Start by calculating descriptive statistics (mean, standard deviation) for each treatment. This will give you an overview of the data distribution. Conduct an ANOVA using Type III sums of squares, which is suitable for unbalanced designs. This can help assess the significance of treatment effects.

Parametric

Ensure that you check the assumptions of ANOVA (normality, homogeneity of variances). If these assumptions are not met, consider transforming your data or using non-parametric methods.

Non-parametric:

If the data do not meet the assumptions for parametric tests, consider using non-parametric methods, such as the Kruskal-Wallis test, which can handle unequal sample sizes.

Post-Hoc: If you find significant treatment effects, conduct post-hoc tests (like Tukey's HSD) to identify which treatments differ from one another. Ensure that the post-hoc method you choose can handle unequal sample sizes.

Visualization: Use box plots or dot plots to visualize the distributions of the response variable for each treatment. This can help in understanding the variability and central tendencies across treatments.

For R code:

library(lme4)

# Assuming 'response' is your dependent variable, 'treatment' is the factor for treatments, and 'replication' is a random effect.

model