The functions 'toWide()', 'toLong()', and 'toCompiled()' converts the data into various formats.
toWide(w)
toLong(w)
toCompiled(w)An instance of an ANOPA object.
A data frame in the requested format.
The proportions of success of a set of n participants can be given using many formats. In what follows, n is the number of participants, p is the number of between-subject factor(s), $q$ is the number of repeated-measure factor(s).
One basic format, called wide, has one line per
participants, with a 1 if a "success" is observed
or a 0 if no success is observed. What a success is
is entirely arbitrary. The proportion of success is then
the number of 1s divided by the number of participants in each group.
The data frame has $n$ lines and $p+q$ columns.
A second format, called long, has, on a line, the
factor name(s) and 1s or 0s to indicate success or not.
The data fame has $n x q$ lines and
4 columns (a Id column to identify the participant; $p$ columns
to identify the groups, one column to identify which within-subject
measure is given and finally, a 1 or 0 for the score of that measurement.
A third format, called compiled, is to have a list of all
the between-subject factors and the number of
success and the total number of participants.
This format is more compact as if there are 6 groups,
the data are all contained in six lines (one line per group).
This format however is only valid for between-subject design as
we cannot infer the correlation between successes/failure.
See the vignette DataFormatsForProportions for more.
# The minimalBSExample contains $n$ of 175 participants categorized according
# to one factor $f = 1$, namely `State of residency` (with three levels)
# for 3 possible cells.
minimalBSExample
#> state s n
#> 1 Florida 31 57
#> 2 Kentucky 25 73
#> 3 Montana 9 45
# Lets incorporate the data in an ANOPA data structure
w <- anopa( {s;n} ~ state, minimalBSExample )
# The data presented using various formats looks like
toWide(w)
#> state s
#> 1 Florida 1
#> 2 Florida 1
#> 3 Florida 1
#> 4 Florida 1
#> 5 Florida 1
#> 6 Florida 1
#> 7 Florida 1
#> 8 Florida 1
#> 9 Florida 1
#> 10 Florida 1
#> 11 Florida 1
#> 12 Florida 1
#> 13 Florida 1
#> 14 Florida 1
#> 15 Florida 1
#> 16 Florida 1
#> 17 Florida 1
#> 18 Florida 1
#> 19 Florida 1
#> 20 Florida 1
#> 21 Florida 1
#> 22 Florida 1
#> 23 Florida 1
#> 24 Florida 1
