# How to validate clusters after calculating Gower distances and Ward's clustering in R

I am trying to apply Ward's clustering on a mixed types dataset, and wanna explain what I did (maybe helpful to others), and I have some questions regarding this analysis, mainly how to validate my clusters.

So, let me explain what I did in detail:

1. I started with a dataset containing 53 variables. These variables are either numerical or binary. The first variable contains the participant number, so will not be used in the clustering. I directly coded the categorical data into binary variables so that I didn't have to transform these variables.

2. Then I checked for normality of the variables for all numerical variables, using the Shapiro-Wilk test. Significance values below 0.05 will be log-transformed in the next step. Binary variables don't need a normality check.

3. I calculated distance using the daisy library. Here, I log-transformed the variables with a value lower than 0.05 in the second step with 'logratio', the other variables were appointed as asymmetric binary and symmetric binary. I read that Gower distance is an appropriate metric for mixed data types, and that's why I carried out this step this way.

gower_dist <- daisy(mydata[, -1], metric = "gower", type = list(logratio = c(4,5,6,7,8,9,10,11,12,13,17,24,25,26,44,45,49,50,51,52), asymm = c(14,15,16,18,19,20,21,23,27,28,29,30,31,32,34,35,36,37,38,39,40,41,42,43,46,47,48), symm = c(1,3)))

1. Then I used Ward's method for clustering, and I plotted a dendogram with the results.
hc1 <- hclust(gower_dist, method = "ward" )

plot(hc1) # display dendogram


This resulted in the following output:

I think that I am in the right direction with my analysis, but have some problems with finding the right number of clusters. I wanted to use pvclust() since it provides p-values for hierarchical clustering, and that is what I am interested in. However, it seems that this package is not usable when using Gower distances. Does anyone know another way to find p-values in R for Ward's clusters using the Gower distance?

Next to this, I have some small doubts on the correctness of my analysis. These are the following: