# sample size and confidence interval

I hope I can phrase my question intelligibly

three groups of sample for a total of 192 individuals - group 1: 40 individuals; group 2: 82 individuals; group 3: 70 individuals.

the 95% CI range of disease-free period after treatment - group 1: 9-14.7 months (median: 12.8); group 2: 5.3-7.6 months (median: 5.7); group 3: 3.6-5.5 months (median: 5.2).

the CI ranges were derived from certain distribution (what kind??) of individual's response (i.e. diseaes-free period) to the treatment. The 'response distribution' is assumed continuous but not the same (new edit) across all three groups (the new edit is a result of my plotting of a putative response distribution for these three groups. as the medians for group 2 and 3 are close, 5.7 v 5.2, but the differences between the median and the upper/lower end of CI are different - group 2: [5.7-5.3],[7.6-5.7]; group 3: [5.2-3.6],[5.5-5.2], I assumed the response distribution for group 2 is right-skewed and that for group 3 is left-skewed). The response distribution for group 1 is left-skewed)

Now more people were enrolled into the three groups without changing significantly the ratio (40:82:70). The total number of individuals is now 1920. Assuming the larger group (of 1920 individuals) has the same/similar distribution of their responses to the treatment as those of the smaller group (of 192 individuals).

Does the 95% CI range of disease free period change due to an increase of the sample size? If yes, is it possible to estimate the 95% CI range of disease free periods for the three groups ?

Any insight to share will be greatly appreciated.

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• It's pretty intelligible, thank you. Re your last question about estimating the likely CIs for the larger group: providing some information about how the CIs are calculated could help people formulate more refined answers. – whuber May 30 '17 at 18:57
• thanks for the quick response. not sure what specific information can help people formulate more refined answers. Any pointer ? – B Chen May 30 '17 at 19:17
• Yes: tell us either the model or the method. Seeing the parenthetical "what kind?" in your edit was quite a surprise, because it suggests a lack of familiarity with the situation. Has someone simply given you some statistics without any further explanation? If so, that's ok--we'll do our best--but it would be better to know how the CIs were computed. – whuber May 30 '17 at 19:21
• Thank you, but unfortunately I have no further info as of now. Based on what I have provided, is it "impossible" to estimate a new 95% CI for the disease-free range? – B Chen May 30 '17 at 19:51
• No, it's not impossible--but we cannot be as precise about it as we might hope. We can only state that for "standard" confidence interval methods, we would expect the widths of the intervals based on ten times as much data to be around $1/\sqrt{10}$ times the widths of the original ones. A subtle issue is that we cannot make any improved statements about where the new intervals might be centered: to do so would be to anticipate that the new data will yield exactly the same estimates as the original data, which we know will not be the case. – whuber May 30 '17 at 19:57

## 2 Answers

No, the sample size doesn't change your interval but what exactly are you measuring? What question are you trying to answer?

Also, your data may be skewed because of the small sample size plus a large and small value. You would assume it's normal for the population, not the sample.