#> 25 Florida 1
#> 26 Florida 1
#> 27 Florida 1
#> 28 Florida 1
#> 29 Florida 1
#> 30 Florida 1
#> 31 Florida 1
#> 32 Florida 0
#> 33 Florida 0
#> 34 Florida 0
#> 35 Florida 0
#> 36 Florida 0
#> 37 Florida 0
#> 38 Florida 0
#> 39 Florida 0
#> 40 Florida 0
#> 41 Florida 0
#> 42 Florida 0
#> 43 Florida 0
#> 44 Florida 0
#> 45 Florida 0
#> 46 Florida 0
#> 47 Florida 0
#> 48 Florida 0
#> 49 Florida 0
#> 50 Florida 0
#> 51 Florida 0
#> 52 Florida 0
#> 53 Florida 0
#> 54 Florida 0
#> 55 Florida 0
#> 56 Florida 0
#> 57 Florida 0
#> 58 Kentucky 1
#> 59 Kentucky 1
#> 60 Kentucky 1
#> 61 Kentucky 1
#> 62 Kentucky 1
#> 63 Kentucky 1
#> 64 Kentucky 1
#> 65 Kentucky 1
#> 66 Kentucky 1
#> 67 Kentucky 1
#> 68 Kentucky 1
#> 69 Kentucky 1
#> 70 Kentucky 1
#> 71 Kentucky 1
#> 72 Kentucky 1
#> 73 Kentucky 1
#> 74 Kentucky 1
#> 75 Kentucky 1
#> 76 Kentucky 1
#> 77 Kentucky 1
#> 78 Kentucky 1
#> 79 Kentucky 1
#> 80 Kentucky 1
#> 81 Kentucky 1
#> 82 Kentucky 1
#> 83 Kentucky 0
#> 84 Kentucky 0
#> 85 Kentucky 0
#> 86 Kentucky 0
#> 87 Kentucky 0
#> 88 Kentucky 0
#> 89 Kentucky 0
#> 90 Kentucky 0
#> 91 Kentucky 0
#> 92 Kentucky 0
#> 93 Kentucky 0
#> 94 Kentucky 0
#> 95 Kentucky 0
#> 96 Kentucky 0
#> 97 Kentucky 0
#> 98 Kentucky 0
#> 99 Kentucky 0
#> 100 Kentucky 0
#> 101 Kentucky 0
#> 102 Kentucky 0
#> 103 Kentucky 0
#> 104 Kentucky 0
#> 105 Kentucky 0
#> 106 Kentucky 0
#> 107 Kentucky 0
#> 108 Kentucky 0
#> 109 Kentucky 0
#> 110 Kentucky 0
#> 111 Kentucky 0
#> 112 Kentucky 0
#> 113 Kentucky 0
#> 114 Kentucky 0
#> 115 Kentucky 0
#> 116 Kentucky 0
#> 117 Kentucky 0
#> 118 Kentucky 0
#> 119 Kentucky 0
#> 120 Kentucky 0
#> 121 Kentucky 0
#> 122 Kentucky 0
#> 123 Kentucky 0
#> 124 Kentucky 0
#> 125 Kentucky 0
#> 126 Kentucky 0
#> 127 Kentucky 0
#> 128 Kentucky 0
#> 129 Kentucky 0
#> 130 Kentucky 0
#> 131 Montana 1
#> 132 Montana 1
#> 133 Montana 1
#> 134 Montana 1
#> 135 Montana 1
#> 136 Montana 1
#> 137 Montana 1
#> 138 Montana 1
#> 139 Montana 1
#> 140 Montana 0
#> 141 Montana 0
#> 142 Montana 0
#> 143 Montana 0
#> 144 Montana 0
#> 145 Montana 0
#> 146 Montana 0
#> 147 Montana 0
#> 148 Montana 0
#> 149 Montana 0
#> 150 Montana 0
#> 151 Montana 0
#> 152 Montana 0
#> 153 Montana 0
#> 154 Montana 0
#> 155 Montana 0
#> 156 Montana 0
#> 157 Montana 0
#> 158 Montana 0
#> 159 Montana 0
#> 160 Montana 0
#> 161 Montana 0
#> 162 Montana 0
