Confidence Interval Calculator & Interpreter

Pro v1.0.0 1 view

Calculate and interpret confidence intervals for means, proportions, and group differences with visualizations and plain-language explanations for business decisions.

What You Get

Quantify uncertainty in estimates with confidence intervals and communicate findings to stakeholders clearly

The Problem

Point estimates like averages or conversion rates don't tell the full story. Stakeholders need to understand the range of plausible values and reliability of estimates. Without proper confidence intervals and interpretation, teams often misinterpret results or fail to account for uncertainty, leading to poor decisions.

The Solution

This skill transforms raw statistical calculations into actionable insights by calculating confidence intervals for means, proportions, and group differences using appropriate statistical methods. It automatically selects the right approach (t-distribution, z-distribution, Wilson score interval) based on your data and design (paired or independent groups), then generates professional matplotlib visualizations with error bars and confidence regions. Beyond calculations, the skill provides plain-language interpretations explaining what confidence intervals mean and what they don't mean, distinguishes between confidence intervals and prediction intervals, and addresses statistical significance testing with effect size calculations.

How It Works

1 Understand the request including type of estimate, confidence level, and audience
2 Validate data sufficiency and check statistical assumptions
3 Calculate appropriate confidence interval using scipy.stats with t-distribution, z-distribution, or Wilson score method
4 Generate professional visualizations with error bars and confidence regions
5 Provide stakeholder-ready interpretation with plain-language explanations
6 Address follow-up questions about statistical significance and practical implications

What You'll Need

Sample data or summary statistics (mean, standard deviation, sample size)
Type of estimate needed (single mean, proportion, or group difference)
Python with scipy, matplotlib, and numpy libraries
Optional: Desired confidence level (defaults to 95%)
Optional: Study design information (paired vs independent groups)

Get This Skill

Requires Pro subscription ($9/month)

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Examples

Checkout System Time Reduction Analysis

Comparing checkout times between old and new systems using Welch's t-test for difference in means. Shows 95% CI for time reduction with effect size (Cohen's d), statistical significance testing, and business impact calculations for deployment decision.

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Email Campaign Open Rate Analysis

Calculating a 95% confidence interval for email campaign open rate using Wilson score method. Demonstrates proportion CI with clear business interpretation comparing to industry benchmarks and actionable recommendations for optimization.

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Customer Support Resolution Time with 90% CI

Single mean confidence interval for customer support resolution times using t-distribution with small sample (n=28) and non-default 90% confidence level. Includes sample size planning guidance and SLA recommendations based on uncertainty estimates.

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