# How to read the output from MANOVA?

I'm testing if/how the two factors C and V affect the dependent variables fric and asp. I have the following code, but I don't know how to interpret the output, for example, does *** mean the factor significantly affects dependent variables? But what do Pillai and approx F mean? What does 1.954e-06 *** mean?

> Y = cbind(data$fric, data$asp)
> fit <- manova(Y~data$C*data$V)
> summary(fit, test="Pillai")

Df        Pillai approx F num Df den Df    Pr(>F)
data$C 3 1.85017 699.75 6 340 < 2.2e-16 *** data$V          3       0.24953     8.08      6    340 3.601e-08 ***
data$C:data$V   9       0.31746     3.56     18    340 1.954e-06 ***

• Check ?summary.manova for an explanation of the output. As described there, Pillai is the test statistic you chose, and unsurprisingly 'approx F' is an approximated F statistic. The astrisks indicate significant p-values (1 astrisk is significant at p<0.05 level, 2 astrisks is p<0.01, and 3 astrisks p<0.001). Also, you can format code by indenting lines by 4 spaces – Slow loris May 28 '16 at 21:06

It appears that factors C and V significantly affect the average value in fric shown above. Their (C,V) interaction is also significant, meaning the mean values of fric change significantly over varying levels of the factors of C and V.

For this model, there's two dependent variables and three independent variables (one is the interaction term). I ran a multivariate regression (MANOVA) on a dataset using two dependent variables and three independent variables, and the results are below:

First, there is a "full model" hypothesis test output as follows:

This is followed by a variable-specific hypothesis test output, as follows:

and finally, there are two regression coefficient tables, one for the regression of each dependent on the independents, as follows:

Overall, you'll need to look at R "vignettes" for the specific model ran and also look at a good multivariate MANOVA chapter to tie everything together. FYI, ANOVA and MANOVA is actually performed using regression, but with dummy indicator variables for the various levels of each categorical factor. The output I showed was based on dependent and independent variables that were all continuously-scaled.

However, based on what is provided, the significance test results apply to both dependent variables simultaneously, since there is not a table that breaks out results for each dependent. So, the only conclusion that can be made from the results provided is that all three predictors explain the variance of both dependent variables simultaneously - only because there is no output which reports results for each dependent variable singly. Therefore, you can't draw any conclusions for fric and asp separately.

• @wrtsvkrfm, it's a multivariate test, but you only discussed one of the response variables. Is it the same for asp? – Ben Ogorek Jan 22 '17 at 22:04