Statistics help. How do check a large data set full of estimates for accuracey by only measureing a few points

Question

I Have a large set of data, but each value was estimated. I need to measure how accurate the estimations are without measuring every point. If I can somehow use statistical sampling or somthing and measure a small percentage of the points then somehow statisticly indicate how accurate the original data set is to determine if I need to measure more points to check it or leave it alone.

What is the scientific method for this?

Thank you much...

My data set is about n=50. They are length measuments in miles that were given to me to check. I'm not sure how they were originally gathered perhaps by roller or off a map. I have taken about 20 measurements by roller and compared to the existing and they seem fairly accurate. But I need a way to prove this statisticly to show why I selected to check that many and not half or more or less or all. Its very time consuming to check them all and this won't be the last time I'm asked to do this. Since the data is road lengths then there is not pattern or curve its just a list of roads and their lengths so the data is totally random as far as patterns. I just need to prove statisticly that its OK not to check all of them, why its OK, how I arrived at the number to actually measure, and if the corelation or whatever its called the accuracy is good enough over that sample to show that I don't have to check them all. Are there standard for this, like if the error is less that a certain amount

Answer 1

You should randomly sample the number of data points you want to check. See how far off the estimates are.

From there it depends on what you want to estimate. Just the average error? The average error in your sample would be your estimate of the average for all the data points.

A better technique would be to create an interval estimate. If your sample is approximately normally distributed, or you have a reasonably large sample (40 or so) you could do this. For a 95% interval, for example, you would calculate the standard deviation of your sample errors and do this:

your sample average +/- t* times your sample standard deviation divided by the square root of the sample size.

Avg +/- t* (s / sqrt(n)).

t* can be found from a t-table for the correct degrees of freedom, which is one less than your sample size.

In the table here:

http://socr.stat.ucla.edu/Applets.dir/T-table.html

you would look in the column for 0.025 if you want a 95% interval.

Then you can be 95% confident that the mean of all the sample errors is within the interval you created. (In other words, if you were to do 100 samples and create the corresponding intervals, 95% of the intervals would capture the true mean.)

Answer 2

Hm... Interesting question... Well my question to you is, why not just ask when their birthday is? By asking that you can find out their Sun easy and maybe a little more about their birth chart easy. And asking it early to someone wouldn't be too weird, I don’t think. Personally, I felt a little...I don't know... 'Disappointed'? When my ex didn't know when my birthday was until it was actually my day. Close to two weeks I think before it even came I told him in a simple manner that my birthday was coming up, but he never asked when it was. A tad little bit hurtful actually... Ah well. Another thing is if they usually act their sign, then you could also compare their behavior and preferences to Zodiac signs. You should have like a 70% chance of being right, eh? Plus it should keep you entertained until you do ask about birth data and maybe you could tell just on your own whether you're compatible or not. Plus, it will help you get better at this. But on to your real question. I would think the time would depend on how the relationship goes. Like if you feel an instant connection and if you two really hit it off and start getting a little more serious a little quicker, then asking about birth data shouldn't be that big a step. He will still probably be a bit confused, who can blame him? But if you already have that connection and bit of seriousness, then he shouldn't take it as such a big thing: Threat, or weird, or otherwise. But how long into the relationship depends I think, on each person, and how they like to move in a relationship, like really quick or nice and slow. If they're shy, if they're jerks you know, if they move quickly because of like emotions; if they're little too emotional, if they're coming off a relationship, all these things play a factor. But either way once you feel a deeper connection I would say is the best time. Starting new relationship and flat out asking, 'okay what's your Zodiac sign?', will scar off anyone I think. It's like asking, 'what's your religion? What's your politically standing?'. You just don't do that, ya know? Well I hope this helps a bit. Much luck to you.

Answer 3

What do you mean by 'accurate'? And what is a large set of data where everything is 'estimated'? I suppose that you mean that there is some error which you hope is random and can be accounted for.

Do you have reason to believe that the data has a certain distribution?

Give me a better idea of what you're asking. I will help me to help you.

MathGuy's suggestions are good. Basically, that assumes that the errors are normally distributed and the t test is used because you're using an estimate for the sigma.