Does margin of error have a falloff?

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Does the margin of error have a falloff curve (i.e. the middle is more likely than the ends, like a normal distribution), or is it 'flat' range of uncertainty? I'm looking for a more clear understanding of "statistical tie". It's been difficult for me to research. Here is an example that hopefully clarifies:

Assume a normal, random survey, A vs B, with a margin of error of 6%. Option A polls at 48%. Option B polls at 52%.

• Can Option A legitimately say they have a 'statistical tie', simply because their 6% range overlaps with B's range?




• Is Option A just as likely to end up with 45% (or 51%) of the vote, as they are 48%?

probability statistics

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asked Aug 6 at 1:17

Stewii

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Does the margin of error have a falloff curve (i.e. the middle is more likely than the ends, like a normal distribution), or is it 'flat' range of uncertainty? I'm looking for a more clear understanding of "statistical tie". It's been difficult for me to research. Here is an example that hopefully clarifies:

Assume a normal, random survey, A vs B, with a margin of error of 6%. Option A polls at 48%. Option B polls at 52%.

• Can Option A legitimately say they have a 'statistical tie', simply because their 6% range overlaps with B's range?




• Is Option A just as likely to end up with 45% (or 51%) of the vote, as they are 48%?

probability statistics

share|cite|improve this question

asked Aug 6 at 1:17

Stewii

31

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

Does the margin of error have a falloff curve (i.e. the middle is more likely than the ends, like a normal distribution), or is it 'flat' range of uncertainty? I'm looking for a more clear understanding of "statistical tie". It's been difficult for me to research. Here is an example that hopefully clarifies:

Assume a normal, random survey, A vs B, with a margin of error of 6%. Option A polls at 48%. Option B polls at 52%.

• Can Option A legitimately say they have a 'statistical tie', simply because their 6% range overlaps with B's range?




• Is Option A just as likely to end up with 45% (or 51%) of the vote, as they are 48%?

probability statistics

share|cite|improve this question

asked Aug 6 at 1:17

Stewii

31

Does the margin of error have a falloff curve (i.e. the middle is more likely than the ends, like a normal distribution), or is it 'flat' range of uncertainty? I'm looking for a more clear understanding of "statistical tie". It's been difficult for me to research. Here is an example that hopefully clarifies:

Assume a normal, random survey, A vs B, with a margin of error of 6%. Option A polls at 48%. Option B polls at 52%.

• Can Option A legitimately say they have a 'statistical tie', simply because their 6% range overlaps with B's range?




• Is Option A just as likely to end up with 45% (or 51%) of the vote, as they are 48%?

probability statistics

share|cite|improve this question

asked Aug 6 at 1:17

Stewii

31

share|cite|improve this question

share|cite|improve this question

asked Aug 6 at 1:17

Stewii

31

asked Aug 6 at 1:17

Stewii

31

asked Aug 6 at 1:17

Stewii

31

31

add a comment | 

add a comment | 

1 Answer
1

active

oldest

votes

up vote
0
down vote



accepted

First one: yes, we can say that there is no 'statistically significant difference .. but of course if you had to put your money and be forced to choose one of the options and were looking for the highest percentage, you would go for option B: just because we are not 95% confident (the value typically used for statistical significance) that option B would be preferred over option A, we might still be 60% confident.

Second one. No. If A polls at 48%, then the actual percentage is more likely around 48% than around 45% ... though with a margin of error of 6% the difference will be quite small. Please note my use of around 48% and around 45% .. you never want to put any kind of confidence in the claim that it is exactly some percentage .. if tou deal with whole numbers, that may simply be impossible (e.g. there is no exact 45% of 101), and if you deal with real numbers, the chance that it is exactly some percentage is infinitesemal.

share|cite|improve this answer

edited Aug 6 at 21:38

answered Aug 6 at 2:37

Bram28

55.2k33982

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Perfectly clear. Thank you!
  – Stewii
  Aug 6 at 21:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Stewii You're welcome! I reread my answer and realized I should make something else clear ... please see my added note at the end
  – Bram28
  Aug 6 at 21:39
  

  
  
  
  

add a comment | 

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
0
down vote



accepted

First one: yes, we can say that there is no 'statistically significant difference .. but of course if you had to put your money and be forced to choose one of the options and were looking for the highest percentage, you would go for option B: just because we are not 95% confident (the value typically used for statistical significance) that option B would be preferred over option A, we might still be 60% confident.

