Summary Statistics Confidence Intervals
This calculator lets you compute confidence intervals directly from summary statistics — the mean, standard deviation, and sample size — rather than needing the original raw data. It is the right tool when:
- You are reading a published paper that reports group means and SDs but does not share the underlying data.
- You are running a meta-analysis from study-level summaries.
- You only have the summary you noted down and not the original observations.
Note: Because this test takes only a handful of summary numbers (mean, SD, n, or successes / total / correlation coefficient) rather than a full dataset, it does not include a built-in Sample Data Generator — you simply enter the numbers directly.
The calculator opens with a single header — Summary Statistics Confidence Intervals — and an introductory note:
"Calculate confidence intervals from summary statistics rather than raw data. Choose between single sample intervals or two sample intervals. Each option includes mean, proportion, and correlation calculations."
Below the description you choose one of two paths.
Step 1 — Choose Single Sample or Two Sample
Two large option cards are shown side by side:
| Card | What it does |
|---|---|
| Single Sample | "Calculate confidence intervals for population parameters from a single sample." Used when you have summary statistics from one group and want a CI for the population value |
| Two Sample | "Calculate confidence intervals for differences between two populations." Used when you have two groups and want a CI for the difference between them |
Each card shows the three parameters it can handle:
- Single Sample → Population Mean (μ), Population Proportion (p), Population Correlation (ρ)
- Two Sample → Difference in Means (μ₁ − μ₂), Difference in Proportions (p₁ − p₂), Difference in Correlations (ρ₁ − ρ₂)
Step 2 — Choose the parameter type
Once you pick Single or Two Sample, you see three large buttons titled Select Parameter Type:
For Single Sample:
| Parameter | What you need |
|---|---|
| Population Mean (μ) — "From sample mean and standard deviation" | Sample mean, standard deviation, sample size |
| Population Proportion (p) — "From number of successes and sample size" | Number of successes, total sample size |
| Population Correlation (ρ) — "From sample correlation coefficient" | Correlation coefficient r (range −0.999 to 0.999), sample size (minimum 4) |
For Two Sample:
| Parameter | What you need (for each of Group 1 and Group 2) |
|---|---|
| Difference in Means (μ₁ − μ₂) — "Compare two population means" | Mean, standard deviation, sample size |
| Difference in Proportions (p₁ − p₂) — "Compare two population proportions" | Number of successes, total sample size |
| Difference in Correlations (ρ₁ − ρ₂) — "Compare two population correlations" | Correlation coefficient, sample size |
Step 3 — Enter your numbers
After choosing a parameter type, the input form shows only the fields you need. Two Sample mode shows the same form twice (one Group 1 column, one Group 2 column).
Each field has placeholder examples to guide you (for example, "e.g., 25.4" for a mean, "e.g., 50" for sample size, "e.g., 0.65" for a correlation).
Below the data fields you also choose a Confidence Level, from a dropdown with three options:
- 90%
- 95% (default)
- 99%
Step 4 — Calculate
Click Calculate Confidence Interval. If anything is missing or invalid, an error message appears explaining what to fix. Common validation messages:
| Message | Cause |
|---|---|
| "Please enter valid positive numbers for all fields" | Some fields are blank, non-numeric, or zero/negative for SD or n |
| "Please enter valid numbers. Successes must be between 0 and total sample size" | Number of successes is negative, larger than the total, or non-numeric |
| "Correlation coefficient must be between -1 and 1 (exclusive)" | The correlation r is at or outside ±1 |
| "Sample size must be greater than 3" | Sample size for correlation is too small (Fisher z transformation requires n > 3) |
| "An error occurred during calculation" | Unexpected error — usually a typo in input |
Step 5 — Read the results
On success, the Results panel appears with three summary cards in a row:
| Card | What it shows |
|---|---|
| Estimate | Labelled depending on what you calculated — Sample Mean, Sample Proportion, Sample Correlation, Mean Difference, etc. — with the value to 4 decimal places (or as a percentage for proportions) |
| Margin of Error | The half-width of the interval (±value) |
| N% CI | The two-sided confidence interval, written as [lower, upper] |
For proportions, all values are displayed as percentages (e.g. 35.00%) rather than decimals.
Below the cards is an Interpretation paragraph generated in plain language. It tells you in words what the CI means and, for two-sample comparisons, whether the difference is statistically significant (i.e. whether the CI includes 0).
Example: "We are 95% confident that the true difference between the Fisher z-transformed correlations lies between −0.0521 and 0.1834. The observed correlation difference (r₁ − r₂) = 0.0612. The difference is not statistically significant (CI includes 0)."
Universal Chat Bot
Once you have results, a UniversalChatBot appears below the results — a chat interface where you can ask the AI to explain the output, discuss what the CI means in your context, or compare with what you would expect. The chatbot helps interpret the result — it does not change the calculation.