How do you interpret "nested" standard deviational ellipse?

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11-03-2015 07:22 AM
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New Contributor II

We would like to explore disparities in Tobacco retail locations in my county. Majority were surveyed by the local health department however, there were 16 that were not surveyed. We would like to use the surveyed location to explore the disparities however, we want to confirm that those that did not participate in the survey, are not located in areas that is potentially different from the area of those surveyed. To answer this question, I thought the best approach would be to calculate the mean centers and standard deviational ellipses ( at one standard deviation) to compare the distribution of surveyed v not surveyed. The mean centers of both, surveyed and not surveyed were within a 1/2 mile of each other however, the ellipse of the not surveyed was with in the ellipses of those surveyed. Because i am relatively new to the field, I just wanted to confirm that my interpretation of the "nested" ellipses results means that we can be confident that  the information collected from the survey "speaks" to the general landscape of tobacco retail in the county. ( see attachment for reference)

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Occasional Contributor

If the size and shape of the SDEs were more closely aligned … then you could say that the distributions were similar and that the surveyed and un-surveyed stores are part of the same “landscape.”

Since the ellipse for the un-surveyed locations is much smaller than the ellipse for the surveyed locations, this seems to indicate the opposite … that the un-surveyed locations are actually not representative of the entire county/study area.  The fact that all of the un-surveyed locations fall into the surveyed ellipse is not sufficient evidence, however …

  • The surveyed ellipse contains the ellipse for the un-surveyed locations.  This is the one bit of evidence that the surveyed locations are representative of the landscape.
  • How were the surveyed locations picked?  This is a very important question to answer in order to be confident that the information collected from the survey is representative of all the tobacco retail in the county.   If there was no bias in how the department picked who was and wasn’t going to be surveyed – that would also be evidence.
  • If all of the un-surveyed locations are within x distance of a surveyed location, then you would need to provide justification that the spatial context for locations at the farthest distances would be homogeneous … it looks like there are surveyed locations very close to every un-surveyed location except 2.  Can you provide any evidence that indicates that those locations would not be different from their closest surveyed locations or from other surveyed locations in the study area? 
  • Schools are shown on your map.  Are they important to the analysis?  If they are then it might be helpful to ensure that surveying around each school meets some threshold to give confidence that the un-surveyed locations are not biasing the sample.  Example: for all schools at least 50% of establishments within 1 mile were surveyed.  Those that did not meet this criteria were excluded from the analysis.

Hope this helps!

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MVP Esteemed Contributor

That all of your not surveyed fell within the standard deviation of those that were surveyed.  It is quite possible that your not surveyed center and SDE would have been different if you had not surveyed points at the extremes of your data distribution

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New Contributor II

Thanks

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Occasional Contributor

If the size and shape of the SDEs were more closely aligned … then you could say that the distributions were similar and that the surveyed and un-surveyed stores are part of the same “landscape.”

Since the ellipse for the un-surveyed locations is much smaller than the ellipse for the surveyed locations, this seems to indicate the opposite … that the un-surveyed locations are actually not representative of the entire county/study area.  The fact that all of the un-surveyed locations fall into the surveyed ellipse is not sufficient evidence, however …

  • The surveyed ellipse contains the ellipse for the un-surveyed locations.  This is the one bit of evidence that the surveyed locations are representative of the landscape.
  • How were the surveyed locations picked?  This is a very important question to answer in order to be confident that the information collected from the survey is representative of all the tobacco retail in the county.   If there was no bias in how the department picked who was and wasn’t going to be surveyed – that would also be evidence.
  • If all of the un-surveyed locations are within x distance of a surveyed location, then you would need to provide justification that the spatial context for locations at the farthest distances would be homogeneous … it looks like there are surveyed locations very close to every un-surveyed location except 2.  Can you provide any evidence that indicates that those locations would not be different from their closest surveyed locations or from other surveyed locations in the study area? 
  • Schools are shown on your map.  Are they important to the analysis?  If they are then it might be helpful to ensure that surveying around each school meets some threshold to give confidence that the un-surveyed locations are not biasing the sample.  Example: for all schools at least 50% of establishments within 1 mile were surveyed.  Those that did not meet this criteria were excluded from the analysis.

Hope this helps!

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New Contributor II

Wow thanks for the detailed response!

The map attached is a rough draft. I included the schools just because I forgot to turn off the layer when I exported the map.

Survey locations were not picked, we contacted all retailers and 16 chose not to participate in the survey.

The only evidence that can indicated that these locations would not be different from closest surveyed locations or other surveyed locations is by understanding the survey data better. For example if our data exploration reviles that store type is the main factor that affects advertising, we can classify the not surveyed by store type and see if they are represented in the surveyed locations.

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Occasional Contributor

Sounds like you are on the right track!