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Im trying to measure the absolute change between two means of systolic bloodpressure, and used a simple method for calculating the confidence interval between to means.

My goal is to estimate the absolute change for the TREND between 1980-2000. So to accomplish this im comparing the first and last year (i.e 1980 and 2000, which i already have an point estimate and 95%Cl for, achieved with proc STDRATE in SAS 9.4, using a backgroundpopulation of holland).

Now to the problem ->

For the year 1980 i have a point estimate with 95%cl for systolic bloodpressure at 94.9(73.1 to 120.8)

For the year 2000 i have a point estimate with 95%cl for systolic bloodpressure at 80.3(70.1 to 96.8)

So the absolute change is -14,6, this means that the asbolute decline is 14.6 with the calculated confidence interval of +/- 22,7 (normal distribution).

Here's the thing-> i cant make any sense of how to interpret an absolute decline of 14.6 (-8.1 to 37.3).

Since im trying to describe trends and already know that systolic hypertension have a decline with 14,6 estimates then how can i describe a lower limit of minus (-)8.1 if its already a decrease.

Hope that this makes any sense, its probably a more epidemiological question then a mathematical or programming one.

In desperate need of help :)!

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Frank49
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You're thinking too hard! A "negative decrease" is just an increase. Your CI says "with 95% confidence, systolic pressure changed between -37.3 and 8.1"

shadowtalker
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  • So your saying that a confidence interval for the lower limit below zero is an actual increase? For all i know u might be fully correct, cant just understand it quite yet. Since most of my variables have an absolute change very close to zero my lower limits are all negative. How can it then be that both the lower limit and upper is greater then the point estimate. For example i just did BMI (body mass index), it showed an absolute decline of 8,6 (-11,2 to 44,1). How would u interpret this? Btw really appreciating ur help! – Frank49 Jul 26 '14 at 14:43
  • Yes. You're stuck in the terminology. A negative decline is an increase. The lower bound on your decline is an upper bound on your change, i.e. your increase. This is why it's generally easier to think in positive units, it can be confusing. BTW, your CI for change includes 0 so you can't reject the null hypothesis of zero change with 95% confidence. – shadowtalker Jul 26 '14 at 16:11
  • Okey. Intuitively It feels that the absolute change is significant. Can it be that whenever an effect is significant, all values in the confidence interval will be on the same side of zero (either all positive or all negative). Can I therefore specify the direction of the effect. There are many situations in which it is very unlikely two conditions will have exactly the same population means. Therefore, even before an experiment is conducted, I know beforehand that the null hypothesis of exactly no difference is false. I might be wrong, if so please be sure to correct me. – Frank49 Jul 26 '14 at 17:41
  • You have not proved that they are equal. You've only failed to rule out the possibility that the means are equal, up to a 1 in 20 chance of having missed a difference. – shadowtalker Jul 26 '14 at 18:41
  • Yes, having values on the same side of 0 is equivalent to having a test statistic above the rejection cutoff. I recommend you sit down with a pen and paper and prove this for yourself, it's a great exercise that really forces you to understand how hypothesis testing and CIs work. – shadowtalker Jul 26 '14 at 18:42
  • And you've uncovered the problem with frequentist statistics: assuming the existence of a single true underlying parameter value tends to be conceptually problematic. This is why people have come to interpret "failure to reject exact equality" as "close enough to equality." All you're doing in the latter case is letting your textbook choose a formula for "close enough" based on sample size and some distributional assumptions. Sometimes that's what you want, other times it isn't. – shadowtalker Jul 26 '14 at 18:46
  • Thank you. Truly instructive. Do you know any book on this specific subject, or does most books in statistic cover this topic? – Frank49 Jul 27 '14 at 12:52
  • Well, the stuff about "negative decrease is an increase" is just math. As far as hypothesis testing goes, I first learned statistics through an econometrics lens, from *Introduction to Econometrics* by Stock & Watson, and then later from *A Second Course in Statistics: Regression Analysis* by Mendenhall & Sincich. They both have a good deal about hypothesis tests. There might also be some good references here: http://stats.stackexchange.com/questions/31800/online-reference-for-review-of-introductory-statistics-material – shadowtalker Jul 27 '14 at 17:36
  • For general stats, I've heard good things about *Statistical Models* by Freedman, *Statistics for Experimenters* by Box, *Statistics in a Nutshell* published by O'Reilly, *Statistics in Plain English* by Urdan. – shadowtalker Jul 27 '14 at 18:11