TRA is an S3 generic that efficiently transforms data by either (column-wise) replacing data values with supplied statistics or sweeping the statistics out of the data. TRA supports grouped operations and data transformation by reference, and is thus a generalization of sweep.

TRA(x, STATS, FUN = "-", ...)
setTRA(x, STATS, FUN = "-", ...) # Shorthand for invisible(TRA(..., set = TRUE))

# Default S3 method
TRA(x, STATS, FUN = "-", g = NULL, set = FALSE, ...)

# S3 method for class 'matrix'
TRA(x, STATS, FUN = "-", g = NULL, set = FALSE, ...)

# S3 method for class 'data.frame'
TRA(x, STATS, FUN = "-", g = NULL, set = FALSE, ...)

# S3 method for class 'grouped_df'
TRA(x, STATS, FUN = "-", keep.group_vars = TRUE, set = FALSE, ...)

Arguments

x

a atomic vector, matrix, data frame or grouped data frame (class 'grouped_df').

STATS

a matching set of summary statistics. See Details and Examples.

FUN

an integer or character string indicating the operation to perform. There are 11 supported operations:

Int. String Description
0"na" or "replace_na"replace missing values in x
1"fill" or "replace_fill"replace data and missing values in x
2"replace"replace data but preserve missing values in x
3"-"subtract (center on STATS)
4"-+"subtract group-statistics but add group-frequency weighted average of group statistics (i.e. center on overall average statistic)
5"/"divide (i.e. scale. For mean-preserving scaling see also fscale)
6"%"compute percentages (divide and multiply by 100)
7"+"add
8"*"multiply
9"%%"modulus (remainder from division by STATS)
10"-%%"subtract modulus (make data divisible by STATS)

g

a factor, GRP object, atomic vector (internally converted to factor) or a list of vectors / factors (internally converted to a GRP object) used to group x. Number of groups must match rows of STATS. See Details.

set

logical. TRUE transforms data by reference i.e. performs in-place modification of the data without creating a copy.

keep.group_vars

grouped_df method: Logical. FALSE removes grouping variables after computation. See Details and Examples.

...

arguments to be passed to or from other methods.

Details

Without groups (g = NULL), TRA is little more than a column based version of sweep, albeit many times more efficient. In this case all methods support an atomic vector of statistics of length NCOL(x) passed to STATS. The matrix and data frame methods also support a 1-row matrix or 1-row data frame / list, respectively. TRA always preserves all attributes of x.

With groups passed to g, STATS needs to be of the same type as x and of appropriate dimensions [such that NCOL(x) == NCOL(STATS) and NROW(STATS) equals the number of groups (i.e. the number of levels if g is a factor)]. If this condition is satisfied, TRA will assume that the first row of STATS is the set of statistics computed on the first group/level of g, the second row on the second group/level etc. and do groupwise replacing or sweeping out accordingly.

For example Let x = c(1.2, 4.6, 2.5, 9.1, 8.7, 3.3), g is an integer vector in 3 groups g = c(1,3,3,2,1,2) and STATS = fmean(x,g) = c(4.95, 6.20, 3.55). Then out = TRA(x,STATS,"-",g) = c(-3.75, 1.05, -1.05, 2.90, 3.75, -2.90) [same as fmean(x, g, TRA = "-")] does the equivalent of the following for-loop: for(i in 1:6) out[i] = x[i] - STATS[g[i]].

Correct computation requires that g as used in fmean and g passed to TRA are exactly the same vector. Using g = c(1,3,3,2,1,2) for fmean and g = c(3,1,1,2,3,2) for TRA will not give the right result. The safest way of programming with TRA is thus to repeatedly employ the same factor or GRP object for all grouped computations. Atomic vectors passed to g will be converted to factors (see qF) and lists will be converted to GRP objects. This is also done by all Fast Statistical Functions and BY, thus together with these functions, TRA can also safely be used with atomic- or list-groups (as long as all functions apply sorted grouping, which is the default in collapse).

If x is a grouped data frame ('grouped_df'), TRA matches the columns of x and STATS and also checks for grouping columns in x and STATS. TRA.grouped_df will then only transform those columns in x for which matching counterparts were found in STATS (exempting grouping columns) and return x again (with columns in the same order). If keep.group_vars = FALSE, the grouping columns are dropped after computation, however the "groups" attribute is not dropped (it can be removed using fungroup() or dplyr::ungroup()).

Value

x with columns replaced or swept out using STATS, (optionally) grouped by g.

Note

In most cases there is no need to call the TRA() function, because of the TRA-argument to all Fast Statistical Functions (ensuring that the exact same grouping vector is used for computing statistics and subsequent transformation). In addition the functions fbetween/B and fwithin/W and fscale/STD provide optimized solutions for frequent scaling, centering and averaging tasks.

Examples

v <- iris$Sepal.Length          # A numeric vector
f <- iris$Species               # A factor
dat <- num_vars(iris)           # Numeric columns
m <- qM(dat)                    # Matrix of numeric data

