Perform some statistical analysis on a matrix to get p-values?

[cwright1]

Suppose I have the following 12 x 12 matrix called my_mat :

0.21	0.9	0.56	0.9	0.22	1.46	9.94	47.61	63.36	65.09	65.21	65.22
1.1	1.09	0.41	1.07	0.44	1.23	12.21	58.51	77.85	79.97	80.13	80.14
1.16	0.62	0.54	0.59	0.58	1.11	12.59	65.26	86.84	89.2	89.38	89.39
0.91	0.62	0.62	0.62	0.67	1.2	6.85	69.4	92.3	94.75	94.96	94.99
0.71	0.67	0.67	0.67	0.72	1.28	7.38	71.7	95.01	97.25	97.55	97.67
0.7	0.7	0.55	0.7	0.75	1.33	7.7	66.97	90.48	92.32	92.55	93.06
0.9	0.56	0.21	0.22	0.22	9.94	1.23	11.74	31.86	33.34	29.71	27.78
1.09	0.41	1.1	0.44	0.44	12.21	1.11	71.7	5	6.32	5.11	4.54
0.62	0.54	1.16	0.58	0.58	7.7	7.7	71.7	1.3	2.42	2.15	1.98
0.62	0.62	0.91	0.67	0.67	1.23	1.23	1.11	0.47	1.75	1.76	1.73
0.67	0.67	0.71	0.72	0.72	1.11	1.11	1.2	0.64	1.86	1.85	1.81

If we plot the matrix as a heatmap, we can see there exists a definite 'hotspot' region, in the upper right quadrant of the data:

library(pheatmap)
pheatmap(my_mat)

I'd like some way to express with a p-value that a given square is or is not significantly different than other squares in the matrix.

Is there some way to do this in R? Can I obtain a matrix of p-values by doing this?

[GreyMerchant]

Hello,

Without knowing what these squares represent and how you derived them it might be erroneous to want to calculate p-values (also to calculate so many would be of little use as we'd already have quite a lot of possible comparisons)

The square itself is a constant and not like a variable with a meaningful mean, standard deviation, variance etc.

[cwright1]

Thanks for the response that does help me understand. This matrix of results is an example of what I'm seeing when I calculate how well two drugs work together - the higher values represent the combination score. The axes are the drug concentrations. So at a particular concentration of Drug1 combined with a particular concentration of Drug2, I get a distinctly high value in the matrix (aka they work very well together at these concentrations). How can I statistically represent this?

Thanks for your comment

[GreyMerchant]

I am assuming you have a value for Drug1 and Drug2 for each person? Do you have some sort of dependent variable that quantifies the efficacy of those drugs used together?

[cwright1]

Yes that's right.
Sample_A = Drug1 (12 concentrations) x Drug2 (12 concentrations).
Repeat for Sample_B, Sample_C, Sample_D.

I average them all into a single matrix based on the % of cells that die (20% for example). Then transform that into a synergy score (how well both drugs perform compared to what you would expect based on each individual drug alone).

So if I get a single cell of the matrix that has a synergy score of 50 (for example), but all other cells of that matrix have scores on the order of ~1-5, that should mean the concentration of Drug1 and Drug2 that give the score of 50 is by far the best.

How could I put a p-value on that cell (containing a score value of 50) ? Saying compared to all other values of the matrix, it is statistically different.

[GreyMerchant]

There is a lot more happening here. I really am not entirely sure if you have independence etc given this averaging. I'd also actually need to see your data with transformations in raw. Consider a reprex: FAQ: How to do a minimal reproducible example ( reprex ) for beginners

You wouldn't want to compare a single cell against all other values in the matrix as you'd be running close to 143 tests with that single cell. I am sure there is a field specific approach in how to determine significance or test this. A two independent samples t-test would already make more sense where you compare one group who received a certain dosage against another group who received a different dosage and then work with H0: There is no significant difference and then H1: There is.