stock here, below the graphic is a Discussion of Margin of error. The closer a poll or election is to 50%, the higher the margin of error. At 10% the margin of error becomes quite a bit smaller. My “conclusion” is at the far bottom if you don’t want to follow the whole discussion.
https://www.oann.com/poll-results
On a poll with 3842 votes what is the “margin of error” and how is it calculated
ChatGPT said:
ChatGPT
The “margin of error” in a poll is a measure of how much you can expect the poll results to vary from the true population values. It’s calculated based on the sample size (the number of votes) and the desired confidence level, typically 95%.
How to Calculate the Margin of Error (MoE)
For a poll with a sample size of 3,842 votes:
Determine the Confidence Level: Most polls use a 95% confidence level, which corresponds to a Z-score of 1.96.
Calculate the Sample Proportion (p): If the poll result shows, for example, 50% for a particular response, then p = 0.5. If the proportion is unknown, 0.5 is commonly used as it provides the largest margin of error, giving a conservative estimate.
Calculate the Standard Error (SE):
SE=p(1−p)n
SE=np(1−p)
where n=3,842n=3,842.
Calculate the Margin of Error:
MoE=Z×SE
MoE=Z×SE
For a 95% confidence level, Z = 1.96.Let’s calculate it based on a sample proportion of 0.5.
Example Calculation
Standard Error (SE):
SE=0.5×(1−0.5)3842=0.253842≈0.008
SE=38420.5×(1−0.5)=38420.25
≈0.008
Margin of Error (MoE):
MoE=1.96×0.008=0.0157 or 1.57%
MoE=1.96×0.008=0.0157 or 1.57%Result
The margin of error for this poll, with 3,842 votes, would be approximately ±1.57% at a 95% confidence level.
This means the true percentage could vary by about 1.57% above or below the reported poll result if the poll is unbiased and random.
You said:
on this same poll if the no votes were 381 and the yes was the remainder then would p=.1, and what would the calc then be
ChatGPT said:
ChatGPT
Yes, if the “No” votes were 381 out of 3,842 total votes, the proportion for “No” (pp) would indeed be:
p=3813842≈0.1
p=3842381≈0.1
With this updated pp, we can recalculate the margin of error.
Updated Calculation Steps
Determine the Sample Proportion (p):
p=0.1p=0.1
Calculate the Standard Error (SE):
SE=p(1−p)n=0.1×(1−0.1)3842
SE=np(1−p)=38420.1×(1−0.1)
Simplifying this:
SE=0.1×0.93842=0.093842≈0.0048
SE=38420.1×0.9
=38420.09
≈0.0048
Calculate the Margin of Error (MoE): Using the Z-score for a 95% confidence level, Z=1.96Z=1.96:
MoE=Z×SE=1.96×0.0048≈0.0094
MoE=Z×SE=1.96×0.0048≈0.0094Result
The margin of error, given p=0.1p=0.1, would be approximately ±0.94% at a 95% confidence level.
This smaller margin of error reflects the lower variability when the proportion pp is further from 0.5.
You said:
what does margin of error actually mean though, like talking to a freshman in highschool
ChatGPT said:
ChatGPT
The margin of error tells you how much you can trust the results of a poll or survey. It gives a range that the real answer is likely to fall within if you asked everyone, not just the people in the poll.
Imagine you’re trying to figure out what everyone in your school thinks about a new lunch option, but instead of asking every student, you only ask 100 people. Let’s say 60% of them say they like it. You might think that means about 60% of the whole school likes it. But because you only asked a sample (the 100 people), the real percentage could be a little higher or lower.
The margin of error tells us how much higher or lower that percentage might realistically be. For example, if the margin of error is ±5%, it means that the real percentage of people who like the lunch option could be anywhere from 55% to 65%.
In short:
Poll result: 60% say “yes”
Margin of error: ±5%
Real range: The true percentage of people who like it is likely between 55% and 65%.So, the margin of error helps us understand how close the poll result is to the “truth” about the entire group!
You said:
so in my example then the no votes could vary from 10% to 9.06% or up to 10.94, it has nothing to do with is there a chance that there are more no votes than yes votes
ChatGPT said:
ChatGPT
Exactly! The margin of error simply tells us how much the reported percentage could vary around the poll’s result. In your example:
You found that 10% of the sample voted "No."
With a margin of error of ±0.94%, the true percentage of "No" votes among everyone could range from 9.06% to 10.94%.But the margin of error doesn’t suggest any possibility of “No” having more votes than “Yes” in this case because:
The overall result: "Yes" votes are significantly higher than "No" votes in the original poll.
The margin of error: It’s only a slight range around the calculated percentage.So, while the percentage for “No” might be a little higher or lower, it’s still within a small range around that 10%, and the gap between “Yes” and “No” would still be large enough that “Yes” remains the majority.
In short, the margin of error lets us say, “The true ‘No’ percentage is probably close to what we found, but there’s a small range of uncertainty.” It doesn’t change the outcome of “Yes” being the clear winner in this poll!