Its more an academic question, so I am hoping some of you who studied statistics in school can provide some light.
Often, when we read about different polls in the media they talk about ‘margin of error’. So, lets say the total US population is 270 million people. Some one polled a total of 1,002 people and came back with a certain result and extrapolate it to say 47% of Americans believe this thing or that thing. Then they say the margin of error is ±3%.
What does it mean? And how is this margin calculated?
So the actual figure may have an error of either + or - 3 % of the people that were surveyed. The percentage saying this thing or that thing would either be 50% or 44%.
I wish I had payed attention to my maths teacher when he was Xplaining this aspect of how it is calculated. I cannot answer your 2nd question.
hmmm... lemme see if I can tackle this - I'm not good at "explaining" stats although I understand them well myself.
For starters, Faisal, the Margin of Error is a summary of the "sampling errors" in a survey. The other types of errors are the non-sampling errors that may arise due to bad wording of questions, or people responding with bias or not responding at all etc.
An estimate +/- MoE is simply meant to give a 95% confidence interval.
In your example, you can say that 44% to 50% of the people favour XYZ at least 95% of the time!
With the MoE, you're just trying to indicate that the results from the sample are going to be somewhat different than the target population simply due to the "luck of the draw"...
For example, the most common sampling error can arise due to the size of the sample. It is expected that your Margin of Error will be around 10% if you take a sample size of 100, it will be around 4.5% if you take a sample of 500 and it will be around 3% if you take a sample of 1000 etc.
Also affecting the MoE are factors including your sampling techniques and the population size.
As a last pointer, for most political campaigns it is said that the media reported MoE should be multiplied by 1.7 to obtain a more accurate estimate - in your example, a 3% MoE would become close to 5.
Thanks guys, this was helpful. Well, the second question was obviously more important, cz the first one is kinda common sense. I am more interested in knowing how the MoE is computer, and here Umer Talib comes to the rescue.
[QUOTE]
*Originally posted by Umar Talib: *
For example, the most common sampling error can arise due to the size of the sample. It is expected that your Margin of Error will be around 10% if you take a sample size of 100, it will be around 4.5% if you take a sample of 500 and it will be around 3% if you take a sample of 1000 etc.
Also affecting the MoE are factors including your sampling techniques and the population size.
[/QUOTE]
Umer, here you have provided standard MoE based on sample sizes. Are you saying a sample size of 1,000 will reduce the MoE to 3%. However, in our case the total population is 270 million plus. A sample of 1,000 is hardly even 0.0003% of the population. Isn't that too low?
There's also the issue of how the sample group is selected which relates to what you are trying to measure. If, for instance, you are trying to predict the outcome of an election, consider the following samples:
All Americans.
Americans old enough to vote.
Americans registered to vote.
Americans registerred and likely to vote.
If GWB's approval rating is 40% among all Americans, that isn't nearly as predictive as the approval rating he has with Americans who are registerred and likely to vote.
When somebody uses poll statistics to advance an argument or "prove" a point, it is really critical that the listener understand thoroughly who and what constituent parts made up the sample group. In most cases, it is more important to know who is in the sample group and how they were chosen than the margin of error.
^^ yeah mv, that’s what I meant when I said the technique for choosing the random sample matters a lot!
Faisal, it is a surprising fact to some - the size of the population generally has little influence on the margin of error.
That is to say that a sample size of 100 in a population of 10,000 will have almost the same margin of error as a sample size of 100
in a population of 10 million.
^^ trust me Waleed it aint rubbish... I regretted not paying attention to stats when I came into the workforce... had to learn it all over again!
You're gonna hafta use it somewhere or another. For me it was when I worked at GE as a consultant and I had to do quality control for them!