When I transformed this data by asin(sqrt(x)) transformation, the didn't follow normality assumption, so the hypothesis of using ANOVA test was eliminated by me
Incidence data are binary. You have number of occurrences and number of non-occurrences. Unless I'm missing something important, you can test this using a chi-squared test.
Can you show us a table of the four cultivars, numbers of occurrences and total numbers??
It depends on the nature of your dependent variable.
If it is just yes/no for each plant, then it is a binary variable as Ronán Michael Conroy suggests, and you can use chi-square tests or logistic regression.
If it is some kind of severity rating (1 - 10, perhaps), you might use Kruskall-Wallis, or ordinal regression.
The interpretation of the Kruskal-Wallis test can be tricky. It compares the medians of groups only if the shape and spread of the data in each group is similar. See the Kruskal–Wallis Test chapter in the following publication.
For ordinal regression, see the Introduction to Cumulative Link Models (CLM) for Ordinal Data and One-way Ordinal ANOVA with CLM chapters in the following publication.
https://www.researchgate.net/publication/305436975_Summary_and_Analysis_of_Extension_Education_Program_Evaluation_in_R
Book Summary and Analysis of Extension Program Evaluation in R
Dear Salvador,
many thanks for your reply and clarification, your suggestions will be more helpful for me in the continuation
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