head(TRA(v, fmean(v)))                # Simple centering [same as fmean(v, TRA = "-") or W(v)]
#> [1] -0.7433333 -0.9433333 -1.1433333 -1.2433333 -0.8433333 -0.4433333
head(TRA(m, fmean(m)))                # [same as sweep(m, 2, fmean(m)), fmean(m, TRA = "-") or W(m)]
#>      Sepal.Length Sepal.Width Petal.Length Petal.Width
#> [1,]   -0.7433333  0.44266667       -2.358  -0.9993333
#> [2,]   -0.9433333 -0.05733333       -2.358  -0.9993333
#> [3,]   -1.1433333  0.14266667       -2.458  -0.9993333
#> [4,]   -1.2433333  0.04266667       -2.258  -0.9993333
#> [5,]   -0.8433333  0.54266667       -2.358  -0.9993333
#> [6,]   -0.4433333  0.84266667       -2.058  -0.7993333
head(TRA(dat, fmean(dat)))            # [same as fmean(dat, TRA = "-") or W(dat)]
#>   Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 1   -0.7433333  0.44266667       -2.358  -0.9993333
#> 2   -0.9433333 -0.05733333       -2.358  -0.9993333
#> 3   -1.1433333  0.14266667       -2.458  -0.9993333
#> 4   -1.2433333  0.04266667       -2.258  -0.9993333
#> 5   -0.8433333  0.54266667       -2.358  -0.9993333
#> 6   -0.4433333  0.84266667       -2.058  -0.7993333
head(TRA(v, fmean(v), "replace"))     # Simple replacing [same as fmean(v, TRA = "replace") or B(v)]
#> [1] 5.843333 5.843333 5.843333 5.843333 5.843333 5.843333
head(TRA(m, fmean(m), "replace"))     # [same as sweep(m, 2, fmean(m)), fmean(m, TRA = 1L) or B(m)]
#>      Sepal.Length Sepal.Width Petal.Length Petal.Width
#> [1,]     5.843333    3.057333        3.758    1.199333
#> [2,]     5.843333    3.057333        3.758    1.199333
#> [3,]     5.843333    3.057333        3.758    1.199333
#> [4,]     5.843333    3.057333        3.758    1.199333
#> [5,]     5.843333    3.057333        3.758    1.199333
#> [6,]     5.843333    3.057333        3.758    1.199333
head(TRA(dat, fmean(dat), "replace")) # [same as fmean(dat, TRA = "replace") or B(dat)]
#>   Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 1     5.843333    3.057333        3.758    1.199333
#> 2     5.843333    3.057333        3.758    1.199333
#> 3     5.843333    3.057333        3.758    1.199333
#> 4     5.843333    3.057333        3.758    1.199333
#> 5     5.843333    3.057333        3.758    1.199333
#> 6     5.843333    3.057333        3.758    1.199333
head(TRA(m, fsd(m), "/"))             # Simple scaling... [same as fsd(m, TRA = "/")]...
#>      Sepal.Length Sepal.Width Petal.Length Petal.Width
#> [1,]     6.158928    8.029986    0.7930671   0.2623854
#> [2,]     5.917402    6.882845    0.7930671   0.2623854
#> [3,]     5.675875    7.341701    0.7364195   0.2623854
#> [4,]     5.555112    7.112273    0.8497148   0.2623854
#> [5,]     6.038165    8.259414    0.7930671   0.2623854
#> [6,]     6.521218    8.947698    0.9630101   0.5247707

# Note: All grouped examples also apply for v and dat...
head(TRA(m, fmean(m, f), "-", f))       # Centering [same as fmean(m, f, TRA = "-") or W(m, f)]
#>      Sepal.Length Sepal.Width Petal.Length Petal.Width
#> [1,]        0.094       0.072       -0.062      -0.046
#> [2,]       -0.106      -0.428       -0.062      -0.046
#> [3,]       -0.306      -0.228       -0.162      -0.046
#> [4,]       -0.406      -0.328        0.038      -0.046
#> [5,]       -0.006       0.172       -0.062      -0.046
#> [6,]        0.394       0.472        0.238       0.154
head(TRA(m, fmean(m, f), "replace", f)) # Replacing [same fmean(m, f, TRA = "replace") or B(m, f)]
#>      Sepal.Length Sepal.Width Petal.Length Petal.Width
#> [1,]        5.006       3.428        1.462       0.246
#> [2,]        5.006       3.428        1.462       0.246
#> [3,]        5.006       3.428        1.462       0.246
#> [4,]        5.006       3.428        1.462       0.246
#> [5,]        5.006       3.428        1.462       0.246
#> [6,]        5.006       3.428        1.462       0.246
head(TRA(m, fsd(m, f), "/", f))         # Scaling [same as fsd(m, f, TRA = "/")]
#>      Sepal.Length Sepal.Width Petal.Length Petal.Width
#> [1,]     14.46851    9.233260     8.061544    1.897793
#> [2,]     13.90112    7.914223     8.061544    1.897793
#> [3,]     13.33372    8.441838     7.485720    1.897793
#> [4,]     13.05003    8.178031     8.637369    1.897793
#> [5,]     14.18481    9.497068     8.061544    1.897793
#> [6,]     15.31960   10.288490     9.789018    3.795585

head(TRA(m, fmean(m, f), "-+", f))      # Centering on the overall mean ...
#>      Sepal.Length Sepal.Width Petal.Length Petal.Width
#> [1,]     5.937333    3.129333        3.696    1.153333
#> [2,]     5.737333    2.629333        3.696    1.153333
#> [3,]     5.537333    2.829333        3.596    1.153333
#> [4,]     5.437333    2.729333        3.796    1.153333
#> [5,]     5.837333    3.229333        3.696    1.153333
#> [6,]     6.237333    3.529333        3.996    1.353333
                                        # [same as fmean(m, f, TRA = "-+") or
                                        #           W(m, f, mean = "overall.mean")]
head(TRA(TRA(m, fmean(m, f), "-", f),   # Also the same thing done manually !!
     fmean(m), "+"))
#>      Sepal.Length Sepal.Width Petal.Length Petal.Width
#> [1,]     5.937333    3.129333        3.696    1.153333
#> [2,]     5.737333    2.629333        3.696    1.153333
#> [3,]     5.537333    2.829333        3.596    1.153333
#> [4,]     5.437333    2.729333        3.796    1.153333
#> [5,]     5.837333    3.229333        3.696    1.153333
#> [6,]     6.237333    3.529333        3.996    1.353333

