#MANOVA Approach #2, with followup univariates
#Draws 100% on jamovi package
#install.packages("jmv")
library(jmv)
jmv::mancova(
data = Wk04b,
deps = vars(DV1, DV2, DV3),
factors = GROUP,
covs = COVA,
boxM = TRUE,
shapiro = TRUE,
qqPlot = TRUE)
##
## MANCOVA
##
## Multivariate Tests
## -------------------------------------------------------------------------------------
## value F df1 df2 p
## -------------------------------------------------------------------------------------
## GROUP Pillai's Trace 0.2109053 3.340041 6 170 0.0038950
## Wilks' Lambda 0.7941477 3.420087 6 168 0.0032774
## Hotelling's Trace 0.2528487 3.497740 6 166 0.0027730
## Roy's Largest Root 0.2245074 6.361042 3 85 0.0006088
##
## COVA Pillai's Trace 0.5822471 39.025267 3 84 < .0000001
## Wilks' Lambda 0.4177529 39.025267 3 84 < .0000001
## Hotelling's Trace 1.3937595 39.025267 3 84 < .0000001
## Roy's Largest Root 1.3937595 39.025267 3 84 < .0000001
## -------------------------------------------------------------------------------------
##
##
## Univariate Tests
## -------------------------------------------------------------------------------------------------------
## Dependent Variable Sum of Squares df Mean Square F p
## -------------------------------------------------------------------------------------------------------
## GROUP DV1 24010.620 2 12005.310 9.3565466 0.0002106
## DV2 16340.323 2 8170.162 6.5344306 0.0022811
## DV3 2648.867 2 1324.433 0.4565292 0.6350048
## COVA DV1 130353.376 1 130353.376 101.5931654 < .0000001
## DV2 142507.344 1 142507.344 113.9762478 < .0000001
## DV3 3564.824 1 3564.824 1.2287871 0.2707335
## Residuals DV1 110345.911 86 1283.092
## DV2 107527.944 86 1250.325
## DV3 249493.909 86 2901.092
## -------------------------------------------------------------------------------------------------------
##
##
## ASSUMPTION CHECKS
##
## Box's Homogeneity of Covariance Matrices Test
## ---------------------------------------------
## <U+03C7>² df p
## ---------------------------------------------
## 10.41164 12 0.5798959
## ---------------------------------------------
##
##
## Shapiro-Wilk Multivariate Normality Test
## ----------------------------------------
## W p
## ----------------------------------------
## 0.9876381 0.5588772
## ----------------------------------------
#This is offered as a followup univariate for one of the DVs
#Note that this function doesn't run unless the IV is explicitly
#coded as a "factor" in R.
#Thus, we used the first lines below to apply more meaningful factor
#label names for the purpose of plotting
Wk04b$GROUP_LBL = factor(Wk04b$GROUP,
levels = c(1,2,3),
labels = c("no depr","mild depr","severe depr"))
jmv::ancova(
formula = DV1 ~ GROUP_LBL + COVA,
data = Wk04b,
effectSize = c("eta", "partEta", "omega"),
homo = TRUE,
norm = TRUE,
qq = TRUE,
postHoc = ~ GROUP_LBL,
postHocCorr = "bonf",
postHocES = "d",
emMeans = ~ GROUP_LBL,
emmPlotData = TRUE,
emmTables = TRUE)
##
## ANCOVA
##
## ANCOVA - DV1
## -----------------------------------------------------------------------------------------------------------------------
## Sum of Squares df Mean Square F p <U+03B7>² <U+03B7>²p <U+03C9>²
## -----------------------------------------------------------------------------------------------------------------------
## GROUP_LBL 10081.56 2 5040.779 3.928619 0.0232980 0.0402007 0.0837148 0.0298153
## COVA 130353.38 1 130353.376 101.593165 < .0000001 0.5197900 0.5415611 0.5120537
## Residuals 110345.91 86 1283.092
## -----------------------------------------------------------------------------------------------------------------------
##
##
## ASSUMPTION CHECKS
##
## Homogeneity of Variances Test (Levene's)
## ----------------------------------------
## F df1 df2 p
## ----------------------------------------
## 1.653518 2 87 0.1973324
## ----------------------------------------
##
##
## Normality Test (Shapiro-Wilk)
## -----------------------------
## Statistic p
## -----------------------------
## 0.9810300 0.2129076
## -----------------------------
##
##
## POST HOC TESTS
##
## Post Hoc Comparisons - GROUP_LBL
## ----------------------------------------------------------------------------------------------------------------------
## GROUP_LBL GROUP_LBL Mean Difference SE df t p-bonferroni Cohen's d
## ----------------------------------------------------------------------------------------------------------------------
## no depr - mild depr -13.30897 9.461160 86.00000 -1.406695 0.4893639 0.1482787
## - severe depr -26.06453 9.298779 86.00000 -2.803006 0.0187670 0.2954627
## mild depr - severe depr -12.75556 9.305962 86.00000 -1.370687 0.5221180 0.1444831
## ----------------------------------------------------------------------------------------------------------------------
##
##
## ESTIMATED MARGINAL MEANS
##
## GROUP_LBL
##
## Estimated Marginal Means - GROUP_LBL
## ---------------------------------------------------------------
## GROUP_LBL Mean SE Lower Upper
## ---------------------------------------------------------------
## no depr 202.5007 6.613706 189.3531 215.6483
## mild depr 215.8097 6.617073 202.6553 228.9640
## severe depr 228.5652 6.539895 215.5643 241.5661
## ---------------------------------------------------------------
