Sampling error example

Question

I've read the sampling error examples in Wikipedia, but I still don't understand. Could you give me a simple and characteristic example for sampling error?

Answer 1

Imagine that you want to know the average height of men on earth. This average height exists but obviously you will never be able to know it (unless you're able to measure several millions men...). What you can do is measure hundreds or thousands of people and calculate the average height of these people. The average height among these people is probably not exactly equal to the average height of men on earth (because they are particular men in the whole population) but, if you did a good job (use a representative sample of the population), it should be close enough. The difference between the quantity that you want to know (average height of men on earth) and its estimation through your sample (average height of men in the sample) is the sampling error.

Answer 2

When you take a sample you do so because you want to know what is happening in the wider population but unless you take a census and ask everyone there will always be a difference between the sample and the population.

There is a good definition below taken from here

A standard deviation is the spread of the scores around the average in a single sample. The standard error is the spread of the averages around the average of averages in a sampling distribution

A classic example is an opinion poll with a 95% confidence interval of + or - 3%

If the headline figure is 45% Democrats and 42% Republicans the reality amongst the real population is anything from 42-48% Democrats and 39-45% Republicans.

Another polling company could do the exact same survey and the results could be 44% and 43%. So which is right? They both are because a sample is only an approximation of the population and if you sample a population many times the results you get are going to vary a little bit.

The larger the sample the smaller the error. Hope that helps.