# Testing whether variance across 6 values is significantly above zero

We estimated a network via the Ising model procedure. The network contains 11 variables, and therefore 55 pairwise associations (these are called edges).

We estimated this network in 6 different samples, leading to six networks.

Our question is now whether a given edge, for instance the edge between variable 1 and 2 (one of the 55 pairwise associations in each network), varies substantially across the six networks.

For each edge, we have 6 values (the edge weight of this edge in each network), and we can compute a variance over these 6 values. We now want to test whether this variance is substantial (i.e. significant from zero).

We can also derive confidence intervals around each edge, if that is helpful. So for the edge between variable 1 and 2, we could have the values (first: edge weight; then confidence interval):

network 1: 4 (CI 3-5)
network 2: 5 (CI 4-6)
network 3: 2 (CI 1-3)
network 4: 3 (CI 2-4)
network 5: 4 (CI 3-5)
network 6: 5 (CI 4-6)


How do we test whether the variance of this particular edge is significantly different from 0? (or, if that is not possible, "substantial" [I know this is open to interpretation]).

• Assuming no measurement error, if the observed variance is nonzero, then it is significantly above zero (at any possible level of significance), because it definitively establishes the variance is nonzero. If there is a possibility of measurement error, then what quantitative information can you provide about its variance? This is such a strange situation that it makes one wonder whether you are asking the question you need to. Could you clarify what you really mean by "significant variability across the ... networks in [an] edge"?
– whuber
Jun 24, 2015 at 16:04
• Thank you. In a minor analysis of a paper, we want to establish whether the 6 networks estimated via Ising Models differ (same variables, but different samples). This is extremely demanding and worth at least a PhD project, so not feasible for this paper. So we look for simpler ways. One idea we had was determine the variability of each edge across the 6 networks, and if this variability is substantial, that provides some information. I could bootstrap confidence interval around each edge in each network. That would provide information about error. Would that help? Jun 24, 2015 at 20:57
• That's quite a different description of the problem! Please edit your post so that readers understand what you're looking for.
– whuber
Jun 24, 2015 at 20:59