Statistical definition for calculation similar to variance

[sciencer]

Variance is a measure of the variation in a data set, defined as Σ(y-mean(y))^2/(n-1). Is there a statistical term for the following calculation:

 

data set

time data

1 10

2 11

3 -22

4 34

5 -45

6 56

7 67

8 -78

 

variation between adjacent data v=(datum(t+1)-datum(t))^2

square root of v to obtain positive values of variation=v^(1/2)

 

Σv^(1/2)

median(v^(1/2))

[Bignose]

It is something related to the time derivative of the data, which certainly can have a lot of meaning. It may also have some meaning as to whether the sample of time t is independent or dependent on samples of time t-1 and earlier or not -- that is, whether it is a Markov process or not.

 

However, generally, if you are sampling a population, the order in which you sample should not matter, so the difference between specific samples usually carries no meaning.

[sciencer]

Thank you. For this data set representing measurement of temperature as a function of time, is it correct that the data would be independent (i.e. Markov process) when the time interval is regular, for example a measurement made every 10 seconds?

[Bignose]

Thank you. For this data set representing measurement of temperature as a function of time, is it correct that the data would be independent (i.e. Markov process) when the time interval is regular, for example a measurement made every 10 seconds?

 

It depends entirely on the process. If a large reason why the temperature fluctuates is random (i.e. a large variation in the ambient atmosphere causing large variations in the convective heat loss), then it may be independent of previous time. If the random component is small, then it may not be. You'll have to determine for your own process whether the assumptions regarding a Markov process as applicable or not.