I'm at a beginner level regarding statistics knowledge and I would very much appreciate any help with this problem.

I have a 10000x2 table (see below, first column is actually the index) where the first column holds binned data representing observations, dataset

**A**, and the second one holds binned data in the same range but for a model:

**B**(you can check here to see where this question is coming from)

Code:

```
A B
1 1 0
2 0 0
3 1 0
4 0 1
5 1 0
6 2 0
7 1 0
8 3 0
9 0 0
10 0 0
11 5 2
12 1 1
13 0 1
(...)
```

**B**with respect to observations

**A**(ie: I need an estimator of how good is model

**B**representing data in

**A**) and I've been advised that

*Fisher's exact test*is what I should apply.

If I use

**R**'s implementation of Fisher's test (fisher.test) using the

*Monte Carlo simulation*option (simulate.p.value=TRUE), I get this:

Code:

```
> test_grid <- read.table("test_grid")
> test_grid
A B
1 1 0
2 0 0
3 1 0
4 0 1
5 1 0
6 2 0
7 1 0
8 3 0
9 0 0
10 0 0
11 5 2
12 1 1
13 0 1
(...)
> fisher.test (test_grid,simulate.p.value=TRUE,B=10000)
Fisher's Exact Test for Count Data with simulated p-value (based on
10000 replicates)
data: test_grid
p-value = 9.999e-05
alternative hypothesis: two.sided
```

- Calculate the
**p-value**for that particular table - Calculate the
**p-values**of all possible combinations of that table that comply with Fisher's fixed-margin condition - Add up only those values less or equal than the
**p-value**obtained for the original table arrangement to obtain the final**p_value**displayed

Now my questions are:

- What is the meaning of the final
**p-value**in this context? How would I describe it? - What would the null hypothesis look like for this problem?

I've been told that in this context, a

*higher***p-value**is what I want because

*the null hypothesis of independence would mean that whether the data come from A or B, you observe a similar distribution across your bins*and that

*the higher the p-value the better the fit*. I think I understand this, but I still have problems phrasing both points above.

Any help would be very much appreciated.

Cheers!