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[JohnW2]

Turned into quite an interesting thread. I'm glad I'm not the only person who dredges up abstract academic nonsense while blundering through DIY stuff. Economics degree in my case which covered a lot of statistics.

Threads here often do find tangents to pursue! For what it's worth, albeit not my primary discipline of professional education, in terms of statistical education I reckon I could probably 'trump' you

I believe I covered mean, mode and median at A level however it's the kind of thing that doesn't sink in until you apply it.

As I said, I think my A-level covered the concepts of most/all types of 'average', although little more than that. Computationally, there was not an awful lot that we could have realistically done in those days, since all we had were pens and paper, slide rules and log tables!

From a consumer point of view I think I had (lazily) assumed that to make that claim some proportion of the bulbs would have to last that long. The mean can be very misleading!

I'm not sure what "that claim" you are referring to, but, in relation to light bulbs etc., that is surely what is being done by making a 'claim' based on the median - the "some proportion" then being 50% - or am I misunderstanding you?

As I said before, because of the relatively high very early failure rate of light bulbs/lamps, if one goes for a much higher centile than the median (e.g. 95%) one is likely to end up with a very unhelpful figure - quite probably just a few hundred hours (at most), even if a very high proportion achieve at least 10,000. Similarly with a mean, since it would not take many very early failures to pull down the mean (which could be orders of magnitude greater) down to an unhelpful/'misleading figure'.

The point about looking at a sub group (crocodile tamers) was that even using median or modal numbers could be very misleading because even if they are the same as the general population the distribution is likely different.

Indeed, but the same is true for the mean or any other 'average'. The problem with so many things (and light bulbs are a prize example) is the shape of the survival curve. No type of single overall 'average', or any other single overall statistic, will give any indication of how many early failures there may be at the same time as giving information about longer-term survival (in the majority). Similar to what you have said, the fact that bulbs lamps are sold with a (median-based) claim that 50% will last for, say, 10,000 years does not preclude the possibility that 49% will only survive for 5 minutes.

That problem could only be overcome by giving more, and more complex, information - but I'm not sure how realistic that would be in relation to the 'general public'. For me, short of giving me the actual failure/survival curves to look at, I think the most useful thing (assuming a roughly 'bathtub' curve) would probably be to give me two figures - one for 'very early failure rate' (e.g. the first 50 or 100 hours), and a separate figure which was some sort of average life expectancy for those which survived that initial period.

Kind Regards, John

 

[ban-all-sheds]

Computationally, there was not an awful lot that we could have realistically done in those days, since all we had were pens and paper, slide rules and log tables!

I can assure you from personal experience doing Computer Science A-level in 1969/70 that it is possible to do this manually using pen and paper. I can equally assure you that it was not much fun.

That problem could only be overcome by giving more, and more complex, information - but I'm not sure how realistic that would be in relation to the 'general public'. For me, short of giving me the actual failure/survival curves to look at, I think the most useful thing (assuming a roughly 'bathtub' curve) would probably be to give me two figures - one for 'very early failure rate' (e.g. the first 50 or 100 hours), and a separate figure which was some sort of average life expectancy for those which survived that initial period.

Or figures which correspond to the existing "x000 hours" figure for the 10%, 25% and 50% (i.e. existing) points, worded along the lines of "10% of these bulbs will not last more than x,000 hours, 25% will not last more than y,000 hours, 50% will not last more than z,000 hours".

But whatever is done the makers will find a way to weasel their way out. Take a look at these:

You should be able to get a feel for the size of it from the pen in the first photo.

There's no way you could realistically share it between 3 people, and it cannot be resealed after opening so as to be kept for the next 2 days. Hands up anybody who thinks that Waitrose genuinely expect a product like that to be shared or kept and eaten in 3 goes.

And yet if you look at the label you'll see that the "traffic lights" refer to ⅓ of a pack.

Cynical, or what?

 

[ConcreteCastle]

John
To condense things a bit:

I meant the claim of a bulb having a life of x,000 hours. I assumed for some reason (without giving it much thought) that this would be the expected lifespan of any given bulb rather than the mean lifespan of all bulbs. So that some proportion much greater than 50% would still be going at that point.

If the survival curve is bathtub shaped I would have thought the plug, i.e. the point where the longer term survivors start to die off is of more interest than the mean.

 

[JohnW2]

I meant the claim of a bulb having a life of x,000 hours. I assumed for some reason (without giving it much thought) that this would be the expected lifespan of any given bulb rather than the mean lifespan of all bulbs.

Indeed, but in statistical terms, the 'expected lifespan of any given bulb' ('at birth') surely would be equal to the 'mean lifespan of all bulbs', wouldn't it? - after all, that's how statistical Expectation works, isn't it? Whether that is a statistic which is of much value to consumers is perhaps a different matter!

If the survival curve is bathtub shaped I would have thought the plug, i.e. the point where the longer term survivors start to die off is of more interest than the mean.

Agreed. As I've said, particularly if (as is likely to be the case with light bulbs), there is an appreciable number of very early failures, then the mean can be potentially very misleading. In that situation, the median is likely to be appreciably closer to the 'plug' than would be the mean. However, I'm not sure that "the point at which longer term survivors start to die off" is necessarily what people most want to know, since that is likely to be considerably less than the lifespan achieved by a high proportion of bulbs. In particular, that "point at which longer term survivors start to die off" might well be similar for bulbs for which 'the lifespan of the majority' is very different (e.g. 10,000, 20,000 or 25,000 hours).

Think of death from 'heart disease', which will probably have a bathtub distribution. Someone interested in knowing the 'expected age of adult deaths due to heart disease' would probably not be very much helped by being told "the age at which longer term survivors start to die off" - which (depending on how one defined that 'starting' point of the rise in the curve) could be very young. I would suggest that they would probably be more interested in knowing the age beyond which 'most' (maybe 50%, hence median) such deaths occurred.

Kind Regards, John

 

[ban-all-sheds]

1. Buy lights with replaceable bulbs.
2. When bulbs die, replace them.
3. And.... breathe....