# Grouped data method
library(magrittr)
iris %>% fgroup_by(Species) %>% TRA(fmean(.))
#>     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
#> 1          0.094       0.072       -0.062      -0.046     setosa
#> 2         -0.106      -0.428       -0.062      -0.046     setosa
#> 3         -0.306      -0.228       -0.162      -0.046     setosa
#> 4         -0.406      -0.328        0.038      -0.046     setosa
#> 5         -0.006       0.172       -0.062      -0.046     setosa
#> 6          0.394       0.472        0.238       0.154     setosa
#> 7         -0.406      -0.028       -0.062       0.054     setosa
#> 8         -0.006      -0.028        0.038      -0.046     setosa
#> 9         -0.606      -0.528       -0.062      -0.046     setosa
#> 10        -0.106      -0.328        0.038      -0.146     setosa
#> 11         0.394       0.272        0.038      -0.046     setosa
#> 12        -0.206      -0.028        0.138      -0.046     setosa
#> 13        -0.206      -0.428       -0.062      -0.146     setosa
#> 14        -0.706      -0.428       -0.362      -0.146     setosa
#> 15         0.794       0.572       -0.262      -0.046     setosa
#> 16         0.694       0.972        0.038       0.154     setosa
#> 17         0.394       0.472       -0.162       0.154     setosa
#> 18         0.094       0.072       -0.062       0.054     setosa
#> 19         0.694       0.372        0.238       0.054     setosa
#> 20         0.094       0.372        0.038       0.054     setosa
#> 21         0.394      -0.028        0.238      -0.046     setosa
#> 22         0.094       0.272        0.038       0.154     setosa
#> 23        -0.406       0.172       -0.462      -0.046     setosa
#> 24         0.094      -0.128        0.238       0.254     setosa
#> 25        -0.206      -0.028        0.438      -0.046     setosa
#> 26        -0.006      -0.428        0.138      -0.046     setosa
#> 27        -0.006      -0.028        0.138       0.154     setosa
#> 28         0.194       0.072        0.038      -0.046     setosa
#> 29         0.194      -0.028       -0.062      -0.046     setosa
#> 30        -0.306      -0.228        0.138      -0.046     setosa
#> 31        -0.206      -0.328        0.138      -0.046     setosa
#> 32         0.394      -0.028        0.038       0.154     setosa
#> 33         0.194       0.672        0.038      -0.146     setosa
#> 34         0.494       0.772       -0.062      -0.046     setosa
#> 35        -0.106      -0.328        0.038      -0.046     setosa
#> 36        -0.006      -0.228       -0.262      -0.046     setosa
#> 37         0.494       0.072       -0.162      -0.046     setosa
#> 38        -0.106       0.172       -0.062      -0.146     setosa
#> 39        -0.606      -0.428       -0.162      -0.046     setosa
#> 40         0.094      -0.028        0.038      -0.046     setosa
#> 41        -0.006       0.072       -0.162       0.054     setosa
#> 42        -0.506      -1.128       -0.162       0.054     setosa
#> 43        -0.606      -0.228       -0.162      -0.046     setosa
#> 44        -0.006       0.072        0.138       0.354     setosa
#> 45         0.094       0.372        0.438       0.154     setosa
#> 46        -0.206      -0.428       -0.062       0.054     setosa
#> 47         0.094       0.372        0.138      -0.046     setosa
#> 48        -0.406      -0.228       -0.062      -0.046     setosa
#> 49         0.294       0.272        0.038      -0.046     setosa
#> 50        -0.006      -0.128       -0.062      -0.046     setosa
#> 51         1.064       0.430        0.440       0.074 versicolor
#> 52         0.464       0.430        0.240       0.174 versicolor
#> 53         0.964       0.330        0.640       0.174 versicolor
#> 54        -0.436      -0.470       -0.260      -0.026 versicolor
#> 55         0.564       0.030        0.340       0.174 versicolor
#> 56        -0.236       0.030        0.240      -0.026 versicolor
#> 57         0.364       0.530        0.440       0.274 versicolor
#> 58        -1.036      -0.370       -0.960      -0.326 versicolor
#> 59         0.664       0.130        0.340      -0.026 versicolor
#> 60        -0.736      -0.070       -0.360       0.074 versicolor
#> 61        -0.936      -0.770       -0.760      -0.326 versicolor
#> 62        -0.036       0.230       -0.060       0.174 versicolor
#> 63         0.064      -0.570       -0.260      -0.326 versicolor
#> 64         0.164       0.130        0.440       0.074 versicolor
#> 65        -0.336       0.130       -0.660      -0.026 versicolor
#> 66         0.764       0.330        0.140       0.074 versicolor
#> 67        -0.336       0.230        0.240       0.174 versicolor
#> 68        -0.136      -0.070       -0.160      -0.326 versicolor
#> 69         0.264      -0.570        0.240       0.174 versicolor
#> 70        -0.336      -0.270       -0.360      -0.226 versicolor
#> 71        -0.036       0.430        0.540       0.474 versicolor
#> 72         0.164       0.030       -0.260      -0.026 versicolor
#> 73         0.364      -0.270        0.640       0.174 versicolor
#> 74         0.164       0.030        0.440      -0.126 versicolor
#> 75         0.464       0.130        0.040      -0.026 versicolor
#> 76         0.664       0.230        0.140       0.074 versicolor
#> 77         0.864       0.030        0.540       0.074 versicolor
#> 78         0.764       0.230        0.740       0.374 versicolor
#> 79         0.064       0.130        0.240       0.174 versicolor
#> 80        -0.236      -0.170       -0.760      -0.326 versicolor
#> 81        -0.436      -0.370       -0.460      -0.226 versicolor
#> 82        -0.436      -0.370       -0.560      -0.326 versicolor
#> 83        -0.136      -0.070       -0.360      -0.126 versicolor
#> 84         0.064      -0.070        0.840       0.274 versicolor
#> 85        -0.536       0.230        0.240       0.174 versicolor
#> 86         0.064       0.630        0.240       0.274 versicolor
#> 87         0.764       0.330        0.440       0.174 versicolor
#> 88         0.364      -0.470        0.140      -0.026 versicolor
#> 89        -0.336       0.230       -0.160      -0.026 versicolor
#> 90        -0.436      -0.270       -0.260      -0.026 versicolor
#> 91        -0.436      -0.170        0.140      -0.126 versicolor
#> 92         0.164       0.230        0.340       0.074 versicolor
#> 93        -0.136      -0.170       -0.260      -0.126 versicolor
#> 94        -0.936      -0.470       -0.960      -0.326 versicolor
#> 95        -0.336      -0.070       -0.060      -0.026 versicolor
#> 96        -0.236       0.230       -0.060      -0.126 versicolor
