When to describe a confidence interval as narrow, and hence a large sample size or wide and hence a small sample size? Thanks
The higher confidence level you want the wider will the interval . For example, 99% confidence interval is wider than 95% confidence interval.
The CI is related to the sample size but to the natural distribution of the variable also. I would use the coeficient of variation (CV) if the variable contains only positive values. In general, CV < 30% is indicative of good model fit; CV between 30%-50% are usually quite wide and CV >50% translate too wide distributions.
The sample size has inverse relation with the margin of error. Confidence interval is= sample statistics plus/minus margin of error. Please clarify your question for more specific answer. Best wishes.
Heba
the confidence interval is calculated this way
CI=a*std_dev/SQRT(N)
where a depends if you want 95% (a=1.96) or 99% (a=2.56) level of confidence, std_dev the standard deviation of the sample and N is the sample size. When N is large CI is small or when the std_dev is small, then CI is small and vice versa.
Best regards
I want to second Heba's question. Are there any expert guidelines on this, similar to Cohen's categories for effect sizes? Thanks for any recommendations on this.
Heba's question is what I had in mind. I need expert judgment on when do we say the CI is wide or narrow.
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