Confidence in One’s Ignorance
Posted by: childbirthtruthsquad on: August 25, 2010
This is from Nick Fogelson of the Academic OB/Gyn. He posted on Mom’s Tinfoil Hat. The response is below. So much for so-called credentials. It is once again about the Wax meta-analysis and the completely erroneous laughable midwifery mantra that its no good because the confidence intervals are so wide!!!
Once again, there is ignorance of the meaning of a confidence interval that excludes or is skewed away from the null hypothesis — no matter how wide. In fact if it is wide is very, very bad, if it is against your position. There’s also an ignorance that this one is probably wide for reasons other than lack of power. Lastly, even if it is from lack of power, the basic conclusion is extremely unlikely to change when interval excludes the null or is skewed.
In response to childbirthtruthsquad on July 27, 2010 at 8:39 pm:
From original comment
The CI gets narrower, most likely around the center of the CI, since there’s a 95% the true is somewhere in there and is normally distributed within it. So, if the CI was about .3-6, the true, when it gets “powered up” (BTW, how does one do that statistically?) will probably be around 3. How […]
>> So, if the CI was about .3-6, the true, when it gets “powered up” (BTW, how does one do that statistically?) will probably be around 3.
Fogelson
“This is really not true. Theoretically the most common true value is in the center, but in aggregate it is most likely that it is not near the center, as there are many other values. In a standard distribution, the center is still only about 20% of the volume of the curve.”
Explain how this is different than what I said. The absolute center is the single most likely value. The fact that all the others combined have a greater likelihood is hardly interesting or a gotcha point. Besides, you are completely missing the point. When power increases (NOT the main problem here BTW) the CIs get narrower. That increases the chance that the true is closer to the mean in absolute terms, because the SD gets smaller.
“In a standard distribution, the center is still only about 20% of the volume of the curve.”
http://en.wikipedia.org/wiki/Standard_deviation
Umm, no. Within one std. deviation is about 2/3 of the data. If you want to target a smaller percentage that is less than 1 SD, that’s your choice, but that’s all it is.
Fogelson
“The point is that you don’t know where in the distribution the truth.”
Uhh, yeah. That’s why God invented confidence intervals. And your point is….?
If they are normally distributed one can calculate the probability of the true value being above or below a value in the CI , below, or in between 2. The single most likely answer, though, is in the exact middle. Try this, see if it helps.
http://davidmlane.com/hyperstat/z_table.html
“ If we could just assume it was in the middle we wouldn’t need more power.”
No one (well, no one who knows what they are talking about) said you needed more power. The reason this one is wide probably isn’t due to lack of power. It is more likely due to the number of non-random variables from combining studies in a meta. If you get your info from the Statistics for Non-Majors book, the simplistic soundbite won’t tell you that wide=lack of power is limited to, well, simplistic situations like single study randomized controls.
And the kicker is, even if it needed more power and you got it, it is unlikely that it would change the basic conclusion of homebirth as deadly and unlikely to change the multiple by which it is that it is very deadly.
We are not assuming the middle. Simply the mathematical fact is that it is the single most likely and as you go farther out on either side one is more and more likely to encompass the true. But going only slightly out captures the bulk pretty quickly. If you lack power and add more subjects, it only make the CI narrower. It is still most likely to be centered around the mean or close to it. And narrower it gets, the more likely the true is closer to the mean.
Got any links to back-up your points?
The most important thing in this example is that the entire CI falls to the right. The right, in this case, is contrary to equal/favorable position of midwifery argument. Everything to the right means the midwives are more deadly. So, the fact that it is wide and the entire interval falls to the right is much, much worse for your argument. When the null is not within the 95% CI, or skewed away from it, the chance of equality between the options is miniscule.
From the link:
http://www.childrens-mercy.org/stats/journal/confidence.asp
“How to Interpret a Confidence Interval
Here’s an example of a confidence interval that excludes the null value. If we assume that larger implies better, then the interval shown below would imply a statistically significant improvement.” (See graphic illustration in link)
When entire 95% confidence interval is to the right of the null, and the right is the opposite of your position it is very, very bad for that position. You have this problem, a problem that widens the CI, that should have *helped you* move towards and encompass and be more centered over the null (i.e. the null supports that homebirth was equal). Nevertheless the entire friggin’ thing was to the right!
The Childbirth Truth Squad 