# Goodness of fit test for categorical data with non-negative real numbersca

#### bakwas

##### New Member
An experiment that I conduct has 5 outcomes: A, B, C and D. I conduct 12 trials for this experiment. I observe, for example:

Outcome : Frequency
A : 2
B : 3
C : 0
D : 5
E : 2

Now, I have a model that predicts the frequency. However, the predictions are non-negative real numbers. For example:

Outcome : Predicted frequency
A : 1.75
B : 2.77
C : 0.11
D : 3.82
E : 3.55

I attempted to use the Pearson's Chi-square goodness of fit test to evaluate . However, since the values of frequency are below 5, I read that this test is not the best choice (= reliable). So, I attempted to use Fisher's exact test. The limitation of Fisher's exact test is that the data has to be non-negative integers.

My question: Is there a way to evaluate the p-value between the observed and predicted sets of data where the predicted data are not integers, but non-negative real numbers. The values of frequency are often lesser than 5.

#### rogojel

##### TS Contributor
hi,
part of the problem is that in the measured dataset you do not have frequencies but the number of occurrences , in the prediction you have probably some kind of frequencies, though they do not sum to 100% . I guess the first step should be to unify the outputs of the experiments and the model and then see how you can compare them.

regards

#### nhoncon

##### New Member
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