Margin of Error

These two concepts have worked together for years. I suspect that the desire to know things finer than the absolute margin of error an instrument can resolve legitimized the mathematics of statistics.

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No. Not really. But thanks anyway.

Marg Inoferror is the statistician on "Car Talk", with Click and Clack.

I'm not sure how significant that is.

The margin of error (confidence interval) is related to the confidence level.

It is the range (at the center of which,usually, will be the mean of the statistic) within which the actual value may vary, to the corresponding level of confidence.

An example:

Take a sample with known concentration of chamical (or say you take a sample and get the YS chacked)

Say we get the statistic as 200. This is the theoritical value.

In actual practice we will find (or may be we know) ,for the same population the actual value is 198 (or may be 207)

Why the difference? (actual 207, but our test has given it to be 200)

This is where the confidence limit and confidence interval comes in picture.

When you calculate the confidence interval (for the confidence limit) , you get the range.

Say we find for 95% confidence limit, the interval to be 10.

So we will say now that though the most probable value is 200, we are 95% confident that the actual value will lie between 190 and 210 (±10)

Note here a couple of things:

a) As the level of confidence increases, the confidence interval increases - obviously, you are 95% sure it is between 190 and 210. But to be 99% sure, it will be say 170-230.

b) It depends upon the sample size - as the sample size increases, it reaches nearer and nearer to the population, and obviously either/both confidence level and confidence interval can be narrowed.

c) Although it is usually(almost always) equispaced from the statistic mean (200 here) but it is always depending upon the distribution, and in case it is too skewed, so will be the interval.

d) It is depending on the standard error of estimate (the random and unaccounted for errors). If you look at the normal distribution chart, the 68% confidence level will give you σ and so on,

e) Please remember that the confidene interval of say 90% means that still there is a 10% chance that you are wrong. But that really does not help. You want to be 99% sure and the interval becomes say 5 times. So you trade off 90% at 200±5 Vs 99% at 200±25.

f) When the sample size is too small with respect to population, randomisation is not properly done etc, two populations are too nearby etc, the statistics may give wrong/opposite answer (that is one of the reasons of failures of poll surveys)

There are many more things to talk about, but in (not so) brief, this might suffice.