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# Calculating Median Channel Shift with Kaluza v1.5

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There are applications where it is valuable to calculate Median Channel Shift between two populations. Previously it wasn't possible to do this in Kaluza because it doesn't have a feature to express statistics in linear bin numbers. Kaluza v1.5 adds exponent and logarithm functions to the information table expression language, which allows us to calculate this.

These expressions are a little complicated, so I recommend that you prepare your expression in a program like Notepad, and then copy and paste it into the information table in Kaluza.

First let's calculate the Median Channel for a population. The easiest thing to do is to just add a statistic to the information table for the median of the population in question. Then you can select the automatically generated equation to get the function for the median. Here's an example:

=MEDIAN("A", "FL2", Logarithmic, 1)

This returns the median of the FL2 parameter of population A from data set 1. The Logarithmic parameter is necessary to tell Kaluza how you want the data binned for the calculation.

To take this to the next step and calculate the Median Channel, we need to have some more information:

1. Number of decades - This is the number of decades to bin the data to, starting from the highest value. A typical value is 4.
2. Number of bins - The number of bins (channels) to use. A typical value is 1024.
3. Maximum input value - This is usually the largest value the source median can have. Because Kaluza scales values by default, this value is 1024. However, if you use the new Full Range Statistics in Kaluza v1.5 then you need to know a little more about your parameter. For Gallios/Navios/FC500 area parameters the number is 1048576. For height parameters for Gallios/Navios/FC500 or for most BD instruments the number is 262144.

So assuming 4 decades, 1024 channels, and a maximum input value of 1048576 the equation for determining the Mean Channel value is:

=LOG(MEDIAN("A", "FL2", Logarithmic, 1)*10^4/1048576)*1024/4

You can take the median statistic you added and modify its information table entry to use this formula and update the label.

To calculate Median Channel Shift then, you just need to do the above for two populations and subtract them. So if you had a composite protocol with a standard in data set one and a sample in data set two, you could calculate the shift of FL2 in the sample for population A by this equation:

=LOG(MEDIAN("A", "FL2", Logarithmic, 2)*10^4/1048576)*1024/4-LOG(MEDIAN("A", "FL2", Logarithmic, 1)*10^4/1048576)*1024/4

Again, these are much easier to work with if you edit them in a program like Notepad.
Using this, you just have to substitute the values and populations for your own data to start calculating Median Channel Shift.

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