Margin of Error: How to?

I'm not too familiar with this type of math, and I'm just asking b/c I'm curious.


How would I calculate a margin of error for a survey I made?
The total population size is 45000.
The sample size is 100.
The question asked has 3 possible options: Yes, No, Abstain.

Thank you.

You should first be curious about your test design. How did you pick the sample size? One normally would want to know the margin of error first.

An important consideration is to simplify your life. Forget that you have Yes, No, and Abstain. Use Yes and Other. Then you can calculate the margin of error on "Yes" with little difficulty.

How many "Yes"s did you get? Let's call it "Y".

Sample Proportion is Y/100 = P (Note: If you want to be conservative, just pick P = 1/2 and forget about Y. This will give maximum margin of error.)
Sample Variance of Proportion = (P)(1-P)/100
Sample Standard Deviation of Proportion = sqrt(P(1-P))/10 = SD

There is kind of a magic number related to a 95% confidence interal. It is often just taken as 2. It's really closer to 1.96, but 2 is more conservative. (Bumps up the margin of error.)

That's about it. Assemble: SD*2/10. Using P = 1/2, I get 0.0098, so it should be good for +/- 1% <== Notice how I increased it AGAIN! Three deliberate increases should help you feel pretty comfortable about it.

tkhunny said:

You should first be curious about your test design. How did you pick the sample size? One normally would want to know the margin of error first.

Click to expand...

I've already collected the data. Just to make it simple, I'm only looking at the first 100 of 167 results (the sample is still growing at a slow pace).
I was just curious to see what I can expect from the data.

An important consideration is to simplify your life. Forget that you have Yes, No, and Abstain. Use Yes and Other. Then you can calculate the margin of error on "Yes" with little difficulty.

How many "Yes"s did you get? Let's call it "Y".

Click to expand...

I know that 76% responded with Y.

Sample Proportion is Y/100 = P (Note: If you want to be conservative, just pick P = 1/2 and forget about Y. This will give maximum margin of error.)
Sample Variance of Proportion = (P)(1-P)/100
Sample Standard Deviation of Proportion = sqrt(P(1-P))/10 = SD

There is kind of a magic number related to a 95% confidence interal. It is often just taken as 2. It's really closer to 1.96, but 2 is more conservative. (Bumps up the margin of error.)

That's about it. Assemble: SD*2/10. Using P = 1/2, I get 0.0098, so it should be good for +/- 1% <== Notice how I increased it AGAIN! Three deliberate increases should help you feel pretty comfortable about it.

Click to expand...

I'm still a bit confused.
Where did the 10 come from the Sample Standard Deviation of Proportion?
How did you get

Assemble: SD*2/10. Using P = 1/2, I get 0.0098

Click to expand...

SD = sqrt(P(1-P))/10
= sqrt(.5(1-.5))/10
= sqrt(.25)/10
= .5/10
= .05

SD * 2/10 = .05 * .4 = .02 ?



If it's not too much trouble...
I came across this: Margin of Error Calculator (Confidence Level 95%)
http://americanresearchgroup.com/moe.html

If I input the values:
[SIZE=-1]Population size - 45000
[/SIZE][SIZE=-1]Sample size - 100

It returns a margin of error: [/SIZE]9.79[SIZE=-1]
[/SIZE]
How does it come to this?

I did overlook the finite population. However, 100/45000 = 0.22%. This is normally considered sufficient to ignore it.

\(\displaystyle 10 = \sqrt{100}\)

0.01? Right. I don't know where 0.0098 came from. I cannot reproduce it. Typing too fast, I guess.

Anyway, with p = 0.76, MOE = 0.0085 < 1%

Finally, you have to make up your mind what it is you are estimating and around what is the margin of error. In this model, we are creating a margin of error around the proportion, 0.76 being the sample proportion. A margin of error of 9 simply would not do. However, saying it is likely to be 0.75-0.77 could be significant. If you are estimating the number of "Yes" from the entire population, then a margin of error around 9 might be exceptional.