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I'd like to calculate the confidence interval of the mean difference. I know that you could potentially use the t.test function in R for this but I can't use the original data, of which the means have been calculated. Therefore I've only got the means and their standard error and confidence interval and not enough observations for the t.test.

My data looks like this:

mean1: 198.21855 se1: 11.36940 lcl1: 176.27362 ucl1: 220.9175

mean2: 87.93562 se2: 30.36013 lcl2: 33.85978 ucl2: 153,4715

And now I want calculate the confidence interval of the mean difference 110,28293 (C.I: ?)

Is there any way to calculate this in R? And if not, how can I calculate this manually?

Christoph
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  • Welcome to CV. Since you’re new here, you may want to take our [tour], which has information for new users. Do you have information on sample sizes? – T.E.G. Aug 10 '23 at 10:30
  • Thanks for welcoming me! I used weighted model-averaging to calculate these values with 3 models. Does this count for the sample size? – Christoph Aug 10 '23 at 10:37
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    I thought the analysis as a simple independent samples t-test. You have means and SE of means ($sd/ \sqrt{n}$) from two samples (or groups if you like). I was asking the number of observations in each group. But I guess you have something else going on here. – T.E.G. Aug 10 '23 at 10:47
  • The concept of a standard error is that it indicates how much the statistic typically varies from one sample to the next, in terms of (the square root) of the sampling variance. The basic rules of variances tell you the SE of the difference of (independent) means is the root sum of the squared SEs. Go on from there. – whuber Aug 10 '23 at 13:38
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    Your means are not halfway between the upper and lower confidence interval limits so something special was done in the original analysis, making it harder to back-calculate the original sample sizes – Henry Aug 10 '23 at 14:30

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