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What does it means for a sample to be random?
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For a sample to be random, I thought it means that every member has an equal chance of being selected.
However, it seems like it is insufficient to just say the above. May I know what is the proper definition for a random sample? What am I missing?
Thanks.
statistics random sampling
asked Jul 23 at 1:28
LanaDR
1647
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up vote
1
down vote
favorite
For a sample to be random, I thought it means that every member has an equal chance of being selected.
However, it seems like it is insufficient to just say the above. May I know what is the proper definition for a random sample? What am I missing?
Thanks.
statistics random sampling
asked Jul 23 at 1:28
LanaDR
1647
This is a pretty broad question; it isn't always clear what "random" means. Your first definition is an example of a uniform distribution, where everything is equally likely. You may be interested in algorithmic information theory, a CS field that talks about this kind of thing.
– rwbogl
Jul 23 at 1:34
"It seems like it is insufficient to just say the above." Have you encountered a particular example of a "random sample" for which it was insufficient? It might help if you would give more detail about what made you ask this question.
– David K
Jul 23 at 3:36
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up vote
1
down vote
favorite
up vote
1
down vote
favorite
For a sample to be random, I thought it means that every member has an equal chance of being selected.
However, it seems like it is insufficient to just say the above. May I know what is the proper definition for a random sample? What am I missing?
Thanks.
statistics random sampling
asked Jul 23 at 1:28
LanaDR
1647
For a sample to be random, I thought it means that every member has an equal chance of being selected.
However, it seems like it is insufficient to just say the above. May I know what is the proper definition for a random sample? What am I missing?
Thanks.
statistics random sampling
asked Jul 23 at 1:28
LanaDR
1647
asked Jul 23 at 1:28
LanaDR
1647
asked Jul 23 at 1:28
LanaDR
1647
asked Jul 23 at 1:28
LanaDR
1647
1647
This is a pretty broad question; it isn't always clear what "random" means. Your first definition is an example of a uniform distribution, where everything is equally likely. You may be interested in algorithmic information theory, a CS field that talks about this kind of thing.
– rwbogl
Jul 23 at 1:34
"It seems like it is insufficient to just say the above." Have you encountered a particular example of a "random sample" for which it was insufficient? It might help if you would give more detail about what made you ask this question.
– David K
Jul 23 at 3:36
add a comment |Â
This is a pretty broad question; it isn't always clear what "random" means. Your first definition is an example of a uniform distribution, where everything is equally likely. You may be interested in algorithmic information theory, a CS field that talks about this kind of thing.
– rwbogl
Jul 23 at 1:34
"It seems like it is insufficient to just say the above." Have you encountered a particular example of a "random sample" for which it was insufficient? It might help if you would give more detail about what made you ask this question.
– David K
Jul 23 at 3:36
This is a pretty broad question; it isn't always clear what "random" means. Your first definition is an example of a uniform distribution, where everything is equally likely. You may be interested in algorithmic information theory, a CS field that talks about this kind of thing.
– rwbogl
Jul 23 at 1:34
This is a pretty broad question; it isn't always clear what "random" means. Your first definition is an example of a uniform distribution, where everything is equally likely. You may be interested in algorithmic information theory, a CS field that talks about this kind of thing.
– rwbogl
Jul 23 at 1:34
"It seems like it is insufficient to just say the above." Have you encountered a particular example of a "random sample" for which it was insufficient? It might help if you would give more detail about what made you ask this question.
– David K
Jul 23 at 3:36
"It seems like it is insufficient to just say the above." Have you encountered a particular example of a "random sample" for which it was insufficient? It might help if you would give more detail about what made you ask this question.