#> 163 Montana 0
#> 164 Montana 0
#> 165 Montana 0
#> 166 Montana 0
#> 167 Montana 0
#> 168 Montana 0
#> 169 Montana 0
#> 170 Montana 0
#> 171 Montana 0
#> 172 Montana 0
#> 173 Montana 0
#> 174 Montana 0
#> 175 Montana 0
# ... has 175 lines, one per participants ($n$) and 2 columns (state, success or failure)
toLong(w)
#> Id state Variable Value
#> 1.s 1 Florida s 1
#> 2.s 2 Florida s 1
#> 3.s 3 Florida s 1
#> 4.s 4 Florida s 1
#> 5.s 5 Florida s 1
#> 6.s 6 Florida s 1
#> 7.s 7 Florida s 1
#> 8.s 8 Florida s 1
#> 9.s 9 Florida s 1
#> 10.s 10 Florida s 1
#> 11.s 11 Florida s 1
#> 12.s 12 Florida s 1
#> 13.s 13 Florida s 1
#> 14.s 14 Florida s 1
#> 15.s 15 Florida s 1
#> 16.s 16 Florida s 1
#> 17.s 17 Florida s 1
#> 18.s 18 Florida s 1
#> 19.s 19 Florida s 1
#> 20.s 20 Florida s 1
#> 21.s 21 Florida s 1
#> 22.s 22 Florida s 1
#> 23.s 23 Florida s 1
#> 24.s 24 Florida s 1
#> 25.s 25 Florida s 1
#> 26.s 26 Florida s 1
#> 27.s 27 Florida s 1
#> 28.s 28 Florida s 1
#> 29.s 29 Florida s 1
#> 30.s 30 Florida s 1
#> 31.s 31 Florida s 1
#> 32.s 32 Florida s 0
#> 33.s 33 Florida s 0
#> 34.s 34 Florida s 0
#> 35.s 35 Florida s 0
#> 36.s 36 Florida s 0
#> 37.s 37 Florida s 0
#> 38.s 38 Florida s 0
#> 39.s 39 Florida s 0
#> 40.s 40 Florida s 0
#> 41.s 41 Florida s 0
#> 42.s 42 Florida s 0
#> 43.s 43 Florida s 0
#> 44.s 44 Florida s 0
#> 45.s 45 Florida s 0
#> 46.s 46 Florida s 0
#> 47.s 47 Florida s 0
#> 48.s 48 Florida s 0
#> 49.s 49 Florida s 0
#> 50.s 50 Florida s 0
#> 51.s 51 Florida s 0
#> 52.s 52 Florida s 0
#> 53.s 53 Florida s 0
#> 54.s 54 Florida s 0
#> 55.s 55 Florida s 0
#> 56.s 56 Florida s 0
#> 57.s 57 Florida s 0
#> 58.s 58 Kentucky s 1
#> 59.s 59 Kentucky s 1
#> 60.s 60 Kentucky s 1
#> 61.s 61 Kentucky s 1
#> 62.s 62 Kentucky s 1
#> 63.s 63 Kentucky s 1
#> 64.s 64 Kentucky s 1
#> 65.s 65 Kentucky s 1
#> 66.s 66 Kentucky s 1
#> 67.s 67 Kentucky s 1
#> 68.s 68 Kentucky s 1
#> 69.s 69 Kentucky s 1
#> 70.s 70 Kentucky s 1
#> 71.s 71 Kentucky s 1
#> 72.s 72 Kentucky s 1
#> 73.s 73 Kentucky s 1
#> 74.s 74 Kentucky s 1
#> 75.s 75 Kentucky s 1
#> 76.s 76 Kentucky s 1
#> 77.s 77 Kentucky s 1
#> 78.s 78 Kentucky s 1
#> 79.s 79 Kentucky s 1
#> 80.s 80 Kentucky s 1
#> 81.s 81 Kentucky s 1
#> 82.s 82 Kentucky s 1
#> 83.s 83 Kentucky s 0
#> 84.s 84 Kentucky s 0
#> 85.s 85 Kentucky s 0
#> 86.s 86 Kentucky s 0
#> 87.s 87 Kentucky s 0
