[finally17]

I would be really really shocked if there is single a non-accelerated public high school program math program in the country that covers standard deviations and confidence intervals. Certainly it's covered, if I recall correctly there's even a stats AP, and most people would be surprised at how far some programs go given the general impression of Americans and math, but most public programs struggle to get through algebra.

Which poses an interesting question because for the average person a basic stats course would probably be more useful.

[mycroft]

1. Covered in first-year Engineering Math (same place we discussed precision (and the cost of precision, and why you don't over-specify precisions when you're planning/purchasing), significant digits, . Covered *again* in Statistics for Engineers in second year, where it came in about the Normal distribution when we were covering all the "usual distributions".

Of course, Engineering is neither Math nor Physics, although it uses a lot of both - the emphasis is very different.

2. Covered - very well, I might add, which of course, the whole book does, even if the math is missing a couple of zeros due to inflation - in "How to Lie With Statistics", by Huff.

Michael.

[slothy]

Re Math education in the UK

A lot of kids in the UK - a country fallaciously perceived (by some) as some educational paradigm, yet is scraping the bottom in european 'League Tables' despite attempts by the Education Minister to massage figures and trump out gaping disparities in the statistics - are leaving school without a basic and 'working' concept of fractions (and its illegitimate 'half-sisters' %ages, decimals, ratios etc) , geometry and basic algebra - never mind more elevated ideas like calculus and advanced trigonometry.

Those that perform well are those that have a succouring environment at home and concerned parents who invest their own time (not necessarily money) and effort.

I have worked with too many young kids who have fallen so far behind that it becomes a Sisyphean task to get them up to speed to barely pass their GCSE. Half the climb is persuading them of the value of having an education - however futile and unaccommodating it may appear to them AT THE TIME. Once this attitude is instilled, they become receptive to learning and achieve beyond their, and of others more judgemental, expectations.

It is a shame that at least here education is becoming undervalued and even sneered at, and this attitude is becoming more and more acceptable.

[beatrix45]

Backward run the sentences until reel the mind. In statistics everything is stated in a sort of backward fashion. The statement you give says:

For A: There are 19 chances out of 20 (assuming the commonly used 95% confidence interval) that candidate A had between 22 and 30% of the vote at the time the survey was taken. There is one chance in 40 that he had more than 30% of the vote and one chance in 40 he had less than 22%.

For B: There are 19 chances out of 20 that B had between 21 and 29% of the vote. One chance in 40 he had more than 29% and a similar probability he had less than 21%.

We are assuming the survey was done correctly with all the statistician's assumptions being met (most surveys, almost all in fact, aren't so pristine, and they fall short at least to some degree). Many political surveys stray so far from the necessary assumptions, that their plus or minus so-and-so statements are pretty much worthless.

That's it folks. That's all. There ain't no more.

[jdonn]

beatrix45, on Dec 5 2007, 08:40 PM, said:

For A: There are 19 chances out of 20 (assuming the commonly used 95% confidence interval) that candidate A had between 22 and 30% of the vote at the time the survey was taken. There is one chance in 40 that he had more than 30% of the vote and one chance in 40 he had less than 22%.

I'm a bit rusty in this stuff, but isn't it NOT (necessarily) true that, given a 95% confidence interval, there is a 2.5% chance the true answer lies below and a 2.5% chance the true answer lies above?

[cherdano]

jdonn, on Dec 5 2007, 07:52 PM, said:

beatrix45, on Dec 5 2007, 08:40 PM, said:

For A: There are 19 chances out of 20 (assuming the commonly used 95% confidence interval) that candidate A had between 22 and 30% of the vote at the time the survey was taken.  There is one chance in 40 that he had more than 30% of the vote and one chance in 40 he had less than 22%.

I'm a bit rusty in this stuff, but isn't it NOT (necessarily) true that, given a 95% confidence interval, there is a 2.5% chance the true answer lies below and a 2.5% chance the true answer lies above?

At these numbers, the distribution is extremely close to being symmetric around 26%. So technically you are right, but the difference is negligible.

[helene_t]

jdonn, on Dec 6 2007, 03:52 AM, said:

I'm a bit rusty in this stuff, but isn't it NOT (necessarily) true that, given a 95% confidence interval, there is a 2.5% chance the true answer lies below and a 2.5% chance the true answer lies above?

Strictly, no, but it is "almost" true and probably easier to understand than the correct definition of confidence intervals (see my first post).

Note: I'm not referring to the problem of approximating the binomial distribution with a normal distribution, or other technicalities specific to this particular model. I'm assuming that we're using an exact method to compute the confidence interval.

[beatrix45]

helene_t, on Dec 6 2007, 01:54 AM, said:

jdonn, on Dec 6 2007, 03:52 AM, said:

I'm a bit rusty in this stuff, but isn't it NOT (necessarily) true that, given a 95% confidence interval, there is a 2.5% chance the true answer lies below and a 2.5% chance the true answer lies above?

Strictly, no, but it is "almost" true and probably easier to understand than the correct definition of confidence intervals (see my previous post).

Note: I'm not referring to the problem of approximating the binomial distribution with a normal distribution, or other technicalities specific to this particular model. I'm assuming that we're using an exact method to compute the confidence interval.

Think Central Limit Theorem. The underlying distribution doesn't matter. The sampling distribution approaches a normal distribution as the sample size increases, and sample size is usually fairly large in election surveys.

In election surveys, you have to assume a two-tailed test - there is no reason to rule out either tail a priori.

The 800 pound gorilla in these applications is whether or not the sample itself is random. For example, what do you do when you can't contact one of your sample survey members? Do you move on to the next name on your list? This implicitly assumes people who are not home are 'just like' the rest. But, maybe they aren't home because they are at work at 8pm dinnertime, and people who work second shift are more likely to vote for a particular candidate.

Also, is the sample member going to vote?

Lots of problems. Typically, the people who pay for this kind of work appreciate and compensate for them. However, when they broadcast survey results as propaganda to try to make some point or another, I suggest you take it with a grain of salt.

[nige1]

Statistics don't lie
People do

[helene_t]

beatrix45, on Dec 6 2007, 04:29 PM, said:

Think Central Limit Theorem. The underlying distribution doesn't matter. The sampling distribution approaches a normal distribution as the sample size increases, and sample size is usually fairly large in election surveys.

When the poll involves small parties projected to get a fraction of a percentage of the votes, the CLT may not be adequate. Anyway, that's not really an issue - exact methods are available for the binomial case as well and I'm sure the polling institutes use adequate methods.

As for the issue of whether the sample is comparable to the set of people who will actually vote, there are a number of ways to deal with that problem. Not that the problem can be eliminated, but polling is actually quite sophisticated, there's far more to it than just computing the percentages and confidence intervals.

But of course, you cannot predict the effect of new information that will reach the electorate after the poll was made.