A fair way to measure the difference of two measurements

[fanfan]

I would like to ask if anybody can help me figure out a fair way to measure the difference of two measurements in percentage.

I have two sets of measurements X and Y, and both are data with unknown noise.
To measure the difference in percentage of these two, both equations can be used (I suppose):

1) I consider that X is the first measurement, and test how different is Y comparing to X
diff1_i = (xi-yi)/xi*100
or
2)
diff2_i = (xi-yi)/((xi+yi)/2)*100

Of course abs(diff2_i) is smaller than abs(diff1_i). But which one is more fair than the other?

By measuring the median or mean of all the difference Ʃdiff1_i or diff2_i (i=1:100), I can test if the two measurements are biased, or the difference is due to random noise in the data, right?
I tend to think that no matter which equation to use, the maximum difference in percentage should be looked into, right?


Fanfan

 

[jvicens]

I can offer some suggestions for measuring the difference between two measurements in percentage.

Firstly, it is important to consider the nature of the data and the purpose of the comparison. Are the two measurements independent of each other, or are they related in some way? This will help determine which equation is more appropriate to use.

If the two measurements are independent, then both equations can be used. However, it is important to note that the first equation (diff1_i = (xi-yi)/xi*100) assumes that the baseline measurement (X) is the more accurate one. This may not always be the case. In this situation, it might be more fair to use the second equation (diff2_i = (xi-yi)/((xi+yi)/2)*100) as it takes into account the average of the two measurements.

On the other hand, if the two measurements are related, such as in a before-and-after scenario, then the second equation would be more appropriate as it accounts for the changes in both measurements.

In terms of determining bias or random noise, calculating the median or mean of all the differences can be a good way to start. However, it might also be helpful to plot the differences on a graph and look for any patterns or trends. This can provide more insight into the nature of the differences.

Ultimately, it is important to consider the context and purpose of the comparison when determining which equation to use. And as you mentioned, it is always a good idea to look at the maximum difference in percentage to ensure that it is not being skewed by outliers.