How reliable are certain scientific statistics?

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The reliability of statistics in science, particularly in fields like biology and medicine, is under scrutiny. Anecdotal evidence, such as knowing multiple women who have given birth naturally after 40, raises questions about the accuracy of statistical data, which often presents a bleak picture of fertility at advanced ages. Variability in statistics, such as differing percentages of conception chances for women over 40, highlights the complexity of interpreting such data. The discussion emphasizes that the fault may lie not in the statistics themselves but in their interpretation, especially when based on small sample sizes. Larger studies provide a clearer picture, demonstrating that while fertility decreases with age, successful pregnancies do still occur, albeit with increased risks. The conversation also touches on the challenges of applying statistical analysis in medical science due to genetic diversity and the ethical implications of sample sizes. Overall, while statistics can inform understanding, they may not fully capture individual experiences or the nuances of biological variability.
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First, sorry if this is in the wrong section. This could span many subjects.

I was pondering on how reliable statistics in science are. My mother's best friend just had a baby naturally at 45 years old. I also know 3 other women who have had babies naturally after 40 (specifically 2 of them at 44, and the other at 45). Yet when I read up on the statistics about how possible it is to have babies after 40 (especially at the mid-40s) it would seem almost impossible that I know 3 women who have naturally had babies (especially since they're all over 44). This makes me think that such statistics are unreliable. This has to be true in medicine and biology since it is difficult to know things about the body with such precision. I can imagine in other parts of science, the same applies, though in physics it's probably less so.

So how reliable are statistics in science? In biology?? With the human body?? In geology? Cosmology? etc

EDIT: Also I'd add about those stats about women being able to naturally make babies in their early-to-mid 40s, there are so many ranges that differ. For example I read one that stated how it's only a 1% chance at 44, when other said its a 30%, and it ranges from the fathers age (the younger the father the better). Yet other statistics say the fathers age is irrelevant. This makes me believe that there exists some faults in certain subjects in scientific statistics.
 
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There are several statistics that you are intermingling erroneously.

One is the statistics of women over 40 who have given birth.
Another is the possibility of a woman over 40 conceiving, due to the physical changes in the body brought about by age.
Another is the chance that a particular individual knows a woman over 40 who has given birth.

The fault lies not in the statistics, but the interpretation.
Sometimes that is difficult to do.
 
Your problem is that you only are looking at a very small sample. Let's suppose that the data shows that only 1 in 100,000 women 40 years old and older will ever be able to conceive a child (I'm completely making this up to demonstrate the phenomenon) and there are ten million 40+ women trying to conceive. That means that 100 of them statistically will. If you only look at those 100 then of course it's going to seem like the original data is wrong, but taken as a whole it makes sense.

Furthermore the chances of conceiving after 40 really aren't as low as you make out to be. According to http://www.extendfertility.com/downloads/documents/NEJM_AdvancedMaternalAge_HowOldIsTooOld.pdf pregnancy rates in women less than 30 years old are 400 in 1000, dropping to 100 in 1000 for over 45s. The miscarriage rate for the latter group is much higher at 90% but that still leaves a relatively large (10 in 1000) number that successfully give birth. That doesn't take into account complications like increasing risk of Down's syndrome (see this paper for more information on the risk of birth defects) but you get the idea.
 
The moral of the story: don't expect statistics to provide protection against pregnancy when more effective means are available.
 
Simply, statistics are more reliable on a subject that is more uniform or presumed to be: subjects like physics and chemistry. When you move into the realm of medical science, the genetic diversity and differences in populations really stress that you have an adequately large, possibly unfeasible/ethical sample sizes. Statistics become even more hairy in the social/political sciences.

Simply because you know three women in the mid forties who have had children doesn't disprove the statistic. The journal that is pulled out of is the journal Fertility and Sterility and their sample size is larger, which trumps your anecdotal experience. The only real conclusion to draw from the statistic is that women over the age of 40 rapidly lose fertility with each passing year.
 
And then there are statistically significant results that are biologically meaningless...

There have been many, many papers over the years written on this subject and our over reliance on 'statistical significance' within biomedical research. A statistically significant phenomena might not mean a damn thing.
 
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