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.