#> 88.s 88 Kentucky s 0
#> 89.s 89 Kentucky s 0
#> 90.s 90 Kentucky s 0
#> 91.s 91 Kentucky s 0
#> 92.s 92 Kentucky s 0
#> 93.s 93 Kentucky s 0
#> 94.s 94 Kentucky s 0
#> 95.s 95 Kentucky s 0
#> 96.s 96 Kentucky s 0
#> 97.s 97 Kentucky s 0
#> 98.s 98 Kentucky s 0
#> 99.s 99 Kentucky s 0
#> 100.s 100 Kentucky s 0
#> 101.s 101 Kentucky s 0
#> 102.s 102 Kentucky s 0
#> 103.s 103 Kentucky s 0
#> 104.s 104 Kentucky s 0
#> 105.s 105 Kentucky s 0
#> 106.s 106 Kentucky s 0
#> 107.s 107 Kentucky s 0
#> 108.s 108 Kentucky s 0
#> 109.s 109 Kentucky s 0
#> 110.s 110 Kentucky s 0
#> 111.s 111 Kentucky s 0
#> 112.s 112 Kentucky s 0
#> 113.s 113 Kentucky s 0
#> 114.s 114 Kentucky s 0
#> 115.s 115 Kentucky s 0
#> 116.s 116 Kentucky s 0
#> 117.s 117 Kentucky s 0
#> 118.s 118 Kentucky s 0
#> 119.s 119 Kentucky s 0
#> 120.s 120 Kentucky s 0
#> 121.s 121 Kentucky s 0
#> 122.s 122 Kentucky s 0
#> 123.s 123 Kentucky s 0
#> 124.s 124 Kentucky s 0
#> 125.s 125 Kentucky s 0
#> 126.s 126 Kentucky s 0
#> 127.s 127 Kentucky s 0
#> 128.s 128 Kentucky s 0
#> 129.s 129 Kentucky s 0
#> 130.s 130 Kentucky s 0
#> 131.s 131 Montana s 1
#> 132.s 132 Montana s 1
#> 133.s 133 Montana s 1
#> 134.s 134 Montana s 1
#> 135.s 135 Montana s 1
#> 136.s 136 Montana s 1
#> 137.s 137 Montana s 1
#> 138.s 138 Montana s 1
#> 139.s 139 Montana s 1
#> 140.s 140 Montana s 0
#> 141.s 141 Montana s 0
#> 142.s 142 Montana s 0
#> 143.s 143 Montana s 0
#> 144.s 144 Montana s 0
#> 145.s 145 Montana s 0
#> 146.s 146 Montana s 0
#> 147.s 147 Montana s 0
#> 148.s 148 Montana s 0
#> 149.s 149 Montana s 0
#> 150.s 150 Montana s 0
#> 151.s 151 Montana s 0
#> 152.s 152 Montana s 0
#> 153.s 153 Montana s 0
#> 154.s 154 Montana s 0
#> 155.s 155 Montana s 0
#> 156.s 156 Montana s 0
#> 157.s 157 Montana s 0
#> 158.s 158 Montana s 0
#> 159.s 159 Montana s 0
#> 160.s 160 Montana s 0
#> 161.s 161 Montana s 0
#> 162.s 162 Montana s 0
#> 163.s 163 Montana s 0
#> 164.s 164 Montana s 0
#> 165.s 165 Montana s 0
#> 166.s 166 Montana s 0
#> 167.s 167 Montana s 0
#> 168.s 168 Montana s 0
#> 169.s 169 Montana s 0
#> 170.s 170 Montana s 0
#> 171.s 171 Montana s 0
#> 172.s 172 Montana s 0
#> 173.s 173 Montana s 0
#> 174.s 174 Montana s 0
#> 175.s 175 Montana s 0
# ... has 175 lines ($n x f$) and 4 columns (participant's `Id`, state name, measure name,
# and success or failure)
toCompiled(w)
