Posted on 09/30/2020 8:30:48 AM PDT by ConservativeInPA
Mathematics and statistics has been a second language for me for 35+ years in my professional life. They are a necessary tool that can be used to measure, estimate, build, engineer and solve programs. They can also be used to persuade. Most people understand that the latter can often be misleading and abused, hence the infamous saying, "Lies and damned lies and statistics."
This morning's lesson focuses on Margin of Error.
The first thing to understand about measuring anything is there is error. It does not matter if it is weight, volume, mass, or public opinion. Margin of Error (MOE) states by how many percent the results of a measurement differs from reality. This is particularly useful in telling lies in public opinion polls.
The second thing to understand is the target of measurement. This is known as population. Public opinion polls target a population of a particular type, such as adults, registered voters and likely voters.
We need to be careful that we do not confuse population with the sample. A sample is small part of the entire population. It is too expensive and time consuming in most cases to measure an entire population, so statistics become a useful to glean relationships from a small part of the population (the sample) and the entire population. Compare the expense of the US Census to an every day opinion poll from the fine statisticians at CNN. (Truth be told, the US Census now relies on sampling and statistics to estimate. The entire population is not actually measured as it once was - but just pretend it was done correctly.)
MOE is the error of what is being measured. The entire population in opinion polls, e.g., register voters, is NOT being measured. It is the sample from the population. The MOE is the error in the what is actually counted.
Sampling is difficult or can be incredibly easy. Here on Free Republic, there are immediate attacks on polls because of over sampling of Democrats and under sampling of Republicans. This is the easy part of sampling. It is intentional and pollsters aim to do so. Pollsters just need to target large cities to obtain samples and they get their over sampling of Democrats. Sampling of the difficult variety is to get results (measurements) that is truly representative of registered or likely voters.
MOE applied to poor sampling just measures the error of the poor sampling. The poor sampling is what is being measure, not the actual population.
The method used to determine MOE makes a difference
There are multiple formulas for MOE. Today we'll look at two methods. The formula used in a poll is usually not disclosed by pollsters which further makes the statistic a damned lie. The simple margin of error formula is as follows:
Where: z stands for the Z-score.
p̂ stands for the sample proportion.
n stands for the sample size.
The formula for margin of error with Finite Population Correction is as follows:
Where: z stands for the Z-score.
p̂ stands for the sample proportion.
n stands for the sample size.
P stands for the population size.
The Finite Population Correction (FPC) factor is needed when the sample size is small in comparison to the target population. For instance, CNN did a poll this morning on last night's debate. They surveyed 568 people. That's the sample size. The entire population would consist of everyone that viewed the debate. As a general rule if the sample size is greater than 5% of the whole population the simple MOE formula can be used. I'll give you a hint, 568 people is not greater than 5% of the total debate viewers. The FPC is important since the size of the sample impacts the metrics drawn from the data, such as the variance and the standard deviation of the sampling distribution.
I'm not going to go into the simple calculations involved in determining MOE. I expect that everyone on Free Republic can plug in numbers in a formula and use a calculator or spreadsheet to do the arithmetic. Instead it is important to point out there is more than one way to determine MOE, and you can make damned lies if the lesser of methods is intentionally chosen over the more appropriate method.
Second, it is important to note that MOE is the error in the sample, not the entire population. The sample is what is being measured, not the population of the whole. If the wrong sample is used the results are already incorrect.
Lastly, the questions of a poll influence the result provided by the sample. I don't know about you, but when I read most polls I often find that they do not even question and provide multiple choice answers that accurately reflect my opinion. This is yet another method to manipulate poll results. Poll questions are intentional. They are often meant to be written in an article to express a predefined opinion of the company paying for the poll.
Thank you. I have been too lazy to put something like this together.
Typical liberal poll:
Who do you prefer as President?
A- Stalwart savior of all that is good, Joe Biden
B- Evil, lying scumbag who wants to kill you, Donald Trump.
Don't feel bad. I cut the post short. I was going to go into the algebra required to reverse engineer the method of MOE a pollster uses. The pollster gives MOE, sample size, etc. Simply solve for FPC, it is 1 then the pollster is using the simple MOE formula and you know they are intentionally lying.
Thanks for the quick explanation of MOE. I use a fair amount of statistics, but polling/sampling isn’t part of that. I had never had to figure out a MOE.
I should note that the MOE used here is for polling. However, there is MOE in anything you measure. For instance, there are a dozen or so reference weights (kilograms) in the world. They are regularly measured, checked, rechecked and so on. There is error in every single measurement (weighing). While the reference weights weigh very very close to a kilogram, they do not weigh exactly one kilogram. And each time they are measured, there is an error in the measurement.
My favorite is the, “is the country headed in the right direction” question. Both sides recognize it’s not! The question always implies that it’s the president who is responsible. The cause/effect is never explored, just the sentiment (emotion) of the moment.
Thanks for this accurate explanation.
I am far more cynical. Knowing the reputation and business model of most who report “poll results”, the total absence of transparency into their process, lack of peer review and accountability, and the enormous value to be had from cheating, I beiI’ve most polls are manufactured. Fake data created by algorithms that can produce any desired outcome with internals to match. In the same way that Obama created a composite girlfriend, any skilled software engineer can create a composite voter, with sufficient randomization but with a clear central tendency.
If you already know the desired outcome, it’s just a matter of creating the data that statistically supports it.
2016 marked the year that polling ceased being an objective way of statistically estimating voter sentiment and became a cheap, fast, easy, and surreptitious tool for influencing public opinion.
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