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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    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





















      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











      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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      share|cite|improve this question




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      asked Aug 6 at 1:17









      Stewii

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          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























          • 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










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          1 Answer
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          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























          • 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














          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























          • 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












          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















          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















          share|cite|improve this answer



          share|cite|improve this answer








          edited Aug 6 at 21:38


























          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
















          • 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












           

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