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  #1  
Old 11-28-2011, 10:13 AM
appdyn appdyn is offline
 
Join Date: Feb 2008
State: Kansas
Professional Status: Gvmt Agency, FNMA, HUD, VA etc.
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Default sample or population?

Annually, our assessment office mails out a form requesting income and expense info from commercial property owners. About 40% respond. The data is analyzed in Excel. As you may know, Excel has two basic formats for calculating standard deviation - that for a sample and that for a population.

My question is: does the body (or total) of responses constitute the 'population' of the responses? That is after all, all that we have received. Or is it a sample since not everyone responded?

To me, a sample would be randomly selected responses from the population of returned surveys. I think I should use the population form of the standard deviation function.

Thank you for your insight.
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Old 11-28-2011, 12:19 PM
skx172 skx172 is offline
 
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sounds like a sample to me,

the sample concept is used in cases where population data is just not reasonable to obtain, such as the case your describe

also if you look at the underlying formula you will find the difference between the two is insignificant with a large number of data points

population


sample


the sample equation gives a more conservative figure by deducting 1 from the numerator.


see here http://www.documentingexcellence.com/stat_tool/SD.htm

STANDARD DEVIATION for a population versus a sample: When a set of data contains all the possible data points for a population the calculation of standard deviation provides a specific value that characterizes that population. Such a specific value for a statistic is called a parameter. However, it is much more likely that the data one is working with is not the complete population, but only a sample. When a sample is used we need to estimate the standard deviation from the sample. In this situation 1 is subtracted from the N number of cases. (See the formulas above) For small samples this N-1 tends to increase the standard deviation slightly, making it a conservative estimate of the population's parameter. As sample size increases the effect of N-1 declines and the results of the two formulas converge


Quote:
Originally Posted by appdyn View Post
Annually, our assessment office mails out a form requesting income and expense info from commercial property owners. About 40% respond. The data is analyzed in Excel. As you may know, Excel has two basic formats for calculating standard deviation - that for a sample and that for a population.

My question is: does the body (or total) of responses constitute the 'population' of the responses? That is after all, all that we have received. Or is it a sample since not everyone responded?

To me, a sample would be randomly selected responses from the population of returned surveys. I think I should use the population form of the standard deviation function.

Thank you for your insight.
  #3  
Old 11-28-2011, 12:47 PM
appdyn appdyn is offline
 
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State: Kansas
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Posts: 27
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SKX172:

Very excellent answer. A sample it is!

Thank you very much.

appdyn
  #4  
Old 11-28-2011, 01:19 PM
Terrel L. Shields's Avatar
Terrel L. Shields Terrel L. Shields is offline
 
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Yep, sample. The sample is "randomly" selected in that you don't know who will answer, so unless the sample is tainted (say a certain religious group held a belief in not providing data and were a significant part of the population...then the sample is flawed) I would aver you have a sample but a significant sample. skx is right on.
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  #5  
Old 11-30-2011, 12:02 PM
CBBoston CBBoston is offline
 
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A best there is selection bias in the respondents which is a bit of a problem. Granted you have a large proportion of the population reporting info. However this is self-reported info. As such it is in of itself unreliable. Wouldn't a property owner have an incentive to report lower income and higher expenses? They sure would and frequently do! Why pay more property tax than you have to. Unless they are giving you actual leases, the income is suspect. Then you've got then expense side. I've seen so many operating statements provided by owner that were undecipherable. I saw one in which the owner was reporting leased auto payment for girlfriends in tow different cities so his wife wouldn't know about them. I know you're trying to work with the best info you can get but you need to have someother benchmark as a point of comparison.
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Old 11-30-2011, 12:05 PM
CBBoston CBBoston is offline
 
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Oh ya, read the piece reference at the top of commercial/industrial page. Its an eye opener for those not well versed in commercial valuation.
  #7  
Old 11-30-2011, 01:51 PM
appdyn appdyn is offline
 
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I agree, CBB, there is a strong potential for bias in the responses. We do cross check the data with other third party sources when possible, but they seem to be getting harder to find.

And since those responses constitute the body of the population is why I thought the population standard deviation would be more appropriate. If however, I drew random samples from the data collected I would deem the sample SD more appropriate. However, the logic of others (both on and off the forum) has persuaded me otherwise.
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