I've got a data set looking at how different groups change over time.
#High Abundance, Low Change HALC<-c(100,99,101,98,99,100,100,101,99,100) #Low Anundance, Low Change LALC<-c(1,2,1,2,2,2,1,2,1,2) #High Abundance, High Absolute Change HAHAC<-c(100,99,98,91,86,50,45,30,21,9) #High Abundance, High Absolute Change LAHAC<-c(9,21,30,45,50,86,91,98,99,100) #High Abundance, Changes 10% HA10C<-c(100,101,102,103,104,104,106,107,108,110) #Low Abundance, Changes 10% LA10C<-c(1,1.01,1.02,1.03,1.04,1.04,1.06,1.07,1.08,1.1) #High Abundance, Changes 100% HA100C<-c(100,110,120,130,140,140,170,175,187,200) #Low Abundance, Changes 100% LA100C<-c(1.00,1.10,1.20,1.30,1.40,1.40,1.70,1.75,1.87,2.00) DF<-c(HALC,LALC,HAHAC,LAHAC,HA10C,LA10C,HA100C,LA100C) DF<-data.frame(HALC,LALC,HAHAC,LAHAC,HA10C,LA10C,HA100C,LA100C) row.names(DF)<-c(1,2,3,4,5,6,7,8,9,10)
I'm running a secondary analysis that turns out to be much more sensitive to relative change within a single group, as opposed to the entire data set. For example, looking at these two groups:
#High Abundance, Changes 10% HA10C<-c(100,101,102,103,104,104,106,107,108,110) #Low Abundance, Changes 10% LA10C<-c(1,1.01,1.02,1.03,1.04,1.04,1.06,1.07,1.08,1.1)
If I run my analysis on the above data, these two groups get weighted exactly the same because both change only 10%.
But in terms of my interest in the dataset, I'm much more concerned with change in units (change relative to the entire data set). AKA That the High Abundance/ 10% change group increased by 10 units is much more important than the Low Abundance/ 10% change which only increased 1 unit.
So can anyone recommend a data transformation that would either:
1 Transform the data to reflect the importance of change in relation to the relative size of the dataset (AKA Even though an increase from 1 to 2 is a 100% change, in relation to the data set it is a very small change)
2 or at least downweight the impact of low relatively small data
Because in the end my secondary analysis is going to give more weight to something that increases from 1 to 2 than 100 to 102 (based on percent change), which I would like to avoid.
As a final note, I need to avoid negative numbers and zeros in my final transformation. And still preserve the change over time aspect of the data (increasing or deceasing over time).