Mathematics Thread

This thread could come in handy. Question for Quant or another math nerd ...

Someone ran a monthlong online survey on his Facebook page using the Likert scale to score the responses.

There are just over 12,000 adults (18-older) in town.

There are 9,000 registered voters in town.

How many of the 12,000/9,000 who took survey is unknown but I can say the percentage is minuscule.

The survey got 112 respondents, so that is a 1.2% rate based on 9,000, and 0.9% rate based on 12,000.

I found this document explaining determination of sample size but don't understand it: 박진우_1.pdf

The survey giver wrote: "We announced at the very top of the video that there were 112 respondents. This would translate to approximately 1.3% of the adult population - more than enough for a statistically sound sample, although we are not representing it as such. This survey represents a simple sampling of opinions to a series of connected questions."

1, hard to know if all 112 respondents live in town
2, if they're not, how does that tweak the sample size
3, is the line "more than enough for a statistically sound sample" even true considering just 112 people took the survey?

 

Aren’t you the one who gets pissy when people use math to compare baseball players?

 

You can get away with 1percent of the registered voters and have a statistically valid sample. National pollsters get much less than one percent and are pretty good. The trick is making sure you get a representative sample, meaning those surveyed demographically make up the look of the voters. You also have to frame your questions in a way to not lead the respondents. The problem with an online poll that isn't targeted is you have no control over who responds and how many times they respond. Basically you have 112 people who found the poll on Facebook who agreed to click the link. The results are going to be meaningless.

 

I was assured there would be no math!

 

The only thing journalists are worse at than journalism!

 

I'm no algematrician, but I do believe that U+I=69

 

I bow in your general direction.

 

What the guy seems not to get is that as the population size increases, the percentage you need to get a sound sample goes down. So if you have a popultion of 50,000, you can get away with 1 percent and have a smaller margin of error (of course, 1 percent of 50k is a lot more than 112 people). But if you have 9-12k, your margin of error will be MUCH larger with a 1.3 percent sample (somewhere around 10 percent). One percent in a national survey is a lot more statistically accurate than 1 percent in a small town.

Also, as Spartan points out, it ultimately doesn't matter how many replied because his sample is flawed because it's not a random sampling of the population -- it's just the people who came to his Facebook page. You have to control the sample to have any kind of statistical significance.