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Random Sample
Coles notes: Statistics & Data.

Random Sample

Cadrache
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Posted 07/30/09 - 01:14 PM: Subject: Random Sample	#1
Could somebody explain to me why and how picking every 3rd name from a phone book is a valid random sample? I thought I'd pick up coles notes as additional material to some maths and stats books I picked up in the last two months and hit a snag on page two....
"...There was a writer who asked why it was that when we find positive experiences we say that only the physical facts are real, but in negative experiences we believe that reality is subjective. He made an example of those who say that in birth only the pain is real, the joy a subjective point of view, but that in death it is the emotional loss that is the reality." - Tony Ballantyne, Recursion. _____________________________________________ Truth is want. - The internal state of matters. Truth is Need. - The external state of affairs.

Kwalish Kid
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Posted 07/30/09 - 01:22 PM:	#2
One assumes that there is no correlation between names that are spaced apart in that way and other factors relevant to the sample? One should get a number of people in the sample who live together, but not necessarily more than one would expect in the underlying population?
"Scientific truth is always paradox, if judged by everyday experience, which catches only the delusive nature of things." - KM, V, P and P Can you pass Religion 101?

Cadrache
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Posted 07/30/09 - 01:40 PM:	#3
Those are questions.... My largest problem at the current moment is that phone books are in alphabetical order.
"...There was a writer who asked why it was that when we find positive experiences we say that only the physical facts are real, but in negative experiences we believe that reality is subjective. He made an example of those who say that in birth only the pain is real, the joy a subjective point of view, but that in death it is the emotional loss that is the reality." - Tony Ballantyne, Recursion. _____________________________________________ Truth is want. - The internal state of matters. Truth is Need. - The external state of affairs.

mrousseau
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Posted 07/31/09 - 01:14 AM:	#4
Hi, so an ordering (alphabetical or other) may be independent to the observation you are hoping to make from the names in the phone book. For example, if you were interested in looking at people's salaries and you were comfortable with the idea that the alphabetical rank of their name and their salary are completely unrelated, then picking every 3rd name of the phone book would work. The idea of the random sample is that each person would have the same probability of being picked. So it might make sense to pick a random number (1-3) before you start and then pick every 3rd name starting at the name 1,2 or 3 which came up in your first random number pick. That way the guy with the name Aaron AArdvark has a chance of being picked. Edited by mrousseau on 07/31/09 - 01:27 AM

Cadrache
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Posted 08/04/09 - 01:51 PM:	#5
It's the statement about you need "equal chance" for any name to be chosen. Application of "aphabetical order" creates a linear system. Choosing every 3rd person is still a linear equation. If you choose your starting position with a smaller or equal value to your jump ratio; you still are performing a linear function; except that it affects the exclusion ratio. Change Aaron Aardvark to A A , then second to A B, and 3rd on the list to A C; and make an assumption that there is only one A A on the list. I completely agree that it increases the "Randomness", so to speak. Instead of A A having a 0 in 3 chance of getting picked, he now has a 1 in 3 chance of being picked; yet what of A B and A C?
"...There was a writer who asked why it was that when we find positive experiences we say that only the physical facts are real, but in negative experiences we believe that reality is subjective. He made an example of those who say that in birth only the pain is real, the joy a subjective point of view, but that in death it is the emotional loss that is the reality." - Tony Ballantyne, Recursion. _____________________________________________ Truth is want. - The internal state of matters. Truth is Need. - The external state of affairs.

Cadrache
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Posted 08/04/09 - 01:59 PM:	#6
Bleh -working and hitting wrong button to switch between screens. To me; each random number value, simply means that the odds of any individual X is on one of 3 different probability graphs which when combined does not quite match your "equal probability" system.
"...There was a writer who asked why it was that when we find positive experiences we say that only the physical facts are real, but in negative experiences we believe that reality is subjective. He made an example of those who say that in birth only the pain is real, the joy a subjective point of view, but that in death it is the emotional loss that is the reality." - Tony Ballantyne, Recursion. _____________________________________________ Truth is want. - The internal state of matters. Truth is Need. - The external state of affairs.

Jurist
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Posted 08/04/09 - 04:51 PM:	#7
Cadrache wrote: It's the statement about you need "equal chance" for any name to be chosen. Application of "aphabetical order" creates a linear system. Choosing every 3rd person is still a linear equation. If you choose your starting position with a smaller or equal value to your jump ratio; you still are performing a linear function; except that it affects the exclusion ratio. Change Aaron Aardvark to A A , then second to A B, and 3rd on the list to A C; and make an assumption that there is only one A A on the list. I completely agree that it increases the "Randomness", so to speak. Instead of A A having a 0 in 3 chance of getting picked, he now has a 1 in 3 chance of being picked; yet what of A B and A C? Why would you assume a fixed quantity of a given combination of letters? Your specific case eliminates AB and AC, but to do the same with an actual phone book, your function would have to look much different to ensure the elimination of any given combination of letters. What if the set looks like this: AA, AAA, AABA, AABC, AABCBBAC, AB , ABBAAA, ABCD, AC, ACBAB, ACC, ACCC, ACCCC?
Just because I'm a lawyer doesn't mean I'm always wrong. -- Me

Cadrache
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Posted 08/05/09 - 02:00 PM:	#8
So, we have a Set A. We'll assume that choosing the set itself doesn't cause an inequality in the chance of choosing equally the random sample. In the original example, choosing every 3rd person excludes the first two people of ever being picked in an alphabetical list. The solution? Choose a number between 1 and 3 so that they have a 1/3 chance of being picked. The problem? You still exclude 2 in 3 people from the list and you can determine prior to the selection which people are excluded. In a true random sample, you shouldn't be able to do that. In the argument concerning salary; you could claim you will look at the first 500 people in the phone book; merely because salary is independant of the name of an individual. Yet it does not give you a valid random sample. Choice of set A, in determination of alphabetical order has an oft times silent positioning factor that nobody tends to mention as well.
"...There was a writer who asked why it was that when we find positive experiences we say that only the physical facts are real, but in negative experiences we believe that reality is subjective. He made an example of those who say that in birth only the pain is real, the joy a subjective point of view, but that in death it is the emotional loss that is the reality." - Tony Ballantyne, Recursion. _____________________________________________ Truth is want. - The internal state of matters. Truth is Need. - The external state of affairs.

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