![]() More details, including additional information about the mathematics of PERMANOVA, can be found in Anderson (2001, 2017), McArdle & Anderson (2001), and Anderson et al. ![]() By avoiding this step, basic ANOVA theory can be applied to data summarized with any distance measure. When using a semimetric distance measure, we cannot determine the locations of centroids from the locations of the data. While this may seem abstract, it is crucial for semimetric distance measures (e.g., Bray-Curtis) that do not satisfy the triangle inequality (please review the lecture on Distance Measures if this does not sound familiar). Anderson (2015) describes this as geometric partitioning. Huygens’ theorem means that variation can be partitioned between and within groups without knowing the location of group centroids. It is known as Huygens’ theorem as it was first formulated by Christiaan Huygens – in the 17th century (Anderson et al. The key insight behind PERMANOVA is that the sum of squared differences between points and their centroid is equal to the sum of the squared interpoint distances divided by the number of points. In conventional statistics, SSW is calculated by subtracting the group mean from the values of individual observations in each group, squaring those differences, and then summing them. Recall that ANOVA partitions the total variation (total sum of squares SST) into a component representing variation between/among groups (SSB) and a component representing variation within groups (SSW). We will end with a consideration of its flexibility and its limitations. As you will see, PERMANOVA is a powerful technique. In addition, it can be thought of visually or geometrically, as we will demonstrate today. Under certain conditions, it is equivalent to MRPP (Reiss et al. PERmutational Multivariate ANalysis of VAriance (PERMANOVA) is a permutation-based technique – it makes no distributional assumptions about multivariate normality or homogeneity of variances. Implementation in R ( vegan::adonis2()).
0 Comments
Leave a Reply. |