Kruskal-Wallis

The Kruskal-Wallis test is an inferential statistic that compares three or more independent groups.  The test is particularly valuable when dealing with small sample sizes, skewed distributions, or when you're working with ranked data.  In biological research, it is not uncommon to encounter situations where the data is not normally distributed, has unequal variances between groups, or consists of ordinal (ranked) data rather than continuous measurements; in these conditions the Kruskal-Wallis test is appropriate.

The Kruskal-Wallis test operates by ranking all observations from smallest to largest across all groups, then comparing the sum of ranks between groups. Instead of comparing means like ANOVA, it compares the median ranks of each group. ​

Null Hypothesis:
"There is not a significant difference in the medians between the groups; any observed differences may be due to chance and sampling error."

For example:  

• There is no significant difference between the number of birds at the different locations; the differences we see in the means of the groups may be due to chance and sampling error.

Alternative Hypothesis:
"There is a significant difference in the medians between the groups; the observed differences are most likely not due to chance or sampling error."

For example:  

• There is a significant difference between the number of birds at the different locations; the difference we see in the means of the groups is mostly likely not due to chance or sampling error.

Kruskal-Wallis calculators  will return a p-value.   A p-value of less than 0.05 means that the null hypothesis is rejected (that there is a significant difference among your groups). However, you do not know which group or groups are causing this to be true. If there is at least one significant difference among the groups, then the p-value will be <0.05.

When the Kruskal-Wallis test yields a significant result, post-hoc testing becomes essential to identify which specific groups differ from one another. Dunn's test is the most commonly used post-hoc in association with the Kruskal-Wallis test. Without post-hoc testing, you would know that differences exist somewhere among your groups but wouldn't be able to pinpoint exactly where those differences occur. The Post-hoc test compares each group to each other group to see if there is a significant difference between then.  A p-value will be provided for each possible pairwise comparison between experimental groups.