Sample Size And Statistical Ambiguity?

[petrushkagoogol]

Consider a sample of 100 people taken for the purpose of finding out how many wear red hats and how many black - 

- If the sample size is 100 and 99 people wear black hats and 1 person red then we could assume that all the people wanted to wear black hats but there was one person who couldn't. 

-If there are 100 such "samples" (100 x 100) and every 100th person wears red hats then our inference could be that every 100th person should be wearing a red hat. 

The percentage of those wearing red hats is exactly the same. (1/100 or 100/10000) but the way we interpret the results is completely different. 

Is this not an ambiguity in statistical analysis ? 

How relevant is sample size in statistics ? 

Please opine.  

 

 

 

[Maine farmer]

More is not always better, unless you are talking about statistics.

 

Maybe there were only 99 black hats to be had!

[petrushkagoogol]

More is not always better, unless you are talking about statistics.

 

Maybe there were only 99 black hats to be had!

 

May be the second conclusion, by virtue of multiple iterations, arises from the fact that there is a TREND. Even though the percentages are identical in both cases, the second differs from the first by virtue of the qualities stated above.

[Turtle]

Consider a sample of 100 people taken for the purpose of finding out how many wear red hats and how many black - 

- If the sample size is 100 and 99 people wear black hats and 1 person red then we could assume that all the people wanted to wear black hats but there was one person who couldn't. 

...

Please opine.  

 

IMO, there is no valid basis for making any such assumption. :evil:

[CraigD]

Is this not an ambiguity in statistical analysis?

I prefer the word “uncertainty” to “ambiguity”, but it’s true that the hypothesis “100 of a population of 10000 wear a red hat” can’t be proven with certainty by sampling 100 members of the population.

 

Consider this extreme case of a population of 9901 people with red hats and 99 with black. A random sample of 100 might pick all 99 black hat and 1 red hatted person, from which we’d conclude that the population is most likely 100 red hats and 9900 black.

 

Statistics accepts and attempts to understand and manage uncertainty. One of the more obvious ways this is done is to calculate the probability of a particular hypothesis being falsely supported by a sample of it. In the example I gave above, the probability is tremendously low,

[math]\frac{99! 9901!}{10000!} \dot=10^{-240}[/math]