A couple of years ago, I wrote a blog post titled "What I Learned From Treating Childbirth as Failure" that conveniently ended up getting published the day before my daughter was born. You should read it first, but to summarize, it demonstrates how we can predict the odds of an event happening during certain time intervals even when the original data is highly censored.
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Since then, several people have asked (two in the comments alone) where I came up with the numbers I stated at the end:
• When should a relative arrive for a seven-day stay to have the greatest chance of being there for the birth if the due date is May 19? (May 17)
• What are the odds of the baby being born on a weekend? (28.6%)
• What are the odds of the baby being born on her great-grandmother's birthday, May 14? (3.7%)
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