🇺🇸 AP Statistics / US Research 🇬🇧 A-Level Statistics 🌐 IB Mathematics 🔬 Clinical Trials

Confidence Interval Calculator

Calculate confidence intervals for a population mean or proportion at 90%, 95%, or 99% confidence. Automatically switches to the t-distribution for small samples (n < 30).

Quick Answer
CI = x̄ ± z* × (s/√n). For n < 30: use t-distribution. 95% CI uses z* = 1.96 (or t* for small samples). Wider interval = more confident.
Country / Domain Standard Confidence Level Critical z* (95%) Context
🇺🇸 US academic research 95%1.96APA, AMA, federal statistics
🇬🇧 UK clinical research 95%1.96NICE, BMJ, NHS trials
🇩🇪 EU clinical trials 95% (99% for drugs)1.96 / 2.576EMA (European Medicines Agency)
🇦🇺 Australia 95%1.96NHMRC — same as US/UK standard
🌐 Epidemiology / WHO 95%1.96Global public health standard
🇯🇵 Japan (medical) 95%1.96PMDA — equivalent to FDA

Frequently Asked Questions

Why is 95% the standard confidence level in most research?

The 95% confidence level (α = 0.05) was established largely by Ronald Fisher in the 1920s as a pragmatic threshold. It became embedded in research practice globally through statistics textbooks and journal reporting standards. The American Psychological Association (APA), British Medical Journal (BMJ), and most international journals require reporting 95% CIs. Some fields (particle physics, drug safety) use 99% or even 99.9999% (5-sigma) due to the consequences of false positives.

How does clinical trial reporting differ between the US and EU?

US FDA: requires 95% CIs for efficacy endpoints, typically two-sided. EU EMA (European Medicines Agency): also uses 95% CIs, but may require 99% for safety data. Both require pre-registration of confidence level before the trial begins. NICE (UK) for health technology appraisals uses 95% CIs and incremental cost-effectiveness ratios (ICERs). The underlying mathematics is identical — only regulatory thresholds and reporting requirements differ.