MANOVA with variables from different datasets - r

Question

This question was already asked on stats.stackexchange, but no one answered. Since I'm not sure which forum is the appropriate one, I post this here again with some data.
I have done experiments on various characteristics of tree bark and now want to compare in how far the five examined tree species differ in regards to the assessed parameters. So, it was suggested that I should use a MANOVA to analyse my data and it seems reasonable to me. My analysis is conducted in R.
However, unlike most examples I've found on how to do a MANOVA (i.e. here, here, here), my data stems from different measurements and from different individuals. Now, I've found only this thread discussing unequal sample sizes, but this targets only sample sizes within the explaining factor.
To illustrate a bit further, imagine I have per tree species...
9 measurements of the bark roughness.
4 measurements of the bark thickness,
3 pH measurements,
5 measurements of the water-holding capacity,
5 measurements of the water retention.
Of course, I could do separate ANOVAs for each of these variables (and I already did), but I think there should be some advantages in a MANOVA, right?
My Question:
Would a MANOVA be appropriate for such kind of data? Can I just ignore my different variable sizes? Is there an alternative way to do this or rather an alternative statistic test? Does my small sample size matter?
My results so far:
In R, I just put all the variables into one data.frame and filled the missing values due to unequal sample size by NAs (that's why there is the nums column in my data.frame below). Then, I ran a MANOVA like this: pH + water content + thickness + roughness ~ tree species with the manova function.
Example Data:
manova_df = structure(list(abbr = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L), .Label = c("AS", "BU", "CL", "MB", "PR"
), class = "factor"), nums = c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L,
9L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 1L, 2L, 3L, 4L, 5L, 6L,
7L, 8L, 9L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 1L, 2L, 3L, 4L,
5L, 6L, 7L, 8L, 9L), comb_rugosity = c(3.44, 2.29, 5.21, 1.45,
2.84, 4.25, 1.54, 2.97, 1.38, 2.45, 9.44, 0, 0.58, 7.71, 5.53,
0.84, 1.22, 1, 10.83, 15.77, 5.5, 8.49, 10.46, 9.16, 5.52, 6.55,
1.77, 10.68, 13.43, 20.8, 8.82, 18.09, 15.1, 15.41, 16.3, 13.2,
2.67, 0.95, 1.49, 2.7, 0, 0.92, 0.83, 0, 1.89), bark_mm = c(9.59,
4.17, 17.23, 8.49, 3.58, NA, NA, NA, NA, 8.06, 13.53, 6.33, 10.96,
12.14, NA, NA, NA, NA, 17.94, 7.33, 10.54, 14.68, 16.66, NA,
NA, NA, NA, 8.52, 8.72, 7.57, 11.89, 6.41, NA, NA, NA, NA, 2.59,
9, 3.26, 5.81, NA, NA, NA, NA, NA), pH = c(6.5, 7.33, 8.17, NA,
NA, NA, NA, NA, NA, 7.84, 3.71, 12.47, 4.39, NA, NA, NA, NA,
NA, 11.04, 6.22, 5.41, 4.29, NA, NA, NA, NA, NA, 9.26, 11.18,
6.3, NA, NA, NA, NA, NA, NA, 8.42, 7.75, 4.33, NA, NA, NA, NA,
NA, NA), whc = c(192, 251, 166, 170, 466, NA, NA, NA, NA, 308,
187, 595, 324, 364, NA, NA, NA, NA, 171, 406, 790, 292, 579,
NA, NA, NA, NA, 672, 251, 700, 245, 260, 485, 383, NA, NA, 325,
481, 338, 476, 968, NA, NA, NA, NA), ret = c(83, 90, 286, 309,
374, NA, NA, NA, NA, 109, 159, 98, 164, 636, NA, NA, NA, NA,
144, 234, 383, 178, 446, NA, NA, NA, NA, 275, 56, 178, 107, 125,
367, 137, NA, NA, 132, 120, 142, 147, 330, NA, NA, NA, NA)), row.names = c(NA,
-45L), class = c("tbl_df", "tbl", "data.frame"))
Which looks like this (where abbr is the tree species, nums is the number of the measurement per tree species and the rest are the tree parameters):
> manova_df
# A tibble: 45 x 7
abbr nums comb_rugosity bark_mm pH whc ret
<fct> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
1 AS 1 3.44 9.59 6.5 192 83
2 AS 2 2.29 4.17 7.33 251 90
3 AS 3 5.21 17.2 8.17 166 286
4 AS 4 1.45 8.49 NA 170 309
5 AS 5 2.84 3.58 NA 466 374
6 AS 6 4.25 NA NA NA NA
7 AS 7 1.54 NA NA NA NA
8 AS 8 2.97 NA NA NA NA
9 AS 9 1.38 NA NA NA NA
10 BU 1 2.45 8.06 7.84 308 109
# ... with 35 more rows
My analysis is pretty straightforward:
mano_mod = manova(cbind(pH, bark_mm, comb_rugosity, whc, ret) ~ abbr, data = manova_df)
> summary(mano_mod)
Df Pillai approx F num Df den Df Pr(>F)
abbr 4 1.5708 1.4226 20 44 0.1628
Residuals 12
I did not include my real data here, but they follow the same structure. The given data are far from being significant, whereas my actual data are! My question is solely regarding the many NAs in my data and if the test is accurate.
(If anything is unclear, please ask.)