Second one. No. If A polls at 48%, then the actual percentage is more likely around 48% than around 45% ... though with a margin of error of 6% the difference will be quite small. Please note my use of around 48% and around 45% .. you never want to put any kind of confidence in the claim that it is exactly some percentage .. if tou deal with whole numbers, that may simply be impossible (e.g. there is no exact 45% of 101), and if you deal with real numbers, the chance that it is exactly some percentage is infinitesemal.

share|cite|improve this answer

edited Aug 6 at 21:38

answered Aug 6 at 2:37

Bram28

55.2k33982

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Perfectly clear. Thank you!
  – Stewii
  Aug 6 at 21:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Stewii You're welcome! I reread my answer and realized I should make something else clear ... please see my added note at the end
  – Bram28
  Aug 6 at 21:39
  

  
  
  
  

add a comment | 

up vote
0
down vote



accepted

First one: yes, we can say that there is no 'statistically significant difference .. but of course if you had to put your money and be forced to choose one of the options and were looking for the highest percentage, you would go for option B: just because we are not 95% confident (the value typically used for statistical significance) that option B would be preferred over option A, we might still be 60% confident.

Second one. No. If A polls at 48%, then the actual percentage is more likely around 48% than around 45% ... though with a margin of error of 6% the difference will be quite small. Please note my use of around 48% and around 45% .. you never want to put any kind of confidence in the claim that it is exactly some percentage .. if tou deal with whole numbers, that may simply be impossible (e.g. there is no exact 45% of 101), and if you deal with real numbers, the chance that it is exactly some percentage is infinitesemal.

share|cite|improve this answer

edited Aug 6 at 21:38

answered Aug 6 at 2:37

Bram28

55.2k33982

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Perfectly clear. Thank you!
  – Stewii
  Aug 6 at 21:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Stewii You're welcome! I reread my answer and realized I should make something else clear ... please see my added note at the end
  – Bram28
  Aug 6 at 21:39
  

  
  
  
  

add a comment | 

up vote
0
down vote



accepted

up vote
0
down vote



accepted

First one: yes, we can say that there is no 'statistically significant difference .. but of course if you had to put your money and be forced to choose one of the options and were looking for the highest percentage, you would go for option B: just because we are not 95% confident (the value typically used for statistical significance) that option B would be preferred over option A, we might still be 60% confident.

Second one. No. If A polls at 48%, then the actual percentage is more likely around 48% than around 45% ... though with a margin of error of 6% the difference will be quite small. Please note my use of around 48% and around 45% .. you never want to put any kind of confidence in the claim that it is exactly some percentage .. if tou deal with whole numbers, that may simply be impossible (e.g. there is no exact 45% of 101), and if you deal with real numbers, the chance that it is exactly some percentage is infinitesemal.

share|cite|improve this answer

edited Aug 6 at 21:38

answered Aug 6 at 2:37

Bram28

55.2k33982

First one: yes, we can say that there is no 'statistically significant difference .. but of course if you had to put your money and be forced to choose one of the options and were looking for the highest percentage, you would go for option B: just because we are not 95% confident (the value typically used for statistical significance) that option B would be preferred over option A, we might still be 60% confident.

Second one. No. If A polls at 48%, then the actual percentage is more likely around 48% than around 45% ... though with a margin of error of 6% the difference will be quite small. Please note my use of around 48% and around 45% .. you never want to put any kind of confidence in the claim that it is exactly some percentage .. if tou deal with whole numbers, that may simply be impossible (e.g. there is no exact 45% of 101), and if you deal with real numbers, the chance that it is exactly some percentage is infinitesemal.

share|cite|improve this answer

edited Aug 6 at 21:38

answered Aug 6 at 2:37

Bram28

55.2k33982

share|cite|improve this answer

share|cite|improve this answer

edited Aug 6 at 21:38

edited Aug 6 at 21:38

edited Aug 6 at 21:38

answered Aug 6 at 2:37

Bram28

55.2k33982

answered Aug 6 at 2:37

Bram28

55.2k33982

answered Aug 6 at 2:37

Bram28

55.2k33982

55.2k33982

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Perfectly clear. Thank you!
  – Stewii
  Aug 6 at 21:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Stewii You're welcome! I reread my answer and realized I should make something else clear ... please see my added note at the end
  – Bram28
  Aug 6 at 21:39
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Perfectly clear. Thank you!
  – Stewii
  Aug 6 at 21:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Stewii You're welcome! I reread my answer and realized I should make something else clear ... please see my added note at the end
  – Bram28
  Aug 6 at 21:39
  

  
  
  
  

Perfectly clear. Thank you!
– Stewii
Aug 6 at 21:09

Perfectly clear. Thank you!
– Stewii
Aug 6 at 21:09

@Stewii You're welcome! I reread my answer and realized I should make something else clear ... please see my added note at the end
– Bram28
Aug 6 at 21:39

@Stewii You're welcome! I reread my answer and realized I should make something else clear ... please see my added note at the end
– Bram28
Aug 6 at 21:39

add a comment | 

 

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