Are you better than an MP at statistics?

[cakeorwine]

There was a survey of 100 MPs which was discussed on More or Less last week.

Can you do better?
There were 3 questions - can you answer them?

1. I toss a coin twice. What is the probability of getting 2 heads? (50% of MPs got this right)
2. I roll a dice 6 times. I get 1,4,2,1,3,6

What is the mean and mode of those numbers?

(About 63% got this right)

3. A diagnostic test has a false positive rate of 1 in 1000. So for every 1000 people who are tested and are negative, 1 will test positivr If someone test positive, what are the chances they actually are positive? 99.9% 99.99 % 99% 1% 0.01% Not enough information to tell

16% of MPs got this right.

So can you do better?

I know the difference between averages etc but can't do the calculations mentally. So likewise, I don't need my MPs to be able to do mental arithmetics instantly.

I DO expect them to be passionate about helping citizens and intelligent enough to seek out answers, which I actually think is the same thing you're getting at, a sort of critical thinking capacity?

My dd is in year 7 and has had variations on all of those questions this year or last year. This is hardly high level statistics.

2) I roll a dice 6 times. I get 1,4,2,1,3,6
what is the mean?

This one is a bit tricky to do mentally because it's not a whole number answer.

1+4+2+1+3+6 = 17
17/6 (because there are 6 rolls) = 2.83

But in the link you provided the question is:

Question 2: Suppose you roll a 6-sided die. The rolls are 1, 3, 4, 1, and 6.
What is mean the mean?

This is much easier because it's 15/5 = 3

(I removed the questions about mode).

I got them all right, aside from the mode question. I couldn't recall what that meant.

And if they're my age or older (50+) they will not have covered this sort of thing at school either.

I’m 50 and we definitely did basic probability and mean/mode/median before what was then O-level.

The last question wouldn’t have been covered, but it’s more about logic and comprehension.

To be fair the More or Less feature acknowledged that faced with question 3 many would feel pressure to provide a clear answer and fear that ‘not enough information’ was a cop out. I wonder how much time was given to think it through?

Also is 100 MPs a fair representation?

@CakesOfVersailles
17/6 or 2 5/6 is the exact answer, nothing wrong with fractions imo

I did a level maths but wouldn't have been able to answer the lay on that basis. Now I work with Bayesian stats a lot so it is obvious. But it would not surprise me that many people have no idea for no3.

No1&2 are primary level maths and everyone should be able to do it.

I think the last question is similar to the ‘As I was going to St Ives’ riddle. The statistics about about false positives encourage you to plunge into analysis of the 1 in 1000, without thinking about the information you need for the question.

It's almost 30 years since I did GCSEs and I knew those, especially that you can't calculate false positives without knowing the background rate, because I take an interest in current affairs.
MPs should really have a grasp of basic maths. How come you need GCSE maths to work in a lot of minimum wage jobs but not to work as an MP?

Also is 100 MPs a fair representation

Surveys of the public ask about 2000 people.

So I would imagine that there would be a very high confidence level when asking 100 MPs out of 625

surveysystem.com/sscalc.htm

Of course, if they only ask MPs in 1 party, or who were just female, then you can't extrapolate the results.

@illyawasthebest

I know the difference between averages etc but can't do the calculations mentally. So likewise, I don't need my MPs to be able to do mental arithmetics instantly.

I DO expect them to be passionate about helping citizens and intelligent enough to seek out answers, which I actually think is the same thing you're getting at, a sort of critical thinking capacity?

I think they could have used a calculator if they wanted. Although yes, the link was a different mean. I just listened to More or Less and tried to remember the questions.

@merrymouse

I think the last question is similar to the ‘As I was going to St Ives’ riddle. The statistics about about false positives encourage you to plunge into analysis of the 1 in 1000, without thinking about the information you need for the question.

Have you ever read ' Thinking Fast and slow'?

So many questions in it where people just hear some numbers and jump in with an answer without slowing down and thinking...

What's the answer to 3?

MPs get paid to do these type of surveys. (£50-£100 usually) IME they complete them as quickly as possible to get them out of the way.

Ministers are not permitted to do them. So none of these 100 MPs are government ministers. So it’s a representative sample of MPs who aren’t ministers.

I can answer them all, but I studied statistics at university.

@Palavah

What's the answer to 3?

It all depends on the prevalence of the thing being tested for in the population.

Imagine a screening test that identifies a disease.

The test has a false positive rate of 1 in 1000.
The prevalence of the disease is 1 in 10,000 people

So the question is - if someone tests positive, what are the chances that the positive test is a true positive.

If you have a higher or lower prevalence, how does this affect this result?

@LatteToday

MPs get paid to do these type of surveys. (£50-£100 usually) IME they complete them as quickly as possible to get them out of the way.

Ministers are not permitted to do them. So none of these 100 MPs are government ministers. So it’s a representative sample of MPs who aren’t ministers.

I can answer them all, but I studied statistics at university.

I don't know if they were paid. It was carried out on behalf of the RSS.

I hope they didn't rush them as they should have used critical thinking to think that the results would be published.

Good point about Ministers.

So it could be an even better sample size for other MPs.

I wonder what Ministers would get? Even the PM

I can answer them all, but I studied statistics at university

1 and 2 are primary level maths.

3 is maths and critical thinking.

The methodology:

"Savanta ComRes surveyed 101 MPs online between 17th November 2021 and 18th January 2022. Data are representative of MPs in the House of Commons by party and region"

Doesn't say how many they contacted and who didn't complete the survey"

So I would imagine that there would be a very high confidence level when asking 100 MPs out of 625

But 100 is still a relatively small number and any small sample size can produce unrepresentative results, particularly if there is a lot of variance in the population.

Also it depends how the question was asked - quick phone call when they weren’t paying much attention? and whether other factors skewed selection e.g. more senior MPs ignored the survey.

I think it’s important that MPs should have a good understanding of risk, but I think the survey raises questions rather than definitively providing evidence that MPs are stupid.

I also think there is a difference between knowing how to work out basic probability questions and recognising that we can all make incorrect assumptions of risk based on instinct, even if we know the theory. I suspect, for instance that Jacob Rees Mogg can immediately answer the coin toss question correctly, but that doesn’t mean he knows his arse from his elbow!

But 100 is still a relatively small number and any small sample size can produce unrepresentative results, particularly if there is a lot of variance in the population

The laws of small numbers.....

I think it’s important that MPs should have a good understanding of risk, but I think the survey raises questions rather than definitively providing evidence that MPs are stupid

Is it being stupid? I think that's not the right word. Does it raise questions about a level of understanding of maths that they need for their job? Yes

But 100 is still a relatively small number and any small sample size can produce unrepresentative results, particularly if there is a lot of variance in the population

Doesn't stop primary schools being judged by the Government with classes of 30 and SATs results.

I agree stupid isn’t really the right word.

I’d rather an MP who knows they don’t know much about statistics, but asks the right questions than one who is completely confident in their own abilities and blunders on regardless.