#> 97        -0.236       0.130       -0.060      -0.026 versicolor
#> 98         0.264       0.130        0.040      -0.026 versicolor
#> 99        -0.836      -0.270       -1.260      -0.226 versicolor
#> 100       -0.236       0.030       -0.160      -0.026 versicolor
#> 101       -0.288       0.326        0.448       0.474  virginica
#> 102       -0.788      -0.274       -0.452      -0.126  virginica
#> 103        0.512       0.026        0.348       0.074  virginica
#> 104       -0.288      -0.074        0.048      -0.226  virginica
#> 105       -0.088       0.026        0.248       0.174  virginica
#> 106        1.012       0.026        1.048       0.074  virginica
#> 107       -1.688      -0.474       -1.052      -0.326  virginica
#> 108        0.712      -0.074        0.748      -0.226  virginica
#> 109        0.112      -0.474        0.248      -0.226  virginica
#> 110        0.612       0.626        0.548       0.474  virginica
#> 111       -0.088       0.226       -0.452      -0.026  virginica
#> 112       -0.188      -0.274       -0.252      -0.126  virginica
#> 113        0.212       0.026       -0.052       0.074  virginica
#> 114       -0.888      -0.474       -0.552      -0.026  virginica
#> 115       -0.788      -0.174       -0.452       0.374  virginica
#> 116       -0.188       0.226       -0.252       0.274  virginica
#> 117       -0.088       0.026       -0.052      -0.226  virginica
#> 118        1.112       0.826        1.148       0.174  virginica
#> 119        1.112      -0.374        1.348       0.274  virginica
#> 120       -0.588      -0.774       -0.552      -0.526  virginica
#> 121        0.312       0.226        0.148       0.274  virginica
#> 122       -0.988      -0.174       -0.652      -0.026  virginica
#> 123        1.112      -0.174        1.148      -0.026  virginica
#> 124       -0.288      -0.274       -0.652      -0.226  virginica
#> 125        0.112       0.326        0.148       0.074  virginica
#> 126        0.612       0.226        0.448      -0.226  virginica
#> 127       -0.388      -0.174       -0.752      -0.226  virginica
#> 128       -0.488       0.026       -0.652      -0.226  virginica
#> 129       -0.188      -0.174        0.048       0.074  virginica
#> 130        0.612       0.026        0.248      -0.426  virginica
#> 131        0.812      -0.174        0.548      -0.126  virginica
#> 132        1.312       0.826        0.848      -0.026  virginica
#> 133       -0.188      -0.174        0.048       0.174  virginica
#> 134       -0.288      -0.174       -0.452      -0.526  virginica
#> 135       -0.488      -0.374        0.048      -0.626  virginica
#> 136        1.112       0.026        0.548       0.274  virginica
#> 137       -0.288       0.426        0.048       0.374  virginica
#> 138       -0.188       0.126       -0.052      -0.226  virginica
#> 139       -0.588       0.026       -0.752      -0.226  virginica
#> 140        0.312       0.126       -0.152       0.074  virginica
#> 141        0.112       0.126        0.048       0.374  virginica
#> 142        0.312       0.126       -0.452       0.274  virginica
#> 143       -0.788      -0.274       -0.452      -0.126  virginica
#> 144        0.212       0.226        0.348       0.274  virginica
#> 145        0.112       0.326        0.148       0.474  virginica
#> 146        0.112       0.026       -0.352       0.274  virginica
#> 147       -0.288      -0.474       -0.552      -0.126  virginica
#> 148       -0.088       0.026       -0.352      -0.026  virginica
#> 149       -0.388       0.426       -0.152       0.274  virginica
#> 150       -0.688       0.026       -0.452      -0.226  virginica
#> 
#> Grouped by:  Species  [3 | 50 (0)] 
iris %>% fgroup_by(Species) %>% fmean(TRA = "-")        # Same thing
#>        Species Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 1       setosa        0.094       0.072       -0.062      -0.046
#> 2       setosa       -0.106      -0.428       -0.062      -0.046
#> 3       setosa       -0.306      -0.228       -0.162      -0.046
#> 4       setosa       -0.406      -0.328        0.038      -0.046
#> 5       setosa       -0.006       0.172       -0.062      -0.046
#> 6       setosa        0.394       0.472        0.238       0.154
#> 7       setosa       -0.406      -0.028       -0.062       0.054
#> 8       setosa       -0.006      -0.028        0.038      -0.046
#> 9       setosa       -0.606      -0.528       -0.062      -0.046
#> 10      setosa       -0.106      -0.328        0.038      -0.146
#> 11      setosa        0.394       0.272        0.038      -0.046
#> 12      setosa       -0.206      -0.028        0.138      -0.046
#> 13      setosa       -0.206      -0.428       -0.062      -0.146
#> 14      setosa       -0.706      -0.428       -0.362      -0.146
#> 15      setosa        0.794       0.572       -0.262      -0.046
#> 16      setosa        0.694       0.972        0.038       0.154
#> 17      setosa        0.394       0.472       -0.162       0.154
#> 18      setosa        0.094       0.072       -0.062       0.054
#> 19      setosa        0.694       0.372        0.238       0.054
#> 20      setosa        0.094       0.372        0.038       0.054
#> 21      setosa        0.394      -0.028        0.238      -0.046
#> 22      setosa        0.094       0.272        0.038       0.154
#> 23      setosa       -0.406       0.172       -0.462      -0.046
#> 24      setosa        0.094      -0.128        0.238       0.254
#> 25      setosa       -0.206      -0.028        0.438      -0.046
#> 26      setosa       -0.006      -0.428        0.138      -0.046
#> 27      setosa       -0.006      -0.028        0.138       0.154
#> 28      setosa        0.194       0.072        0.038      -0.046
#> 29      setosa        0.194      -0.028       -0.062      -0.046
#> 30      setosa       -0.306      -0.228        0.138      -0.046
#> 31      setosa       -0.206      -0.328        0.138      -0.046
#> 32      setosa        0.394      -0.028        0.038       0.154
#> 33      setosa        0.194       0.672        0.038      -0.146
#> 34      setosa        0.494       0.772       -0.062      -0.046
#> 35      setosa       -0.106      -0.328        0.038      -0.046
#> 36      setosa       -0.006      -0.228       -0.262      -0.046
#> 37      setosa        0.494       0.072       -0.162      -0.046
#> 38      setosa       -0.106       0.172       -0.062      -0.146
#> 39      setosa       -0.606      -0.428       -0.162      -0.046
#> 40      setosa        0.094      -0.028        0.038      -0.046
#> 41      setosa       -0.006       0.072       -0.162       0.054
