# How to use PACz appropriately?

Hi Mike,

Phase-amplitude coupling was laid out in the Chapter 30 of ANTS. To handle three potential confounds, you applied a nonparametric permutation testing to obtain a standardized Z-value of PAC: PACz. This was a very elegant method and your explanation was also very convincing. I have three questions about how to use PACz appropriately.

1. In my understanding, PACz can be generally used in two ways. First, the PACz value ifself can manifest whether the coupling exists in one frequency pair by being compared with one statistical threshold. Second, the PACz values reflect the coupling strength so they can be compared between different values. Am I correct?

2. For the exploratory application, you advised to select a salient region in frequency-frequency space across all conditions and then to compare PACs in this specific frequency pair between conditions. Could I directly compare frequency-frequency space between different conditions using cluster-based permutation test?

3. How to handle baseline? It seems inappropriate to use similar methods of baseline correction from time-frequency power analysis. Do we need to consider the influence of baseline coupling level and how?

For the third question, you can subtract PACz from a baseline period if you want. PACz values are inherently scale-independent, so there is no impact of 1/f that requires a nonlinear solution (e.g., dB) like for time-frequency power.

Thank you very much, Mike. I’m sorry that I have two more questions. Hope you could give some comments.

1. Regarding the number of cycles at phase-frequency, which influences the temporal precision, I found out a little inconsistency in the codes of Figure 30.8. In the line 427 of chapter30.m, you used the variable cfc_time_window_idx determined by cycle number(cfc_numcycles) and phase frequency(freq4phase). However, in the loop of phase frequencies, the variable cfc_time_window_idx was not updated and it corresponded to a constant time interval. As a result, for the phase frequency other than 10 Hz, the number of cycles would vary. For example, the phase frequency of 20 Hz had 6 cycles, which would decrease the temporal precision. I tried the constant number of cycles that corresponded to the varying cfc_time_window_idx. The result was a little different from Figure 30.8a (see the below figure).

I am wondering whether you deliberately used the varying number of cycles here. I think that the constant number of cycles (e.g. 3) would have better temporal precision.

1. Regarding the nonparametric permutation testing in PACz, we can get a single PACz value for each frequency pair by shuffling and then concatenating trials, just as Figure 30.8b showed. The trial information was lost in this way. To obtain single-trial PACz, the similar permutation testing can be performed within each trial. Averaging single-trial PACz, we could also get a single PACz value. I tried both strategies and found a little difference (see the below figure).

How do you see the difference? Did Figure 30.8b have higher SNR? Would you recommend to compute single-trial PACz in analysis?

Oh, great catch! I don’t remember if that was intentional, but it’s certainly possible that that’s a small bug in the code.

The difficulty with these kinds of parameters is that there is no right or wrong; there are only choices. The important thing is to pick a set of parameters and apply it equally to all conditions/channels/subjects/etc.

As for single-trial PACz: No, I don’t really recommend that. Computationally it’s fine; the issue is that the effect size of CFC is really really small except in the rodent hippocampus during active exploration. I’d be concerned that the effect size is too small to reliably detect on the single-trial level.

Insightful explanations! Thank you so much!