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I have the expected ratio of four parameters A, B, C and D

A : B : C : D 3.9 : 12.0 : 24.3 : 59.8

I perform three experiments which provides me ratios of A,B,C and D. As the results show, the ratios obtained in Experiment 1 are more closer to the Expected ratio Experiment 3 seems to be the worst

A : B : C : D Experiment 1 3.9 : 12.0 : 24.3 : 59.8
Experiment 2 0.7 : 2.0 : 25.6 : 71.7
Experiment 3 3.9 : 29.9 : 53.3 : 7.2

Please suggest a single metric that can clearly indicate the closeness of values obtained in various experiments (as compared to the Expected ratio)

Need to do this for a lot of experiments

Monzoor
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  • It depends on what you mean by 'close'. Common choices would be mean absolute error, mean (absolute) relative error, mean square error, ... $ \quad $ what are the values measuring? – Glen_b May 05 '14 at 11:34

1 Answers1

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You can use the chi-square goodness of fit to measure similarity.

The more the deviation from theoretical expectation, the larger will the chi-square stat be.

Similar outcomes would mean chi-square stat would be small.

If you use R, this is a sample code:

expected_proportion=c(3.9 , 12.0 , 24.3 , 59.8) chisq.test(table(outcomes),p=expected)

Arun Jose
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