How Can I Calculate Sample Accuracy for a Web Poll?

  • Context: Undergrad 
  • Thread starter Thread starter bradles
  • Start date Start date
  • Tags Tags
    Accuracy
Click For Summary
SUMMARY

This discussion focuses on calculating sample accuracy for a web poll with a sample size of 40 respondents regarding spending habits. The average spending was estimated to be approximately $1530, with a standard deviation of about $1070. A 95% confidence interval for the sample mean was calculated as $1530 ± $340. The challenge of working with binned data, particularly the open-ended last category, was highlighted as a limitation in achieving precise calculations.

PREREQUISITES
  • Understanding of basic statistics, including mean and standard deviation
  • Familiarity with confidence intervals and their calculations
  • Knowledge of binned data and its implications for statistical analysis
  • Ability to perform calculations involving square roots and basic algebra
NEXT STEPS
  • Learn how to calculate confidence intervals for different sample sizes and distributions
  • Explore methods for handling binned data in statistical analysis
  • Research techniques for improving data collection methods in web polls
  • Study the implications of open-ended categories in survey data analysis
USEFUL FOR

Statisticians, data analysts, market researchers, and anyone involved in designing or analyzing web polls will benefit from this discussion.

bradles
Messages
6
Reaction score
0
Ok. I'm fairly new so go easy on me. I apologise if this is posted in the wrong section.

Can someone point me in the right direction of being able to work out samples of a web poll. A web poll I did returned the following results for a sample of 40 people and spending habits of a particular item.

Code: 
Range		Poll	%
$0 - $500	6	15.00%
$501 - $800	6	15.00%
$801 - $1000	6	15.00%
$1001 - $1200	3	7.50%
$1201 - $1500	2	5.00%
$1501 - $2000	5	12.50%
$2001 - $3000	7	17.50%
$3001+		5	12.50%

What I'd like to be able to figure out is:
(1) what would be the average; and
(2) How accurate my sample size is (eg., We can be 99% sure that the average is x with a +/- 5% error margin) <-- I hope that makes sense.

Brad
 
Physics news on Phys.org
Brad, you make it hard for yourself by having access only to "binned" data, but especially so by having an "open bin" on the last category.

You estimate the mean by summing the category centers times the relative frequencies, as in : 250 * 0.15 + 650 * 0.15 + 900 * 0.15 + 1100 * 0.075 + ...

You'll have to just guess a category center on the last bin though. You can get a lower bound on the mean by taking it as 3001 but there is unfortunately no upper bound.

I took the cat-center of the last bin to be 3600 (for no particularly good reason) and got a mean (average) of about $1530.

There are a few ways you can estimate the standard deviation for the raw data, I estimated it to be about 1070. The standard deviation for the sample mean is estimated as the standard deviation of the raw data divided by the square-root of the sample size. So you get the estimate of :

Std-dev = 1070/sqr(40), which is approx 170.

You get a 95% confidence interval on the sample mean by going roughly +/- two standard deviations, so that's $1530 +/- $340 for a 95% confidence level.

Remember however that all my calculations are a bit shaky from the fact that I had to guess a category center (3600) for the last bin. So take the results with a grain of salt.
 
Last edited:
Thanks Uart,

Thats great. I see what you mean about binned data, especially the open ended upper range of the last category. I'm still learning. This is handy to reference. I'm going to see if I can experiment with it a bit more for collecting better data and getting better results.

Sorry this reply is belated...for some reason I wasn't alerted by email to your reply. Do I have to set something on the forum to be alerted by email? I just noticed I can set the Notification Type to an individual thread to : "Instant email notification" but is there a way you can make this the default?

Thanks again.

Brad