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### Help with difficult analysis for a begginer

Posted: Wed Jan 10, 2018 9:58 pm
Hello, I'm a masters student and I need some help analyzing my data. I will do my best to explain what is the type of data that I possess.

I work with electrical recording of individual nerve cells in live rats. Consider, for the sake of my explanation, that my N is the number of cells that I have (not the number of rats). I also made the noob mistake of devising my protocol without the statistical analysis in mind, so I don't have room to change it anymore. It is what it is.

Ok, so, this is the situation: each cell that I'm recording has its own frequency of firing in what I call the 'basal' condition, where the rat is in a certain environment and no stimulus was presented to the animal. You can see without doing any tests that these frequencies fall within certain ranges. Some cells have a basal frequency of around 1~2Hz, others have it around 4~6Hz, others 15~20Hz and very rarely it goes above that. Their firing pattern doesn't appear to be a normal distribution to me. For example, a cell within the 1~2Hz range will usually spike 1 time per second, sometimes it will spike 2 times per second, more rarely 3 times per second (similar to a geometric or chi-squared distribution according to the picture of this link: http://blog.cloudera.com/blog/2015/12/common-probability-distributions-the-data-scientists-crib-sheet/).

Alright, then I proceed to introduce a neutral stimulus to the rat, and I keep recording the same cells. In thesis, the neutral stimulus shouldn't change the behavior of the cells, and that is usually what happens. After that, I introduce an adverse stimulus. In this moment a number of things appear to be happen: certain cells appear to increase their firing rate, others appear to decrease and others appear to remain unchanged (I can say that because I plotted a graphic with the average firing rate of cells accross the different points of the experiment). Importantly: cells appear to change their behavior regardless of their 'basal' firing rate, that is: a cell that was firing at 1~2Hz may start to fire at 4Hz, a cell that was firing at 4~6Hz may start to fire at 10Hz, or fall to 2Hz, without a clear pattern (at least to me) between initial firing rate and cell behavior in face of the adverse stimulus. Finally, the next day I reintroduce the animal to the place where he faced the adverse stimulus. You can say that this is, in itself, a type of stimulus. Let's say that is the 'bad place stimulus'. Here I also receive a different array of patterns from the cells (some decrease their firing rate, other increase, etc.).

Okay, after I plot the behavior of each individual cell in a graphic, some patterns appear clear as day. For instance: some cells increase their firing after and during the adverse stimulus. These same cells, in the next day, are already back to their usual 'basal' firing rate. Some other cells increase only during the 'bad place stimulus'. Some cells increase after the initial stimulus and remain like so for the whole of the next day. And finally, some cells remain unchanged during such stimulus. Some have similar behaviors, but they decrease their firing rate instead of increasing.

Here are my questions:

1) it appears to me that, in simple statistical terms, the behavior of the cells is my dependent variable, and the stimulus are my independent variables, is that correct?

2) I have an issue that I don't know how to resolve, statistically. I see these clear groups of cells with particular behaviors, and I'm not sure if I can group them only by the fact that I 'know' they have particular behaviors. For example, can I put together all my cells that change their firing rate only during the presentation of the adverse stimulus and call them 'adverse stimulus cells'? And could I also do that for the cells that change during the 'bad place stimulus' and so on?

3) If the answer to the question above is 'yes, you can', my follow up question: how can I show, statistically, that the behavior of a particular group of cells change or doesn't change after the introduction of a stimulus with a good degree of confidence? Two things trouble me:

(i) the firing rates of the individual cells are different from each other, so I believe I would have to normalize their firing rate by their total number of spikes if I were to group them (but I'm not sure if I should or should not do that) and

(ii) I don't know if I can, for example, simply test the behavior of the cells BEFORE the introduction of the adverse stimulus vs. their behavior AFTER the introduction of the stimulus, because most tests that I know assume that the samples are independent from each other when making such comparisons, which I believe it is not my case (the cells are still the same, they are just in a before/after scenario).

4) If the answer to question 2) is 'no, you can't', how can I show statistically that each individual cell could be grouped with other cells based on the similarities of their firing pattern? And, after that, I refer back to question 3): how can I show, confidently, that the behavior of a particular cell is changing in face of the stimulus that I'm giving to the animal?

Thank you so much for any help you can provide, I'm also trying to sift through the literature to see if I can have the answer to my questions, but that is a very complicated task.