and in more depth, they show us that magin of error is not a simple equasion with absolutes.
It is a ratio. And the ratio is derived mathematically from many observations about polling and sampling.
But rather a formula that can be manipulated and adjusted to say pretty much whatever I want it to. IOWs margins of error can and usually are misleading.
I think you are still too far away from even understanding what a margin of error is to make such a sweeping judgment.
The only difference is before the evidence. IOW's the evidence collected in both are the absolutes.
So in some respects, a margin of error is based on absolutes.
water quality results came back X, Y number of times. The number of people that responded X, Y number of times. and after this collection of evidence, we do the calculations.
OK, now we are getting into a source of confusion. One thing I did not go into, but the articles did, is "level of confidence". Level of confidence is not the same thing as margin of error, but you are using an example of level of confidence as if it were an example of margin of error.
What you normally see at the bottom of an opinion poll, underneath the tabulation of the results, is a sentence with two figures in it. It is usually worded along the lines of "This poll is correct within 3%, 19 times out of 20"
3% is the margin of error.
19 out of 20 is the level of confidence. As you can see this is not the same as 3%. It is 95%.
So what this is saying is that 95% of the time (19 times out of 20) you can count on the true answer being within 3% of the polling figures. 5% of the time, the poll figures may be outside that margin of error.
Let's try this with a scientific sampling. Not one that would happen in real life, but it will do for an illustration. Let's say my doctor wants a very thorough review of my blood sugar. So instead of having the nurse take one test, he asks her to draw about 60 millilitres of blood into a test tube and divide it into 20 samples of 3 millilitres each. Then each of these 20 samples is analysed.
19 of the samples give a reading somewhere between 5.2 and 6.9% (acceptable). One gives a reading of 32%. (unacceptably high).
Should the doctor tell me my blood sugar levels are ok or that they are unacceptably high?
I forget the exact numbers, but the approval rating for President Bush was low, again I don't remember the numbers, but for the sake of discussion let's say 25. The approval rating for the media reporting President Bushes approval rating was lower, for the sake of discussion 20.
Two different subjects. Two different polls. Two different results. What else would you expect?
Now apply this to our discussion. Because of how margin of error is calculated, I can test for anything and get a low margin of error. I can test whether a mouse is in the cookie jar and the margin of error would be less than 1%, but that doesn't mean that the mouse lives in the cookie jar or that mice live in all cookie jars, or that the mouse is always in the cookie jar. What it means is that every time I tested, the mouse was there.
Not quite. What happened is that every time you tested, you got a positive result. But did you get a positive result because the mouse was there or even when the mouse was not there. (Ditto in reverse. Sometimes you may get a negative result even though the mouse is there.)
This is not about margin of error,. but about level of confidence in the test. If the test results correlate well with the actual presence or absence of the mouse, we have a high level of confidence in the test. If the test gives a lot of false positives (test says mouse is there, but it really isn't) and false negatives (test says mouse is not there, but it really is), we have a low level of confidence in the test.
But, if we factor in that my children may have been playing a trick,
Again, this speaks to level of confidence, not margin of error. For one thing, the test is only to show if the mouse is there or not. It is not about why the mouse is there. If the kids put it in or took it out while you were not looking, and the test correctly reports that the mouse is or is not there, nothing is wrong with the test.
On the other hand, if the kids have rigged up something that creates a false positive (makes it look as if the mouse is there when it is not) or a false negative (hides the presence of the mouse even when it is there), then they have damaged the confidence one can have in the results. But it is still a level of confidence question, not a margin of error question.
Answer the blood sugar question above, and then we can explore further what a margin of error really is. So far you have really dealt with level of confidence, and that is a different factor.
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