How Can I Calculate Sample Accuracy for a Web Poll?

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In summary, Brad is asking for help with working out samples of a web poll on spending habits. He has data for a sample of 40 people in different spending ranges, but is struggling with estimating the average and accuracy of his results due to an "open bin" in the last category. Uart provides some calculations and estimates for the mean and standard deviation, but notes that they are not completely accurate due to the guess of a category center for the last bin. Brad thanks Uart and expresses interest in experimenting with the data further. He also asks about setting up email notifications for replies on the forum.
  • #1
bradles
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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
 
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  • #2
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.
 
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  • #3
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
 

FAQ: How Can I Calculate Sample Accuracy for a Web Poll?

How do you calculate sample accuracy?

To calculate sample accuracy, you need to divide the number of correct predictions by the total number of predictions. This will give you a decimal value, which can then be multiplied by 100 to get the accuracy percentage. For example, if you have 80 correct predictions out of 100 total predictions, the sample accuracy would be 80/100 = 0.8 or 80%.

What is the importance of sample accuracy in scientific research?

Sample accuracy is important in scientific research because it helps to determine how well a sample represents the entire population. It allows researchers to make informed conclusions and generalizations about the population based on the data collected from the sample.

How does sample size affect sample accuracy?

The larger the sample size, the more accurate the results will be. This is because a larger sample size reduces the effects of random chance and provides a more representative sample of the population. However, there is a point of diminishing returns, where increasing the sample size does not significantly improve the accuracy.

What are some factors that can affect sample accuracy?

Some factors that can affect sample accuracy include biased sampling methods, measurement errors, and sample selection bias. Biased sampling methods, such as only selecting participants from a certain demographic, can lead to an inaccurate representation of the population. Measurement errors, such as faulty equipment or human error, can also impact the accuracy of the sample. Lastly, sample selection bias occurs when certain groups are over or underrepresented in the sample, which can skew the results.

How can you improve sample accuracy?

To improve sample accuracy, researchers can use random sampling techniques to ensure the sample is representative of the population. They can also increase the sample size to reduce the effects of random chance. It is also important to carefully select and train individuals collecting data to minimize measurement errors. Lastly, researchers should be aware of any potential biases and take steps to minimize their impact on the sample.

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