#> 42      setosa       -0.506      -1.128       -0.162       0.054
#> 43      setosa       -0.606      -0.228       -0.162      -0.046
#> 44      setosa       -0.006       0.072        0.138       0.354
#> 45      setosa        0.094       0.372        0.438       0.154
#> 46      setosa       -0.206      -0.428       -0.062       0.054
#> 47      setosa        0.094       0.372        0.138      -0.046
#> 48      setosa       -0.406      -0.228       -0.062      -0.046
#> 49      setosa        0.294       0.272        0.038      -0.046
#> 50      setosa       -0.006      -0.128       -0.062      -0.046
#> 51  versicolor        1.064       0.430        0.440       0.074
#> 52  versicolor        0.464       0.430        0.240       0.174
#> 53  versicolor        0.964       0.330        0.640       0.174
#> 54  versicolor       -0.436      -0.470       -0.260      -0.026
#> 55  versicolor        0.564       0.030        0.340       0.174
#> 56  versicolor       -0.236       0.030        0.240      -0.026
#> 57  versicolor        0.364       0.530        0.440       0.274
#> 58  versicolor       -1.036      -0.370       -0.960      -0.326
#> 59  versicolor        0.664       0.130        0.340      -0.026
#> 60  versicolor       -0.736      -0.070       -0.360       0.074
#> 61  versicolor       -0.936      -0.770       -0.760      -0.326
#> 62  versicolor       -0.036       0.230       -0.060       0.174
#> 63  versicolor        0.064      -0.570       -0.260      -0.326
#> 64  versicolor        0.164       0.130        0.440       0.074
#> 65  versicolor       -0.336       0.130       -0.660      -0.026
#> 66  versicolor        0.764       0.330        0.140       0.074
#> 67  versicolor       -0.336       0.230        0.240       0.174
#> 68  versicolor       -0.136      -0.070       -0.160      -0.326
#> 69  versicolor        0.264      -0.570        0.240       0.174
#> 70  versicolor       -0.336      -0.270       -0.360      -0.226
#> 71  versicolor       -0.036       0.430        0.540       0.474
#> 72  versicolor        0.164       0.030       -0.260      -0.026
#> 73  versicolor        0.364      -0.270        0.640       0.174
#> 74  versicolor        0.164       0.030        0.440      -0.126
#> 75  versicolor        0.464       0.130        0.040      -0.026
#> 76  versicolor        0.664       0.230        0.140       0.074
#> 77  versicolor        0.864       0.030        0.540       0.074
#> 78  versicolor        0.764       0.230        0.740       0.374
#> 79  versicolor        0.064       0.130        0.240       0.174
#> 80  versicolor       -0.236      -0.170       -0.760      -0.326
#> 81  versicolor       -0.436      -0.370       -0.460      -0.226
#> 82  versicolor       -0.436      -0.370       -0.560      -0.326
#> 83  versicolor       -0.136      -0.070       -0.360      -0.126
#> 84  versicolor        0.064      -0.070        0.840       0.274
#> 85  versicolor       -0.536       0.230        0.240       0.174
#> 86  versicolor        0.064       0.630        0.240       0.274
#> 87  versicolor        0.764       0.330        0.440       0.174
#> 88  versicolor        0.364      -0.470        0.140      -0.026
#> 89  versicolor       -0.336       0.230       -0.160      -0.026
#> 90  versicolor       -0.436      -0.270       -0.260      -0.026
#> 91  versicolor       -0.436      -0.170        0.140      -0.126
#> 92  versicolor        0.164       0.230        0.340       0.074
#> 93  versicolor       -0.136      -0.170       -0.260      -0.126
#> 94  versicolor       -0.936      -0.470       -0.960      -0.326
#> 95  versicolor       -0.336      -0.070       -0.060      -0.026
#> 96  versicolor       -0.236       0.230       -0.060      -0.126
#> 97  versicolor       -0.236       0.130       -0.060      -0.026
#> 98  versicolor        0.264       0.130        0.040      -0.026
#> 99  versicolor       -0.836      -0.270       -1.260      -0.226
#> 100 versicolor       -0.236       0.030       -0.160      -0.026
#> 101  virginica       -0.288       0.326        0.448       0.474
#> 102  virginica       -0.788      -0.274       -0.452      -0.126
#> 103  virginica        0.512       0.026        0.348       0.074
#> 104  virginica       -0.288      -0.074        0.048      -0.226
#> 105  virginica       -0.088       0.026        0.248       0.174
#> 106  virginica        1.012       0.026        1.048       0.074
#> 107  virginica       -1.688      -0.474       -1.052      -0.326
#> 108  virginica        0.712      -0.074        0.748      -0.226
#> 109  virginica        0.112      -0.474        0.248      -0.226
#> 110  virginica        0.612       0.626        0.548       0.474
#> 111  virginica       -0.088       0.226       -0.452      -0.026
#> 112  virginica       -0.188      -0.274       -0.252      -0.126
#> 113  virginica        0.212       0.026       -0.052       0.074
#> 114  virginica       -0.888      -0.474       -0.552      -0.026
#> 115  virginica       -0.788      -0.174       -0.452       0.374
#> 116  virginica       -0.188       0.226       -0.252       0.274
#> 117  virginica       -0.088       0.026       -0.052      -0.226
#> 118  virginica        1.112       0.826        1.148       0.174
#> 119  virginica        1.112      -0.374        1.348       0.274
#> 120  virginica       -0.588      -0.774       -0.552      -0.526
#> 121  virginica        0.312       0.226        0.148       0.274
#> 122  virginica       -0.988      -0.174       -0.652      -0.026
#> 123  virginica        1.112      -0.174        1.148      -0.026
#> 124  virginica       -0.288      -0.274       -0.652      -0.226
#> 125  virginica        0.112       0.326        0.148       0.074
#> 126  virginica        0.612       0.226        0.448      -0.226
#> 127  virginica       -0.388      -0.174       -0.752      -0.226
#> 128  virginica       -0.488       0.026       -0.652      -0.226
#> 129  virginica       -0.188      -0.174        0.048       0.074
#> 130  virginica        0.612       0.026        0.248      -0.426
#> 131  virginica        0.812      -0.174        0.548      -0.126
#> 132  virginica        1.312       0.826        0.848      -0.026
#> 133  virginica       -0.188      -0.174        0.048       0.174
#> 134  virginica       -0.288      -0.174       -0.452      -0.526
#> 135  virginica       -0.488      -0.374        0.048      -0.626
#> 136  virginica        1.112       0.026        0.548       0.274
#> 137  virginica       -0.288       0.426        0.048       0.374
#> 138  virginica       -0.188       0.126       -0.052      -0.226
#> 139  virginica       -0.588       0.026       -0.752      -0.226
