- Top Features:
- War Room
- Glenn Greenwald
- Broadsheet
- Joan Walsh
- Camille Paglia
- Since You Asked
- Follow Salon:
Read other letters about this article
Just a quick note regarding how to properly interpret a confidence interval. The theory behind it goes like this: You are searching for a number that truly exists, in this case the percentage of people saying they will vote for candidate X. This is called the population proportion. You take a random sample (because you can't sample everybody) and figure out what proportion in your sample say they will vote for candidate X. This is the sample proportion.
The population proportion is fixed but unknown, and the sample proportion is known but based on a random sample and hence the sample proportion is considered random. Also, anything computed using using the sample proportion is random as well. Therefore the confidence interval is random as well.
If Obama's sample proportion is 51 with a margin of error (based on 95% confidence) is 3.5, the confidence interval is 47.5 to 54.5. Does this mean that there is a 95% chance that the true population proportion is between 47.5 and 54.5? No! No no no. The true population proportion is fixed -- there's no chance anything about it. It's your confidence interval that's got that random element, so the correct interpretation is that there's a 95% chance that the confidence interval you computed covers the true population proportion.
Think of it like a ring toss game, where the confidence interval is the ring and the true population proportion is the peg. You know that when you toss the ring, there's a 95% chance that it will go over the peg. Unfortunately you never know if the ring is actually over the peg since the population proportion is never known.
It's a subtle difference but it's really important when we're bombarded by so many poll numbers each day. It's not the true proportion that's jumping around (although we would expect it to gradually change over time) it's the sample proportions and their confidence intervals jumping around. It's not the world being erratic, it's us.
