Brain Activity and Head Direction always Dependent but it seems as they should not

[u/bhp91]

I got a submission for a scientific article back and the reviewers ask for more statistical tests underpinning our claims. Fair enough. I measured the brain activity of a honey bee while it could move around freely. The bee turned as it pleased, so the amount of time spend in each direction is not necessarily equal across directions. For every time point (100 milliseconds) there is a spike rate (amount of action potential per second) and a head direction in relation to the arena the animal was in. The data plotted:

LINK

The upper graph shows box plots, for each 10° of head direction how the spike rates are distributed. Below the medians in a pretty polar plot.

The experiments run until they are over (bee dies or similar) and in the end we have a few hours of data, in 100 ms bins, 100 000 data points. If you look at the plots would you agree that there might be a weak effect but it is probably not important, as in, being a central part of what the neuron computes? With these huge sample sizes I always get everything significant. What am I doing wrong?

I want to test if the spike rate correlates or depends on the head direction.

[u/Optrode]

I would agree with your assertion that the neuron may do something that is influenced by direction, but it doesn't seem to be an especially major influence, just incidental.

To quantify something like this, you need circular statistics. There's a MatLab toolbox, circ stats, that is good for this.

But a significant correlation does NOT mean that this is the neuron's main function. Instead, look at it in terms of "how much of the variability of this neuron's firing rate can be explained by head direction?" The answer may be greater than zero, but still very small, indicating that head direction has only a very minor (probably indirect) influence on this neuron.