Can the variability for the same thing sometimes change acro

Can the variability for the same thing sometimes change across time, or with other circumstances? If so, can anyone share any examples of this?

Solution

The variability is generally refers to the difference in the means of two or more groups of a variable at a given point of time under stipulated experimental environment. It is computed as the sum of squared deviations from the overall mean divide by the sample size less 1(n-1).

Group 1 Group 2

Observation 1 2 6
Observation 2 3 7
Observation 3 1 5
Mean 2 6
Sums of Squares (SS) 2 2

------------------------------------------------------------
Overall Mean 4
Total Sums of Squares 28

In this example, the SS of the two groups is 2 each yielding a total of 4. If, however, we ignore the within the group membership and calculate the SS of all the observations taken together from the overall mean 4 we get an SS of 28.

This difference in the variability of the same variable under study is attributable to the within the group membership also known as the error variance.

The sample taken for the same variable is generated using different sampling methods. The same variable here could be studied for variablity with different smple composition i.e. the observations 1,2 and 3 would be different. THe SS and mean values so generated would be different contributing to changed variability.

Thus, any changes in the experimental group for the same variable would yield changed variability.

If the model under study is further elaborated by incorporating an independent variable affecting the sensitivity of the study the variability of the variable would be affected. For example, if the observations in the model are a sample of population and are further categorised into males and females, the means of males and females would different and the SS would then change, changing the variability of the sample means in turn.

Thus,incorporation of additional factors influencing the model affects varaibility of the same thing over time.