Statistical representation

[Jupitus]

Folks - in the world of statistics, what is considered a 'representative sample'. For example, if I asked 200 people what the best anti-deodorant was, and only 30 replied, could I take the response as a decent representation of the truth?

Sorry for the anal question, but it is quite important to me. Thanks in advance...

 

[Deebs]

Ah I get it, you want to ask 3 people (your family) if you are short and if they all answer no try and convince us it was a "representative sample". Well no, 3 people is not enough.

As to polls, most of them are of small numbers so I guess it is down to intepretation. Look at all the hair adverts (ah sorry, you don't have much hair so won't) and you see most say "from a survey of 81 people".

 

[Jupitus]

Ah I get it, you want to ask 3 people (your family) if you are short and if they all answer no try and convince us it was a "representative sample". Well no, 3 people is not enough.

As to polls, most of them are of small numbers so I guess it is down to intepretation. Look at all the hair adverts (ah sorry, you don't have much hair so won't) and you see most say "from a survey of 81 people".

Thanks for making me smile

 

[Deebs]

I would make you laugh but I have mislaid my "hidden" camera shot of Sydrik in the buff. Actually that would make you cringe. Back to the drawing board

 

[Will]

The greater the number of responses, the more representative it is. But I couldn't pick an exact point where it goes from shit to representative. I'd suggest trying to get at least 50, ideally 100.

 

[Sydrik]

if you look closely at that photo you will actually find the tunnel i am standing in is Deebs' left nostril and the dark plant to my left is actually his nasal hair. Luckily it came in handy as something to grab hold of when he sneezed....

 

[Deebs]

And if you look even closer you will find that the bird to Syd's left is infact a turkey (kindly donated by Bernard Matthews) and not his real girlfriend much to his surprise. I do keep telling him to lay off the poultry.

As for standing in my nostril, we all know that crusties and snot live in nostrils, Syd is part of the furniture..

 

[Sydrik]

once when he sneezed hard enough i ended up in the right hand side, it was like moving house. a whole new cave to decorate

 

[Deebs]

once when he sneezed hard enough i ended up in the right hand side, it was like moving house. a whole new cave to decorate

Tis true, the Noel Edmond's goatee tickled my left nostril so much I sneezed. Good job it was a monster sneeze, it is so hard to shift several tons of lard....

 

[Sydrik]

Lard is unlikely to be a problem when you have the occassional refugee escaping from your nasal cavity shouting 'sheet zis iz not the chunnel'

 

[Deebs]

Ah is that the same as when the bird you are giving one to makes a "cluck cluck" noise and your hands come away with not hair but feathers? If so, I know where you are coming from, sucks .....

 

[Sydrik]

Any hole's a goal!!!!

 

[Deebs]

Damn right, never a truer statement said

 

[Draylor]

With apologies for being even slightly on topic:

Folks - in the world of statistics, what is considered a 'representative sample'.

Its not so much about the sample size, as the content of the sample.

If you asked only old people youd get an answer that wasnt representative of the population in general, as a random example.

 

[mank!]

you also have to take into account how you obtained the sample, i.e. randomly, selectively, specifically blah blah

 

[dysfunction]

A representative sample should cover all aspects of a population.

So your sample therefore would not be relied on size but on the characteristics of the population.

You therefore need to define the population completely before taking a sample. eg: If most people like cheese, have blonde hair, drive a car, eat Yorky bars then your sample of the population needs to incorporate all those stats.

 

[DaGaffer]

Depends on your population size and the level of confidence ("confidence interval") you want in the outcome. With the UK population (but actually it scales equally well for populations over say, 100,000) you need a sample size of around 1037 to give you 99% confidence in the results (with an error rate of 2% either way), a sample size of 600 to give you 95% confidence, a sample size of 425-ish to give you 90% confidence.

If you assume a sample size of approx 1000 you will get a high confidence in your results for pretty much any population size. If you were doing a survey in the UK, you'd also have to make sure you got the sample distribution right; there's no point trying to get a representative sample of UK population if surveyed all 1000 people in the same locale.

 

[Sydrik]

thank god someone actaully came forward with some good answers after deebs and I hijacked Jup's post last night... (big nosed bastard)

 

[rynnor]

Yes - around 1000 is a good point at which you'll be reasonably accurate - the reason is down to poisson distribution and the chi squared test but I'm too lazy to dig it out

 

[dysfunction]

Wtf you talking sample sizes of 1000. He only has a population of 200!!

Dont you people read the first post??

 

[DaGaffer]

Wtf you talking sample sizes of 1000. He only has a population of 200!!

Dont you people read the first post??

No, of course we didn't. (shit).

OK then, there isn't really a direct answer to his question as it depends what he wants a "representative sample" to be. For instance, using his figures of a sample of 30 from a population of 200, if you wanted a 95% confidence in your answer, and say 30% of your (30) respondents gave a particular response, with that sample size you would have a confidence interval of about 11, which basically means there's room for error in that 30% being a representative answer of 11% either way; so you can be 95% confident that between 19 & 41% of the total population would give that response. You can decide to reduce the confidence level, which would narrow the margin of error, or increase the margin of error and raise your confidence level, or of course raise your sample size.

Its quite difficult with small populations; for example in this case, to get 95% confidence with only a +/- 5% error, you'd need to have a sample of 132; two-thirds of your population.

 

[rynnor]

Wtf you talking sample sizes of 1000. He only has a population of 200!!

Dont you people read the first post??

In such a small population do the lot

 

[Jupitus]

No, of course we didn't. (shit).

OK then, there isn't really a direct answer to his question as it depends what he wants a "representative sample" to be. For instance, using his figures of a sample of 30 from a population of 200, if you wanted a 95% confidence in your answer, and say 30% of your (30) respondents gave a particular response, with that sample size you would have a confidence interval of about 11, which basically means there's room for error in that 30% being a representative answer of 11% either way; so you can be 95% confident that between 19 & 41% of the total population would give that response. You can decide to reduce the confidence level, which would narrow the margin of error, or increase the margin of error and raise your confidence level, or of course raise your sample size.

Its quite difficult with small populations; for example in this case, to get 95% confidence with only a +/- 5% error, you'd need to have a sample of 132; two-thirds of your population.

Thanks for that, DG - It's really an overall estimate I am after. 39 out of 234 people responded to a survey and rather than drill down to each answer I am trying to figure out how reliably we can read the overall results as a whole...

 

[Guest]

our survey said 39 out of 234 people think that the plane won't take off ?

 

[DaGaffer]

Thanks for that, DG - It's really an overall estimate I am after. 39 out of 234 people responded to a survey and rather than drill down to each answer I am trying to figure out how reliably we can read the overall results as a whole...

OK for your sample size at a 95% confidence level (standard measure for statisiticians), you're going to have a pretty wide margin of error for any of the answers; 16% (ish) either way.

 

[Draylor]

Meh, it depends on the question really.

Chances are if only 15% of people asked responded those are the people most interested in the subject matter, and their answers will be very biased as a result so any attempt at a general conclusion from that will be utter bollocks.