Flag dynamics

[JohnW2]

I've seen such stats on TV, where they have said something similar to 97% out of 45 people asked, agreed that A was better than B.

There's not necessarily anything wrong with that, but it obviously depends upon how the 45 people were selected, what question was asked (and how) etc. etc.

Of course, one thing to watch for is that such a 'dichotomous' statement is totally non-quantitative - i.e. that, whilst it may be true that 97% of all people think that A is 'better' than B, the extent of the perceived difference between A and B might be so small as to be of no practical importance/relevance.

That is one of the most common misinterpretations of data. Even if completely true, a difference (even if quantified) between A and B may be (mathematically) 'highly statistically significant', yet so small in magnitude to be of no interest or practical use.

One very common ploy (essentially an 'abuse of statistics', even though it contains no 'lies') to look out for is a statement like "97% of 45 people who expressed a preference agreed that A was better than B" - since that could be roughly true if the figures were, for example:

I person thought A was better
1,000 thought that there was no difference between A and B
44 people thought that B was better than A

The 'small print' of adverts (TV, internet or printed) often reveals the "who expressed a preference" qualification

 

[blup]

There's not necessarily anything wrong with that, but it obviously depends upon how the 45 people were selected, what question was asked (and how) etc. etc.

Of course, one thing to watch for is that such a 'dichotomous' statement is totally non-quantitative - i.e. that, whilst it may be true that 97% of all people think that A is 'better' than B, the extent of the perceived difference between A and B might be so small as to be of no practical importance/relevance.

That is one of the most common misinterpretations of data. Even if completely true, a difference (even if quantified) between A and B may be (mathematically) 'highly statistically significant', yet so small in magnitude to be of no interest or practical use.

One very common ploy (essentially an 'abuse of statistics', even though it contains no 'lies') to look out for is a statement like "97% of 45 people who expressed a preference agreed that A was better than B" - since that could be roughly true if the figures were, for example:

I person thought A was better
1,000 thought that there was no difference between A and B
44 people thought that B was better than A

The 'small print' of adverts (TV, internet or printed) often reveals the "who expressed a preference" qualification

Cost is an interesting factor in marketing: people might buy a piece of jewellery at a certain price but not if it is sold at a lower price because of perceptions about quality. It happened at a local charity near me when they significantly increased the price of tea and coffee and got more custom.

 

[Harry Bloomfield]

There's not necessarily anything wrong with that, but it obviously depends upon how the 45 people were selected, what question was asked (and how) etc. etc.

With only two possible options, how can there be 97% of 45 people?

 

[JohnW2]

It occurs to me that, amidst these discussions about survey sample size, I have not said anything about the report/claim that gave rise to the discussion.

If I understand correctly, the report was that, with a sample size of 2043, 58% of respondents (I presume 1,185) expressed the view that "more Union Flags and St George Cross flags should be flown". Is that correct?

If so, then IF the sample of 2043 people was reasonably representative of the entire UK population (ideally a true 'random sample') and IF an appropriate question was asked, and asked in a manner that was as unbiased as possible (see below **), then this would indicate that we could be 95% confident that between about 56% and 60% of the UK population held that view. That would generally be regarded as a pretty precise estimate - but such is totally dependent upon those two major IFs above.

[ *** There are many possible variants of the question which might have en asked. The following few might all resut in somewhat different answers:

Should more of these flags be flown?
Should less of these flags be flown?
Should more or less of these flags be flown?
Do you agree that more of these flags should be flown?
Do you agree that less of these flags should be flown?​

Attempts at somewhat more sophisticated (and semi-quantitative) questions might be of the form:

On a scale from 1 to 10 (1='Strongly Disagree', 10='Strongly Agree') indicate whether or not you agree that more of these flags should be flown.​

In all cases, there should also be "don't know"/"undecided"/"no preference/view" answers available and recorded, so that relevant responders do not get 'overlooked'in the analysis, thereby potentially distorting the results / conclusions. ]

 

[JohnW2]

With only two possible options, how can there be 97% of 45 people?

In terms of precise maths, one obviously can't. That's why I assumed 44/45 in my example, which is 97.777.... % I imagine that they did mean 44/45, which they should have rounded to 98%, not 97%

 

[JohnW2]

duplicate deleted

 

[Harry Bloomfield]

which is 97.777.... %

You simply cannot have 97.777% of a person

 

[EFLImpudence]

Should more of these flags be flown?​

Should less of these flags be flown?​

Should more or less of these flags be flown?​

Do you agree that more of these flags should be flown?​

Do you agree that less of these flags should be flown?​

Fewer.

 

[JohnW2]

Cost is an interesting factor in marketing: people might buy a piece of jewellery at a certain price but not if it is sold at a lower price because of perceptions about quality. It happened at a local charity near me when they significantly increased the price of tea and coffee and got more custom.

I'm not sure what that has got to do with this discussion, but I totally agree. I may well have previously told this story stemming from my days in the 6th form at school, some 60 years ago ....

... there had traditionally been Saturday Night School Dances, but interest/attendance had been waning to the extent that we were contemplating stopping them. A series of people had tried all sorts of ploys and gimmicks to try to attract attendees, but with very little effect, and the buck was eventually passed to me!

Like those before me, all of the changes/gimmicks I tried had very little effect. As a last resort, when I was also about to 'give up', I dramatically increased the price of tickets, to a level which ought to have been 'unaffordable' for most school kids. Everyone started coming, presumably on the basis that "it's so expensive that it must be good" - and these (very expensive) weekly events thereafter remained a great success for the rest of my time at school- and I, of course, became a "hero"

It seems that there are a lot of 'gullible' people in this world

 

[JohnW2]

You simply cannot have 97.777% of a person

One can't, but you're just being silly. A very high proportion of proportions cannot be expressed as percentages as whole numbers, but most people find it easier to conceptualise ('approximate', rounded) percentages than fractions.

It's likely that all that was wrong was their rounding.

 

[JohnW2]

Fewer.

Indeed

 

[Harry Bloomfield]

It's likely that all that was wrong was their rounding.

There was no rounding needed, no room for error.

 

[JohnW2]

There was no rounding needed, no room for error.

What are you talking about?

If (as I imagine was the situation) they had said "44/45" you would presumably not be moaning. However, as I said, people generally find percentages easier to understand and work with than fractions/proportions and, in most cases (like this one) conversion to a percentage will require some rounding (or, as in this case, and many others, a screen (or piece of paper) of infinite size!).

Which do you find 'easier to understand' 19/45 or 42% (rounded) ?

 

[morqthana]

Does a "gentlemanly discussion" include saying things which aren't true?

He's displaying the flag of a proscribed terrorist organisation in this country, the United Kingdom.

You just won't stop, will you:

Yet, one individual in this forum, is risking upto 6 months on bread and water, in his use of that very flag as his logo/avatar..

And yet you dare to complain about what I write.

 

[morqthana]

I'm, with Sunray here "twice as cheap" is a very odd statement,

I said "I've always assumed they mean "half the price".

Not that "twice as cheap" means "half the price". Although I suppose in the minds of those who use it, it does.

on a par with the commonly seen "100% less" etc. (which I suspect usually is meant to mean '50% less') or, even worse "at least 100% reduction"

Many people don't understand percentages. I remember once having quite a job to explain to someone, in the context of moaning about an example of shrinkflation (a despicable practice, IMO) where they'd reduced the size of a product from 600ml to 500ml and kept the price the same
was a 20% price hike, not the 16.7% he'd come up with.

And how many times have you seen a doubling of something as a "200% increase"?

Or where an increase in a probability from 10% to 15% is described as a 5% increase?