In your case, you have a control group and three concentrations of a drug, with three replicate wells for each group, and you experimented three times. You want to compare the effect of each drug concentration with the control group.

The Kruskal-Wallis test is a nonparametric test used to compare the medians of three or more independent groups when the data do not meet the assumptions of normality and equal variances required for parametric tests like ANOVA. The Kruskal-Wallis test assesses whether there are any differences among the groups, but it does not provide information on which specific groups differ significantly from each other.

The Dunn test is a post hoc test commonly used after the Kruskal-Wallis test to compare group differences pairwise. It adjusts for multiple comparisons and allows you to identify which groups are significantly different from each other. However, in your case, the Dunn test did not show any significant results.

On the other hand, the analysis of variance (ANOVA) test is a parametric test used to compare means among three or more groups, assuming that the data meet the assumptions of normality and equal variances. Dunnett's post hoc analysis is specifically designed for ANOVA comparisons with a control group. It compares each treatment group with the control group, allowing you to determine if there are any significant differences between each drug concentration and the control group.

Given that you have a control group and want to compare each concentration of the drug with the control, it seems more appropriate to use ANOVA with Dunnett's post hoc analysis in your case. This approach will allow you to compare each drug concentration group with the control group and assess the significance of those differences while properly accounting for multiple comparisons.

Remember to check the assumptions of ANOVA, including normality and equal variances, and verify that they are met in your data. If the assumptions are not met, you may need to consider alternative nonparametric methods or transformations of the data to meet the assumptions.

It's worth noting that the choice of statistical test should also consider the specific nature of your data, research question, and any additional considerations that may be relevant to your study. Consulting with a statistician or a subject matter expert in your field can provide further guidance on the most appropriate analysis for your specific situation.