#> state s Count
#> 1 Florida 31 57
#> 2 Kentucky 25 73
#> 3 Montana 9 45
# ... has 3 lines and 3 columns ($f$ + 2: number of succes and number of participants).
# This second example is from a mixed-design. It indicates the
# state of a machine, grouped in three categories (the sole between-subject
# factor) and at four different moments.
# The four measurements times are before treatment, post-treatment,
# 1 week later, and finally, 5 weeks later.
minimalMxExample
#> Status bpre bpost b1week b5week
#> 1 Broken 1 1 1 0
#> 2 Broken 1 1 0 0
#> 3 Broken 0 0 1 1
#> 4 Broken 1 1 1 1
#> 5 Broken 0 0 1 1
#> 6 Broken 1 0 1 1
#> 7 Broken 1 1 0 1
#> 8 Broken 0 1 1 0
#> 9 Repaired 1 1 0 0
#> 10 Repaired 0 1 0 1
#> 11 Repaired 1 1 0 0
#> 12 Repaired 0 0 1 0
#> 13 Repaired 0 0 0 0
#> 14 Repaired 1 0 0 0
#> 15 Repaired 0 0 0 0
#> 16 Repaired 0 0 0 1
#> 17 Repaired 0 0 1 0
#> 18 New 0 0 0 1
#> 19 New 0 0 1 0
#> 20 New 0 0 0 0
#> 21 New 0 0 1 0
#> 22 New 0 0 0 0
#> 23 New 0 1 0 0
#> 24 New 0 0 1 0
#> 25 New 1 1 0 0
#> 26 New 0 0 0 1
#> 27 New 1 1 1 0
# Lets incorporate the data in an ANOPA data structure
w <- anopa( cbind(bpre,bpost,b1week,b5week) ~ Status,
minimalMxExample,
WSFactors = "Moment(4)" )
#> ANOPA::fyi: Here is how the within-subject variables are understood:
#> Moment Variable
#> 1 bpre
#> 2 bpost
#> 3 b1week
#> 4 b5week
# -- Wide format --
# Wide format is actually the format of minimalMxExample
# (27 lines with 8 subjects in the first group and 9 in the second)
toWide(w)
#> Status bpre bpost b1week b5week
#> 1 Broken 1 1 1 0
#> 2 Broken 1 1 0 0
#> 3 Broken 0 0 1 1
#> 4 Broken 1 1 1 1
#> 5 Broken 0 0 1 1
#> 6 Broken 1 0 1 1
#> 7 Broken 1 1 0 1
#> 8 Broken 0 1 1 0
#> 9 Repaired 1 1 0 0
#> 10 Repaired 0 1 0 1
#> 11 Repaired 1 1 0 0
#> 12 Repaired 0 0 1 0
#> 13 Repaired 0 0 0 0
#> 14 Repaired 1 0 0 0
#> 15 Repaired 0 0 0 0
#> 16 Repaired 0 0 0 1
#> 17 Repaired 0 0 1 0
#> 18 New 0 0 0 1
#> 19 New 0 0 1 0
#> 20 New 0 0 0 0
#> 21 New 0 0 1 0
#> 22 New 0 0 0 0
#> 23 New 0 1 0 0
#> 24 New 0 0 1 0
#> 25 New 1 1 0 0
#> 26 New 0 0 0 1
#> 27 New 1 1 1 0
# -- Long format --
# (27 times 4 lines = 108 lines, 4 columns, that is Id, group, measurement, success or failure)
toLong(w)
#> Id Status Variable Value
#> 1.bpre 1 Broken bpre 1
#> 1.bpost 1 Broken bpost 1
#> 1.b1week 1 Broken b1week 1
#> 1.b5week 1 Broken b5week 0
#> 2.bpre 2 Broken bpre 1
#> 2.bpost 2 Broken bpost 1
#> 2.b1week 2 Broken b1week 0
#> 2.b5week 2 Broken b5week 0
#> 3.bpre 3 Broken bpre 0
#> 3.bpost 3 Broken bpost 0
#> 3.b1week 3 Broken b1week 1
#> 3.b5week 3 Broken b5week 1
#> 4.bpre 4 Broken bpre 1
#> 4.bpost 4 Broken bpost 1
#> 4.b1week 4 Broken b1week 1
#> 4.b5week 4 Broken b5week 1
#> 5.bpre 5 Broken bpre 0
#> 5.bpost 5 Broken bpost 0
#> 5.b1week 5 Broken b1week 1
#> 5.b5week 5 Broken b5week 1
#> 6.bpre 6 Broken bpre 1
#> 6.bpost 6 Broken bpost 0
#> 6.b1week 6 Broken b1week 1
