+00 0.000000e+00 0.000000e+00
5 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
$are.nearly.equal
[1] TRUE
number of stimuli pairs used for comparison: 45
summary of corresponding S-index values:
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.300 0.720 1.000 1.019 1.300 1.880
summary of corresponding Fechnerian distance G values:
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.3000 0.6800 0.8900 0.8844 1.1600 1.4300
Pearson correlation: 0.9061073
C-index: 0.05321164
comparison level: 2
List of 4
$ pairs.used.for.comparison:'data.frame': 6 obs. of 3 variables:
..$ stimuli.pairs : chr [1:6] "S.3" "U.3" "S.4" "S.5" ...
..$ S.index : num [1:6] 1.56 1.28 1.69 1.88 1.54 1.86
..$ Fechnerian.distance.G: num [1:6] 1.28 1.16 1.19 1.38 1.28 1.08
$ Pearson.correlation : num 0.143
$ C.index : num 0.0999
$ comparison.level : num 5
- attr(*, "class")= chr "summary.fechner"
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