smstests

The goal of smstests is to produce simple multivariate statistical tests for means and variances / covariances for one single factor with two or more levels, including multiple two-sample t- and Levene’s tests, Hotelling’s $T^2$ test, extended two-sample Levene’s tests for multivariate data, one-way MANOVA, van Valen’s test and Box’s M test.

Installation

You can install the development version of smstests from GitHub with:

# install.packages("devtools") # In case devtools is not installed
devtools::install_github("ganava4/smstests")

Example

library(smstests)
## basic example code
data(skulls)
# Box's M test using an F-approximation
BoxM.skulls <- BoxM.F(skulls, Period)
summary.BoxM.F(BoxM.skulls, long = TRUE)

 Box's M-test for Homogeneity of Covariance Matrices (F approximation)

 Data: skulls 
 Variables: Maximum_breadth Basibregmatic_height Basialveolar_length Nasal_height 
 Factor: Period 
 Levels: Early predynastic Late predynastic 12th and 13th Dynasty Ptolemaic period Roman period 

Covariance matrix for each group
Early predynastic 
                     Maximum_breadth Basibregmatic_height Basialveolar_length
Maximum_breadth            26.309195            4.1517241           0.4540230
Basibregmatic_height        4.151724           19.9724138          -0.7931034
Basialveolar_length         0.454023           -0.7931034          34.6264368
Nasal_height                7.245977            0.3931034          -1.9195402
                     Nasal_height
Maximum_breadth         7.2459770
Basibregmatic_height    0.3931034
Basialveolar_length    -1.9195402
Nasal_height            7.6367816

Late predynastic 
                     Maximum_breadth Basibregmatic_height Basialveolar_length
Maximum_breadth            23.136782             1.010345           4.7678161
Basibregmatic_height        1.010345            21.596552           3.3655172
Basialveolar_length         4.767816             3.365517          18.8919540
Nasal_height                1.842529             5.624138           0.1908046
                     Nasal_height
Maximum_breadth         1.8425287
Basibregmatic_height    5.6241379
Basialveolar_length     0.1908046
Nasal_height            8.7367816

12th and 13th Dynasty 
                     Maximum_breadth Basibregmatic_height Basialveolar_length
Maximum_breadth           12.1195402           0.78620690          -0.7747126
Basibregmatic_height       0.7862069          24.78620690           3.5931034
Basialveolar_length       -0.7747126           3.59310345          20.7229885
Nasal_height               0.8988506          -0.08965517           1.6701149
                     Nasal_height
Maximum_breadth        0.89885057
Basibregmatic_height  -0.08965517
Basialveolar_length    1.67011494
Nasal_height          12.59885057

Ptolemaic period 
                     Maximum_breadth Basibregmatic_height Basialveolar_length
Maximum_breadth            15.362069            -5.534483           -2.172414
Basibregmatic_height       -5.534483            26.355172            8.110345
Basialveolar_length        -2.172414             8.110345           21.085057
Nasal_height                2.051724             6.148276            5.328736
                     Nasal_height
Maximum_breadth          2.051724
Basibregmatic_height     6.148276
Basialveolar_length      5.328736
Nasal_height             7.964368

Roman period 
                     Maximum_breadth Basibregmatic_height Basialveolar_length
Maximum_breadth           28.6264368           -0.2298851          -1.8793103
Basibregmatic_height      -0.2298851           24.7126437          11.7241379
Basialveolar_length       -1.8793103           11.7241379          25.5689655
Nasal_height              -1.9942529            2.1494253           0.3965517
                     Nasal_height
Maximum_breadth        -1.9942529
Basibregmatic_height    2.1494253
Basialveolar_length     0.3965517
Nasal_height           13.8264368

Pooled Covariance Matrix
                     Maximum_breadth Basibregmatic_height Basialveolar_length
Maximum_breadth          21.11080460           0.03678161          0.07908046
Basibregmatic_height      0.03678161          23.48459770          5.20000000
Basialveolar_length       0.07908046           5.20000000         24.17908046
Nasal_height              2.00896552           2.84505747          1.13333333
                     Nasal_height
Maximum_breadth          2.008966
Basibregmatic_height     2.845057
Basialveolar_length      1.133333
Nasal_height            10.152644

 Box's M = 2.8725e-11 
 F statistic = 1.1406 , Num df = 40.0 , Den df = 46378.7 , p-value = 0.2498