#> 6.b5week 6 Broken b5week 1
#> 7.bpre 7 Broken bpre 1
#> 7.bpost 7 Broken bpost 1
#> 7.b1week 7 Broken b1week 0
#> 7.b5week 7 Broken b5week 1
#> 8.bpre 8 Broken bpre 0
#> 8.bpost 8 Broken bpost 1
#> 8.b1week 8 Broken b1week 1
#> 8.b5week 8 Broken b5week 0
#> 9.bpre 9 Repaired bpre 1
#> 9.bpost 9 Repaired bpost 1
#> 9.b1week 9 Repaired b1week 0
#> 9.b5week 9 Repaired b5week 0
#> 10.bpre 10 Repaired bpre 0
#> 10.bpost 10 Repaired bpost 1
#> 10.b1week 10 Repaired b1week 0
#> 10.b5week 10 Repaired b5week 1
#> 11.bpre 11 Repaired bpre 1
#> 11.bpost 11 Repaired bpost 1
#> 11.b1week 11 Repaired b1week 0
#> 11.b5week 11 Repaired b5week 0
#> 12.bpre 12 Repaired bpre 0
#> 12.bpost 12 Repaired bpost 0
#> 12.b1week 12 Repaired b1week 1
#> 12.b5week 12 Repaired b5week 0
#> 13.bpre 13 Repaired bpre 0
#> 13.bpost 13 Repaired bpost 0
#> 13.b1week 13 Repaired b1week 0
#> 13.b5week 13 Repaired b5week 0
#> 14.bpre 14 Repaired bpre 1
#> 14.bpost 14 Repaired bpost 0
#> 14.b1week 14 Repaired b1week 0
#> 14.b5week 14 Repaired b5week 0
#> 15.bpre 15 Repaired bpre 0
#> 15.bpost 15 Repaired bpost 0
#> 15.b1week 15 Repaired b1week 0
#> 15.b5week 15 Repaired b5week 0
#> 16.bpre 16 Repaired bpre 0
#> 16.bpost 16 Repaired bpost 0
#> 16.b1week 16 Repaired b1week 0
#> 16.b5week 16 Repaired b5week 1
#> 17.bpre 17 Repaired bpre 0
#> 17.bpost 17 Repaired bpost 0
#> 17.b1week 17 Repaired b1week 1
#> 17.b5week 17 Repaired b5week 0
#> 18.bpre 18 New bpre 0
#> 18.bpost 18 New bpost 0
#> 18.b1week 18 New b1week 0
#> 18.b5week 18 New b5week 1
#> 19.bpre 19 New bpre 0
#> 19.bpost 19 New bpost 0
#> 19.b1week 19 New b1week 1
#> 19.b5week 19 New b5week 0
#> 20.bpre 20 New bpre 0
#> 20.bpost 20 New bpost 0
#> 20.b1week 20 New b1week 0
#> 20.b5week 20 New b5week 0
#> 21.bpre 21 New bpre 0
#> 21.bpost 21 New bpost 0
#> 21.b1week 21 New b1week 1
#> 21.b5week 21 New b5week 0
#> 22.bpre 22 New bpre 0
#> 22.bpost 22 New bpost 0
#> 22.b1week 22 New b1week 0
#> 22.b5week 22 New b5week 0
#> 23.bpre 23 New bpre 0
#> 23.bpost 23 New bpost 1
#> 23.b1week 23 New b1week 0
#> 23.b5week 23 New b5week 0
#> 24.bpre 24 New bpre 0
#> 24.bpost 24 New bpost 0
#> 24.b1week 24 New b1week 1
#> 24.b5week 24 New b5week 0
#> 25.bpre 25 New bpre 1
#> 25.bpost 25 New bpost 1
#> 25.b1week 25 New b1week 0
#> 25.b5week 25 New b5week 0
#> 26.bpre 26 New bpre 0
#> 26.bpost 26 New bpost 0
#> 26.b1week 26 New b1week 0
#> 26.b5week 26 New b5week 1
#> 27.bpre 27 New bpre 1
#> 27.bpost 27 New bpost 1
#> 27.b1week 27 New b1week 1
#> 27.b5week 27 New b5week 0
# -- Compiled format --
# (three lines as there are three groups, 7 columns, that is,
# the group, the 4 measurements, the number of particpants, and the
# correlation between measurements for each group measured by unitary alphas)
toCompiled(w)
#> Status bpre bpost b1week b5week Count uAlpha
#> 1 Broken 5 5 6 5 8 -0.15204678
#> 2 New 2 3 4 2 10 -0.03463203
#> 3 Repaired 3 3 2 2 9 -0.10416667