# Compare variances between 2 time series groups

I have a set of 40 subjects that performed a task while the variables of interest were being recorded at regular time intervals (0, 1, 2,.... 10 seconds). The task was performed twice, once with and once without the aid of computer feedback.

For most of the variables, the distribution across subjects at each time point is a normal distribution. But for a few, they are heavily skewed.

I'd like to know if the variance of the collected variables between the subjects was significantly different during the feedback-assisted task.

What is the best way to do this?

• What could be 'best' might depend on a number of things; what are you trying to do best at? – Glen_b -Reinstate Monica Jan 11 '14 at 3:40
• First is the issue of a mixture of skewed and normal data, should I use a test based on medians that is more robust to skewness for all variables? Also, I'm thinking I should treat the observations (feedback/ no feedback) as paired samples for each subject at each timepoint, but I'd also like to quantify any significant change in the variance over time. – orangozhang Jan 11 '14 at 9:42

I was going to suggest Levene's test, but Wikipedia seems to imply that the Brown-Forsythe test would be better for your heavily skewed variables. Levene's test might be a little more powerful for the normally distributed ones.

If you only have two time points corresponding to each time the task was performed, I think this should be pretty straightforward. If you have other time intervals (during which no task was performed) that you want to pool with when the task was performed without feedback, and then compare that pooled variance with the variance during the feedback-assisted task, that might be a little trickier. Hopefully I'm just reading too much into "regular time intervals," and you can ignore this paragraph!