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I would like to optimize a physical model using kolmogorov-smirnov test between the experimental data and generated data. The output of ks.text(x,y) give me the distance D and the p-value. Which is the relation between them and which is suitable for my task? namely i should take the model that give me a smaller distance or a smaller p-value?

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A low p-value means that it is likeley that the data is different from the model. So you want a high p-value to have a good fitting.

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This is not entirely true. Small p-value (smaller than your threshold 0.01, 0.05) tells you that the null hypothesis is false while having a big p-value tells that you can't false it (this it's not the same as saying that null hypothesis is true). –  Daniel Sep 6 at 18:35
    
@Daniel: Yes that's right. But I thought at that level the answer is "good enough". Don't you agree? –  Manuel Kuehner Sep 8 at 7:02

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