#> 140  virginica        0.312       0.126       -0.152       0.074
#> 141  virginica        0.112       0.126        0.048       0.374
#> 142  virginica        0.312       0.126       -0.452       0.274
#> 143  virginica       -0.788      -0.274       -0.452      -0.126
#> 144  virginica        0.212       0.226        0.348       0.274
#> 145  virginica        0.112       0.326        0.148       0.474
#> 146  virginica        0.112       0.026       -0.352       0.274
#> 147  virginica       -0.288      -0.474       -0.552      -0.126
#> 148  virginica       -0.088       0.026       -0.352      -0.026
#> 149  virginica       -0.388       0.426       -0.152       0.274
#> 150  virginica       -0.688       0.026       -0.452      -0.226
#> 
#> Grouped by:  Species  [3 | 50 (0)] 
iris %>% fgroup_by(Species) %>% TRA(fmean(.)[c(2,4)])   # Only transforming 2 columns
#>     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
#> 1          0.094         3.5       -0.062         0.2     setosa
#> 2         -0.106         3.0       -0.062         0.2     setosa
#> 3         -0.306         3.2       -0.162         0.2     setosa
#> 4         -0.406         3.1        0.038         0.2     setosa
#> 5         -0.006         3.6       -0.062         0.2     setosa
#> 6          0.394         3.9        0.238         0.4     setosa
#> 7         -0.406         3.4       -0.062         0.3     setosa
#> 8         -0.006         3.4        0.038         0.2     setosa
#> 9         -0.606         2.9       -0.062         0.2     setosa
#> 10        -0.106         3.1        0.038         0.1     setosa
#> 11         0.394         3.7        0.038         0.2     setosa
#> 12        -0.206         3.4        0.138         0.2     setosa
#> 13        -0.206         3.0       -0.062         0.1     setosa
#> 14        -0.706         3.0       -0.362         0.1     setosa
#> 15         0.794         4.0       -0.262         0.2     setosa
#> 16         0.694         4.4        0.038         0.4     setosa
#> 17         0.394         3.9       -0.162         0.4     setosa
#> 18         0.094         3.5       -0.062         0.3     setosa
#> 19         0.694         3.8        0.238         0.3     setosa
#> 20         0.094         3.8        0.038         0.3     setosa
#> 21         0.394         3.4        0.238         0.2     setosa
#> 22         0.094         3.7        0.038         0.4     setosa
#> 23        -0.406         3.6       -0.462         0.2     setosa
#> 24         0.094         3.3        0.238         0.5     setosa
#> 25        -0.206         3.4        0.438         0.2     setosa
#> 26        -0.006         3.0        0.138         0.2     setosa
#> 27        -0.006         3.4        0.138         0.4     setosa
#> 28         0.194         3.5        0.038         0.2     setosa
#> 29         0.194         3.4       -0.062         0.2     setosa
#> 30        -0.306         3.2        0.138         0.2     setosa
#> 31        -0.206         3.1        0.138         0.2     setosa
#> 32         0.394         3.4        0.038         0.4     setosa
#> 33         0.194         4.1        0.038         0.1     setosa
#> 34         0.494         4.2       -0.062         0.2     setosa
#> 35        -0.106         3.1        0.038         0.2     setosa
#> 36        -0.006         3.2       -0.262         0.2     setosa
#> 37         0.494         3.5       -0.162         0.2     setosa
#> 38        -0.106         3.6       -0.062         0.1     setosa
#> 39        -0.606         3.0       -0.162         0.2     setosa
#> 40         0.094         3.4        0.038         0.2     setosa
#> 41        -0.006         3.5       -0.162         0.3     setosa
#> 42        -0.506         2.3       -0.162         0.3     setosa
#> 43        -0.606         3.2       -0.162         0.2     setosa
#> 44        -0.006         3.5        0.138         0.6     setosa
#> 45         0.094         3.8        0.438         0.4     setosa
#> 46        -0.206         3.0       -0.062         0.3     setosa
#> 47         0.094         3.8        0.138         0.2     setosa
#> 48        -0.406         3.2       -0.062         0.2     setosa
#> 49         0.294         3.7        0.038         0.2     setosa
#> 50        -0.006         3.3       -0.062         0.2     setosa
#> 51         1.064         3.2        0.440         1.4 versicolor
#> 52         0.464         3.2        0.240         1.5 versicolor
#> 53         0.964         3.1        0.640         1.5 versicolor
#> 54        -0.436         2.3       -0.260         1.3 versicolor
#> 55         0.564         2.8        0.340         1.5 versicolor
#> 56        -0.236         2.8        0.240         1.3 versicolor
#> 57         0.364         3.3        0.440         1.6 versicolor
#> 58        -1.036         2.4       -0.960         1.0 versicolor
#> 59         0.664         2.9        0.340         1.3 versicolor
#> 60        -0.736         2.7       -0.360         1.4 versicolor
#> 61        -0.936         2.0       -0.760         1.0 versicolor
#> 62        -0.036         3.0       -0.060         1.5 versicolor
#> 63         0.064         2.2       -0.260         1.0 versicolor
#> 64         0.164         2.9        0.440         1.4 versicolor
#> 65        -0.336         2.9       -0.660         1.3 versicolor
#> 66         0.764         3.1        0.140         1.4 versicolor
#> 67        -0.336         3.0        0.240         1.5 versicolor
#> 68        -0.136         2.7       -0.160         1.0 versicolor
#> 69         0.264         2.2        0.240         1.5 versicolor
#> 70        -0.336         2.5       -0.360         1.1 versicolor
#> 71        -0.036         3.2        0.540         1.8 versicolor
#> 72         0.164         2.8       -0.260         1.3 versicolor
#> 73         0.364         2.5        0.640         1.5 versicolor
#> 74         0.164         2.8        0.440         1.2 versicolor
#> 75         0.464         2.9        0.040         1.3 versicolor
#> 76         0.664         3.0        0.140         1.4 versicolor
#> 77         0.864         2.8        0.540         1.4 versicolor
#> 78         0.764         3.0        0.740         1.7 versicolor
#> 79         0.064         2.9        0.240         1.5 versicolor
#> 80        -0.236         2.6       -0.760         1.0 versicolor
#> 81        -0.436         2.4       -0.460         1.1 versicolor
#> 82        -0.436         2.4       -0.560         1.0 versicolor
#> 83        -0.136         2.7       -0.360         1.2 versicolor
#> 84         0.064         2.7        0.840         1.6 versicolor