– David K
Jul 23 at 3:36
add a comment |Â
2 Answers
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If you're sampling $m$ items (without replacement) from a finite population of items, you want every set of $m$ distinct items in the population to have equal probability of being your sample. If sampling with replacement, you want every ordered $m$-tuple to have equal probability of being your sample.
answered Jul 23 at 1:41
Robert Israel
304k22201441
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up vote
1
down vote
Technically, "random" does not simply mean that each element is "equally probable" or "equally likely" to appear. That is just one particular distribution: the uniform distribution. Instead, samples can be "random" even if there probabilities are unequal. For example, a "weighted coin" which has a 60% of being HEADS, 40% chance of being TAILS is technically random.
answered Jul 23 at 1:44
David G. Stork
7,6312929
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
If you're sampling $m$ items (without replacement) from a finite population of items, you want every set of $m$ distinct items in the population to have equal probability of being your sample. If sampling with replacement, you want every ordered $m$-tuple to have equal probability of being your sample.
answered Jul 23 at 1:41
Robert Israel
304k22201441
add a comment |Â
up vote
2
down vote
If you're sampling $m$ items (without replacement) from a finite population of items, you want every set of $m$ distinct items in the population to have equal probability of being your sample. If sampling with replacement, you want every ordered $m$-tuple to have equal probability of being your sample.
answered Jul 23 at 1:41
Robert Israel
304k22201441
add a comment |Â
up vote
2
down vote
up vote
2
down vote
If you're sampling $m$ items (without replacement) from a finite population of items, you want every set of $m$ distinct items in the population to have equal probability of being your sample. If sampling with replacement, you want every ordered $m$-tuple to have equal probability of being your sample.
answered Jul 23 at 1:41
Robert Israel
304k22201441
If you're sampling $m$ items (without replacement) from a finite population of items, you want every set of $m$ distinct items in the population to have equal probability of being your sample. If sampling with replacement, you want every ordered $m$-tuple to have equal probability of being your sample.
answered Jul 23 at 1:41
Robert Israel
304k22201441
answered Jul 23 at 1:41
Robert Israel
304k22201441
answered Jul 23 at 1:41
Robert Israel
304k22201441
answered Jul 23 at 1:41
Robert Israel
304k22201441
304k22201441
add a comment |Â
add a comment |Â
up vote
1
down vote
Technically, "random" does not simply mean that each element is "equally probable" or "equally likely" to appear. That is just one particular distribution: the uniform distribution. Instead, samples can be "random" even if there probabilities are unequal. For example, a "weighted coin" which has a 60% of being HEADS, 40% chance of being TAILS is technically random.
answered Jul 23 at 1:44
David G. Stork
7,6312929
add a comment |Â
up vote
1
down vote
Technically, "random" does not simply mean that each element is "equally probable" or "equally likely" to appear. That is just one particular distribution: the uniform distribution. Instead, samples can be "random" even if there probabilities are unequal. For example, a "weighted coin" which has a 60% of being HEADS, 40% chance of being TAILS is technically random.
answered Jul 23 at 1:44
David G. Stork
7,6312929
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Technically, "random" does not simply mean that each element is "equally probable" or "equally likely" to appear. That is just one particular distribution: the uniform distribution. Instead, samples can be "random" even if there probabilities are unequal. For example, a "weighted coin" which has a 60% of being HEADS, 40% chance of being TAILS is technically random.
answered Jul 23 at 1:44
David G. Stork
7,6312929
Technically, "random" does not simply mean that each element is "equally probable" or "equally likely" to appear. That is just one particular distribution: the uniform distribution. Instead, samples can be "random" even if there probabilities are unequal. For example, a "weighted coin" which has a 60% of being HEADS, 40% chance of being TAILS is technically random.
answered Jul 23 at 1:44
David G. Stork
7,6312929
answered Jul 23 at 1:44
David G. Stork
7,6312929
answered Jul 23 at 1:44
David G. Stork
7,6312929
answered Jul 23 at 1:44
David G. Stork
7,6312929
7,6312929
add a comment |Â
add a comment |Â
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This is a pretty broad question; it isn't always clear what "random" means. Your first definition is an example of a uniform distribution, where everything is equally likely. You may be interested in algorithmic information theory, a CS field that talks about this kind of thing.
– rwbogl
Jul 23 at 1:34
"It seems like it is insufficient to just say the above." Have you encountered a particular example of a "random sample" for which it was insufficient? It might help if you would give more detail about what made you ask this question.
– David K
Jul 23 at 3:36