Wdt_data.1 <- rawdata %*% diag ( 1 / col.max ) In this standardization, each element is divided by its column maximum and then divided by the row total col.max <- apply ( rawdata, 2, max ) Difficult to understand individual data values after standardization.Equalize emphasis among sample units and among species.prop.data %Ĭomplete ( N, nesting ( spp ), fill = list ( ttl = 0 )) To do this we will do our first standardization and adjust each element by the row total (total number by site). Spreads end of scale while compressing the middleīefore we apply the transformation we need to change our rawdata matrix into a proportion matrix.Useful for proportion data with a positive skew.Transforms proportion data ($0 \ge x \le 1$).Needless to say, that althought there are some strong feelings out there against using this transformation, I will go over it so that you know what it is doing. Whenever I think of arcsine transformation, I think of this manuscript “The arcsine is asinine: the analysis of proportions in ecology”. pa_trans 0, 1, 0 )Īpply ( rawdata, c ( 1, 2 ), function ( x ) pa_trans ( x )) # In this function, we will have one parameters. To do this transformation we will write a function that will change any x>0 to a 1. Severe transformation: loose a lot of info.Most useful when there is not a lot of quantitative info present (lots of zeros or low abundances).Transforms quantitative data to non-quantitative data.To illustrate how the level of the power influences the compression, we will use transformations of 2,3,4,5,10 of x values ranging from 1:100.Īs can be observed above, as the level of the power increases the level of compression of the data decreases. Pwr_trans ( x = 16, trans = 2 ) # 4 pwr_trans ( x = 0, trans = 2 ) # 0 x is the data to be transformed and trans will be power of the transformation (i.e., a trans of 2 will be a square root transformation $x^$ ) pwr_trans 0, x ^ ( 1 / trans ), 0 ) In this function, we will have two parameters. To do this transformation we will write a function that will give us the ability to do several different power levels. We will create a simple matrix that we will use as the basis for many of our transformations and standardizations rawdata 0. Standardizations adjust elements by a row or column statistic (e.g., max, sum, mean)įirst we will go over Transformations and then to the Standardizations Create some data Transformations are applied to each element of the data matrix, independent of the other elements There are many packages out there (i.e, vegan) to automatically make these transformations but it is important to understand when and why we make these transformations and so next time you see that a function is doing a Wisconsin Double transformation, you know what just happened to your data.Ī great reference that has considerably more detail about when and why to use these transformations can be found in Ecologically meaningful transformations for ordination of species data What are the differences between Transformations and Standardizations? Kevin McGarigals Applied Multivariate Course with some modifications here and there. We will go over several data transformations and standardizations (aka relativisations) commonly used in multivariate statistics.