# How to transform a data set to downweight (relative) small numbers

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).

• Perhaps I missed something. What analysis were you running? – Glen_b Mar 8 '14 at 22:13
• The final analysis would be nMDS, which I'm finding to be usefull but too sensitive to small changes. Thus I'm hoping to find a transformation to lessen this effect – Vinterwoo Mar 8 '14 at 23:17