#> 85        -0.536         3.0        0.240         1.5 versicolor
#> 86         0.064         3.4        0.240         1.6 versicolor
#> 87         0.764         3.1        0.440         1.5 versicolor
#> 88         0.364         2.3        0.140         1.3 versicolor
#> 89        -0.336         3.0       -0.160         1.3 versicolor
#> 90        -0.436         2.5       -0.260         1.3 versicolor
#> 91        -0.436         2.6        0.140         1.2 versicolor
#> 92         0.164         3.0        0.340         1.4 versicolor
#> 93        -0.136         2.6       -0.260         1.2 versicolor
#> 94        -0.936         2.3       -0.960         1.0 versicolor
#> 95        -0.336         2.7       -0.060         1.3 versicolor
#> 96        -0.236         3.0       -0.060         1.2 versicolor
#> 97        -0.236         2.9       -0.060         1.3 versicolor
#> 98         0.264         2.9        0.040         1.3 versicolor
#> 99        -0.836         2.5       -1.260         1.1 versicolor
#> 100       -0.236         2.8       -0.160         1.3 versicolor
#> 101       -0.288         3.3        0.448         2.5  virginica
#> 102       -0.788         2.7       -0.452         1.9  virginica
#> 103        0.512         3.0        0.348         2.1  virginica
#> 104       -0.288         2.9        0.048         1.8  virginica
#> 105       -0.088         3.0        0.248         2.2  virginica
#> 106        1.012         3.0        1.048         2.1  virginica
#> 107       -1.688         2.5       -1.052         1.7  virginica
#> 108        0.712         2.9        0.748         1.8  virginica
#> 109        0.112         2.5        0.248         1.8  virginica
#> 110        0.612         3.6        0.548         2.5  virginica
#> 111       -0.088         3.2       -0.452         2.0  virginica
#> 112       -0.188         2.7       -0.252         1.9  virginica
#> 113        0.212         3.0       -0.052         2.1  virginica
#> 114       -0.888         2.5       -0.552         2.0  virginica
#> 115       -0.788         2.8       -0.452         2.4  virginica
#> 116       -0.188         3.2       -0.252         2.3  virginica
#> 117       -0.088         3.0       -0.052         1.8  virginica
#> 118        1.112         3.8        1.148         2.2  virginica
#> 119        1.112         2.6        1.348         2.3  virginica
#> 120       -0.588         2.2       -0.552         1.5  virginica
#> 121        0.312         3.2        0.148         2.3  virginica
#> 122       -0.988         2.8       -0.652         2.0  virginica
#> 123        1.112         2.8        1.148         2.0  virginica
#> 124       -0.288         2.7       -0.652         1.8  virginica
#> 125        0.112         3.3        0.148         2.1  virginica
#> 126        0.612         3.2        0.448         1.8  virginica
#> 127       -0.388         2.8       -0.752         1.8  virginica
#> 128       -0.488         3.0       -0.652         1.8  virginica
#> 129       -0.188         2.8        0.048         2.1  virginica
#> 130        0.612         3.0        0.248         1.6  virginica
#> 131        0.812         2.8        0.548         1.9  virginica
#> 132        1.312         3.8        0.848         2.0  virginica
#> 133       -0.188         2.8        0.048         2.2  virginica
#> 134       -0.288         2.8       -0.452         1.5  virginica
#> 135       -0.488         2.6        0.048         1.4  virginica
#> 136        1.112         3.0        0.548         2.3  virginica
#> 137       -0.288         3.4        0.048         2.4  virginica
#> 138       -0.188         3.1       -0.052         1.8  virginica
#> 139       -0.588         3.0       -0.752         1.8  virginica
#> 140        0.312         3.1       -0.152         2.1  virginica
#> 141        0.112         3.1        0.048         2.4  virginica
#> 142        0.312         3.1       -0.452         2.3  virginica
#> 143       -0.788         2.7       -0.452         1.9  virginica
#> 144        0.212         3.2        0.348         2.3  virginica
#> 145        0.112         3.3        0.148         2.5  virginica
#> 146        0.112         3.0       -0.352         2.3  virginica
#> 147       -0.288         2.5       -0.552         1.9  virginica
#> 148       -0.088         3.0       -0.352         2.0  virginica
#> 149       -0.388         3.4       -0.152         2.3  virginica
#> 150       -0.688         3.0       -0.452         1.8  virginica
#> 
#> Grouped by:  Species  [3 | 50 (0)] 
iris %>% fgroup_by(Species) %>% TRA(fmean(.)[c(2,4)],   # Dropping species column
                                        keep.group_vars = FALSE)
#>     Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 1          0.094         3.5       -0.062         0.2
#> 2         -0.106         3.0       -0.062         0.2
#> 3         -0.306         3.2       -0.162         0.2
#> 4         -0.406         3.1        0.038         0.2
#> 5         -0.006         3.6       -0.062         0.2
#> 6          0.394         3.9        0.238         0.4
#> 7         -0.406         3.4       -0.062         0.3
#> 8         -0.006         3.4        0.038         0.2
#> 9         -0.606         2.9       -0.062         0.2
#> 10        -0.106         3.1        0.038         0.1
#> 11         0.394         3.7        0.038         0.2
#> 12        -0.206         3.4        0.138         0.2
#> 13        -0.206         3.0       -0.062         0.1
#> 14        -0.706         3.0       -0.362         0.1
#> 15         0.794         4.0       -0.262         0.2
#> 16         0.694         4.4        0.038         0.4
#> 17         0.394         3.9       -0.162         0.4
#> 18         0.094         3.5       -0.062         0.3
#> 19         0.694         3.8        0.238         0.3
#> 20         0.094         3.8        0.038         0.3
#> 21         0.394         3.4        0.238         0.2
#> 22         0.094         3.7        0.038         0.4
#> 23        -0.406         3.6       -0.462         0.2
#> 24         0.094         3.3        0.238         0.5
#> 25        -0.206         3.4        0.438         0.2
#> 26        -0.006         3.0        0.138         0.2
#> 27        -0.006         3.4        0.138         0.4
#> 28         0.194         3.5        0.038         0.2
#> 29         0.194         3.4       -0.062         0.2
#> 30        -0.306         3.2        0.138         0.2
#> 31        -0.206         3.1        0.138         0.2
#> 32         0.394         3.4        0.038         0.4
#> 33         0.194         4.1        0.038         0.1
#> 34         0.494         4.2       -0.062         0.2
