Rita and Paola.... the story so far.
Rita had an identical twin sister, called Paola.
The fact they were identical twins means they had the same DNA.
We have two 'key' questions regarding Rita and her use of NGF eye-drops:
Q1. Did Rita live 'significantly' longer than her twin sister Paola ?
Q2. Did Rita enjoy better cognitive health than her sister Paola ?
We can't begin to answer Q2 yet, but progress has been made on Q1
I'm told that the convention is 2 standard deviation points for expressing
variance using +/- values from a mean.
So... we want to know if Rita lived (statistically) significantly longer than Paola.
We know when they both died and the difference is 12.16 years.
I've taken the twin study data reported here : http://www.ncbi.nlm..../pubmed/1302428
as a reference data set. Their data say that identical twins die with a difference
in years of 5.6 years +/- 6.65 years.
What does that mean ?
It means if you study 100 twins, and record the date of their deaths,
you can create a distribution of data expressing the duration between their deaths.
eg.
Sam and Peter died in Jan 1971 and July 1973 ..... so that data point is 2.5 (years)
Julie and Samantha died in Jan 2000 and April 2003... so that data point is 3.25 (years)
... i'm sure you get the idea.
Do that 100 times and you'll have 100 numbers that range from 0 to .. upto .... about 20.
Now take the average of those numbers.
In the case of the cited twin study, the average was 5.6 years.
That means approximately 50% of the data were below 5.6 years
and approximately 50% of the data were above 5.6 years.
In terms of Rita and Paola, this means that Rita should have died
within 5.6 years of Paola (on average).... that is.. 5.6 years before
or 5.6 years after Paola (i.e. within 5.6 years of each other, on average)
So the question is:
Is it statistically significant that Rita died 12.16 years after Paola ?
To answer that question, it's usual to refer to the normal distribution.
In a nutshell, we look at the distance from the centre of the distribution
to the data point of interest (12.16 years)
... and then count the % of the distribution between the
data point and the end of the distribution.
The results provided by the twins study are: 5.6 +/- 6.65.
So 5.6 + 6.65 = 12.25. years.
(5.6 is the middle of the distribution,
and 6.65 is years from the centre to 2 standard deviation points)
Looking at the Normal distribution table supplied above
we see that 1.7% of the population exist beyond +2 standard deviation points.
So there's only 1.7% chance that one twin will die 12.25 years after the other twin.
Rita died 12.16 years after Paola, that's very nearly as much as 12.25
At a rough guess, perhaps there's only a 2% chance that Rita would die 12.16 years after Paola.
The standard level of statistical significance is 5%.
Anything less than 5% is deemed statistically significant.
Clearly... 2% is less than 5%.
Meaning... Rita lived longer than Paola than would be expected by chance.
It's a statistically significant difference in their lifespans.
And now that I've figured that out, it seems obvious, that of-course, living 12 years longer
than someone that died at the age of 91 is clearly significant.
Intuitively it seems obvious because, the likelihood of you dying in the next 12 months,
is much, much greater when you are 91, than it is when you're, say, 21.
The chances of you surviving another year, decrease every year.
And those survival chances decline dramatically after your 70s.
So to live 12 years longer than someone in their 91st year, is actually quite an achievement.
In summary,
I'm told that the "+/-" convention is to express a variance to 2 standard deviation points.
Assuming this is correct, it means that:
Rita lived longer than Paola than would be expected by chance.
It's a statistically significant difference in their lifespans.
We might, not unreasonably, wonder if Rita's use of NGF eye drops was a factor in her
remarkable longevity.
Edited by playground, 03 June 2015 - 03:34 PM.