When using the Kruskal-Wallis test as a non-parametric alternative to ANOVA, some assumptions and conditions should be the same or similar between the two:
- Independence: Observations within each group should be independent of each other.
- Groups: The variable used should have two or more independent groups (often three or more).
- Random Sampling: Samples are assumed to be randomly selected.
- Group Distribution Shape: The data in each group should have a similar distribution shape (similar variability and shape, but not necessarily normal).
- Measurement Level: The dependent variable should be at least ordinal or continuous.
- Sample Size: Each group should have a sufficient sample size (often recommended at least 5 observations).
However, unlike classical ANOVA which assumes normally distributed residuals and homogeneity of variances, the Kruskal-Wallis test does not assume normality of the data and is more robust to outliers and skewed distributions. The key similarity is that both tests assume independent samples and that the groups come from populations with similar distribution shapes (but Kruskal- Wallis is less strict about exact distribution types). In summary, the key assumptions that should be the same when using Kruskal-Wallis for ANOVA are:
- Independence of observations
- Groups are independent
- Groups have a similar shape of distribution (similar variability)
- Random sampling from populations
The Kruskal-Wallis test differs by not requiring normality or equal variances, making it a preferred choice for non-normal or ordinal data where ANOVA assumptions are violated.