#> 35        -0.106         3.1        0.038         0.2
#> 36        -0.006         3.2       -0.262         0.2
#> 37         0.494         3.5       -0.162         0.2
#> 38        -0.106         3.6       -0.062         0.1
#> 39        -0.606         3.0       -0.162         0.2
#> 40         0.094         3.4        0.038         0.2
#> 41        -0.006         3.5       -0.162         0.3
#> 42        -0.506         2.3       -0.162         0.3
#> 43        -0.606         3.2       -0.162         0.2
#> 44        -0.006         3.5        0.138         0.6
#> 45         0.094         3.8        0.438         0.4
#> 46        -0.206         3.0       -0.062         0.3
#> 47         0.094         3.8        0.138         0.2
#> 48        -0.406         3.2       -0.062         0.2
#> 49         0.294         3.7        0.038         0.2
#> 50        -0.006         3.3       -0.062         0.2
#> 51         1.064         3.2        0.440         1.4
#> 52         0.464         3.2        0.240         1.5
#> 53         0.964         3.1        0.640         1.5
#> 54        -0.436         2.3       -0.260         1.3
#> 55         0.564         2.8        0.340         1.5
#> 56        -0.236         2.8        0.240         1.3
#> 57         0.364         3.3        0.440         1.6
#> 58        -1.036         2.4       -0.960         1.0
#> 59         0.664         2.9        0.340         1.3
#> 60        -0.736         2.7       -0.360         1.4
#> 61        -0.936         2.0       -0.760         1.0
#> 62        -0.036         3.0       -0.060         1.5
#> 63         0.064         2.2       -0.260         1.0
#> 64         0.164         2.9        0.440         1.4
#> 65        -0.336         2.9       -0.660         1.3
#> 66         0.764         3.1        0.140         1.4
#> 67        -0.336         3.0        0.240         1.5
#> 68        -0.136         2.7       -0.160         1.0
#> 69         0.264         2.2        0.240         1.5
#> 70        -0.336         2.5       -0.360         1.1
#> 71        -0.036         3.2        0.540         1.8
#> 72         0.164         2.8       -0.260         1.3
#> 73         0.364         2.5        0.640         1.5
#> 74         0.164         2.8        0.440         1.2
#> 75         0.464         2.9        0.040         1.3
#> 76         0.664         3.0        0.140         1.4
#> 77         0.864         2.8        0.540         1.4
#> 78         0.764         3.0        0.740         1.7
#> 79         0.064         2.9        0.240         1.5
#> 80        -0.236         2.6       -0.760         1.0
#> 81        -0.436         2.4       -0.460         1.1
#> 82        -0.436         2.4       -0.560         1.0
#> 83        -0.136         2.7       -0.360         1.2
#> 84         0.064         2.7        0.840         1.6
#> 85        -0.536         3.0        0.240         1.5
#> 86         0.064         3.4        0.240         1.6
#> 87         0.764         3.1        0.440         1.5
#> 88         0.364         2.3        0.140         1.3
#> 89        -0.336         3.0       -0.160         1.3
#> 90        -0.436         2.5       -0.260         1.3
#> 91        -0.436         2.6        0.140         1.2
#> 92         0.164         3.0        0.340         1.4
#> 93        -0.136         2.6       -0.260         1.2
#> 94        -0.936         2.3       -0.960         1.0
#> 95        -0.336         2.7       -0.060         1.3
#> 96        -0.236         3.0       -0.060         1.2
#> 97        -0.236         2.9       -0.060         1.3
#> 98         0.264         2.9        0.040         1.3
#> 99        -0.836         2.5       -1.260         1.1
#> 100       -0.236         2.8       -0.160         1.3
#> 101       -0.288         3.3        0.448         2.5
#> 102       -0.788         2.7       -0.452         1.9
#> 103        0.512         3.0        0.348         2.1
#> 104       -0.288         2.9        0.048         1.8
#> 105       -0.088         3.0        0.248         2.2
#> 106        1.012         3.0        1.048         2.1
#> 107       -1.688         2.5       -1.052         1.7
#> 108        0.712         2.9        0.748         1.8
#> 109        0.112         2.5        0.248         1.8
#> 110        0.612         3.6        0.548         2.5
#> 111       -0.088         3.2       -0.452         2.0
#> 112       -0.188         2.7       -0.252         1.9
#> 113        0.212         3.0       -0.052         2.1
#> 114       -0.888         2.5       -0.552         2.0
#> 115       -0.788         2.8       -0.452         2.4
#> 116       -0.188         3.2       -0.252         2.3
#> 117       -0.088         3.0       -0.052         1.8
#> 118        1.112         3.8        1.148         2.2
#> 119        1.112         2.6        1.348         2.3
#> 120       -0.588         2.2       -0.552         1.5
#> 121        0.312         3.2        0.148         2.3
#> 122       -0.988         2.8       -0.652         2.0
#> 123        1.112         2.8        1.148         2.0
#> 124       -0.288         2.7       -0.652         1.8
#> 125        0.112         3.3        0.148         2.1
#> 126        0.612         3.2        0.448         1.8
#> 127       -0.388         2.8       -0.752         1.8
#> 128       -0.488         3.0       -0.652         1.8
#> 129       -0.188         2.8        0.048         2.1
#> 130        0.612         3.0        0.248         1.6
#> 131        0.812         2.8        0.548         1.9
#> 132        1.312         3.8        0.848         2.0
#> 133       -0.188         2.8        0.048         2.2
#> 134       -0.288         2.8       -0.452         1.5
#> 135       -0.488         2.6        0.048         1.4
#> 136        1.112         3.0        0.548         2.3
#> 137       -0.288         3.4        0.048         2.4
#> 138       -0.188         3.1       -0.052         1.8
#> 139       -0.588         3.0       -0.752         1.8
#> 140        0.312         3.1       -0.152         2.1
#> 141        0.112         3.1        0.048         2.4
#> 142        0.312         3.1       -0.452         2.3
#> 143       -0.788         2.7       -0.452         1.9
#> 144        0.212         3.2        0.348         2.3
#> 145        0.112         3.3        0.148         2.5
#> 146        0.112         3.0       -0.352         2.3
#> 147       -0.288         2.5       -0.552         1.9
#> 148       -0.088         3.0       -0.352         2.0
#> 149       -0.388         3.4       -0.152         2.3
#> 150       -0.688         3.0       -0.452         1.8
#> 
#> Grouped by:  Species  [3 | 50 (0)]