Degrees of freedom (statistics)

[bunnahabhain]

Hi everybody

I am not sure if I understand my statistics textbooks correctly. Numerous equations refer to the degrees of freedom. What exactly is this?
Example: I run a calibration with 6 concentration levels. Each level is injected in duplicate. Is the number n I use to calculate the degrees of freedom 6 (because there are 6 concentration levels) or 12 (because I have measured 12 data points)?

Thanks for enlightenment,
Jörg

[pancaker]

There are a number of types and ways of calculating degrees of freedom. It depends on the type statistical analysis you are carrying out.

Each statistical analysis may call for the use of a different number. Pay close attention to the definition of 'n'. Typically 'N' (uppercase) refers to the total number of measurements.

In this case you can consider your total DoF to be 11. Also known as "within groups" DoF.

You also have...

You have 5 DoF in your treatments. (6 - 1) aka "between groups DOF"
You have 6 DoF of freedom for error (12 - 6).

[bunnahabhain]

OK thank you but I still don't understand

The reason why I'm asking is the following: I am trying to set up an excel sheet that does linear calibration and weighted linear calibration (as described by John Dolan in LCGC "Calibration Curves, Part V: Curve Weighting" July 2009).
The equation used for this calculation is here:

(Miller, 1984, Statistics for analytical chemistry)

Don't bother the process how the weights are calculated, I am interested in which n to use: Number of injections or number of concentration levels together with mean of peak areas. This is, if I understand it correctly, the same n I have to use for calculation of r² and residual standard deviation etc.

Any further guidance?
Jörg

[chemstation]

Are you using the Excel function Linest http://www.excelfunctions.net/Excel-Lin ... ction.html

As a guick search for excel linest weighted regression

http://www.mrexcel.com/forum/excel-ques ... ssion.html

Alex

[pancaker]

I think maybe you're just confusing the terminology. The variable
"n" rarely denotes degrees of freedom, which is usually represented by the Greek nu ( v ) or "df".

In those equations, "n" pretty clearly refers to your total number of data points-- 12. It does not refer to degrees of freedom.