I am trying to understand what a permutation test in a perMANOVA is. Can someone either explain how data is being substituted for each permutation or direct me to a good visualization on youtube?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
I think Wikipedia comments on Resampling (Statistics), where I like this naming convention over 'Permutation Test', is good on this topic, to quote, in part:
The test proceeds as follows. First, the difference in means between the two samples is calculated: this is the observed value of the test statistic, ${T_{\text{obs}}}$.
Next, the observations of groups ${A}$ and ${B}$ are pooled, and the difference in sample means is calculated and recorded for every possible way of dividing the pooled values into two groups of size ${n_{A}}$ and ${n_{B}}$ (i.e., for every permutation of the group labels A and B). The set of these calculated differences is the exact distribution of possible differences (for this sample) under the null hypothesis that group labels are exchangeable (i.e., are randomly assigned).
The one-sided p-value of the test is calculated as the proportion of sampled permutations where the difference in means was greater than or equal to ${T_{\text{obs}}}$. The two-sided p-value of the test is calculated as the proportion of sampled permutations where the absolute difference was greater than or equal to ${T_{\text{obs}}}$.
So, basically, in your particular experimental design, you re-shuttle the data into all possible combinations, to ascertain the likelihood of what you observed (in terms of differences) assuming random allocation of the same data is occurring. Limits on feasibility lends to the alternative employment of bootstrapping techniques.
