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# How to Interpret Index of Dispersion (ID) in ENA SMART Output?

This question was posted the Assessment and Surveillance forum area and has 3 replies.

### Mark Myatt

Frequent user

21 May 2014, 20:14

The SMART people should be able to respond with more detail than I can. I can offer a general interpretation of the variance to mean ratio (VMR or index of dispersion). The VMR tell you about the 'clumpiness' of your data. Interpretation is: ``` 0 <= VMR < 1 More uniform than expected VMR = 1 Randomly distributed (following a Poisson distribution) VMR > 1 Clumped distribution ``` I assume the p-value given is for a chi-square test with the null hypothesis that the VMR = 1. VMR > 1 and p > 0.05 means that the observed VMR is not significantly different from 1 and there is only weak evidence that cases are very clumpy. I would guess that the observed VMR is quite close to one or you have a small sample size. I hope this helps.

### Tamsin

Forum Moderator, ENN

Forum moderator

22 May 2014, 08:27

From Anonymous 1476: Dear Mark Myatt, Thank you very much for such very brief and clear information. I know that for any test statistics if P-Value >0.05 there is no significant evidence to reject the null hypothesis. I have calculated the sample size with ENA software. As the end of the assessment, I have gotten 431 children included in the Anthropometric measurement from 564 households visited. From the statistics point of view, I think the sample size is not small. May be there is some point with my data quality or latest version of ENA I have used (November 2013 version). I will agree with your point of clumpiness. Really, I have gotten very valuable information from your idea and let us keep in touch. With Regards

### Mark Myatt

Frequent user

22 May 2014, 14:42

Thank you for your kind comments. The sample size calculation in ENA is for the sample required to estimate a prevalence with a specified precision. I think that no considerate is given to the power for the test associated with the ID. I'd guess that the sample will big enough in most (if not all) SMART surveys for this test to have useful power. What was your ID (effect size) and p-value? I'd guess the ID was not very large.