Calculator Inputs
Enter raw data, or leave raw data blank and use summary statistics.
Example Data Table
| Scenario | Input Type | Values | Confidence | Use |
|---|---|---|---|---|
| One sample | Raw data | 12, 14, 15, 16, 18 | 95% | Estimate one population mean |
| Paired sample | Two matched lists | Before and after readings | 95% | Estimate mean paired change |
| Welch two sample | Summary statistics | n, mean, and standard deviation | 99% | Compare unequal variance groups |
Formula Used
One Sample and Paired Sample
Confidence interval = estimate ± t critical × standard error
Standard error = sample standard deviation / √n
Degrees of freedom = n - 1
Independent Samples
Estimate = mean one - mean two
Welch SE = √((s1² / n1) + (s2² / n2))
Pooled SE = √(sp² × (1 / n1 + 1 / n2))
t statistic = (estimate - hypothesized value) / standard error
How to Use This Calculator
- Select the correct test type.
- Choose the confidence level.
- Enter the hypothesized value, usually zero.
- Paste raw values, or enter summary statistics.
- Choose Welch or pooled variance for independent samples.
- Press the calculate button.
- Review the interval, t statistic, p value, and graph.
- Export the results as CSV or PDF.
Statistics Guide
What This Interval Means
A t test confidence interval estimates a likely range for a true mean or mean difference. It is useful when the population standard deviation is unknown. That is common in practical statistics. The interval combines the sample estimate, standard error, degrees of freedom, and a t critical value.
Supported Test Types
This calculator supports one sample, paired sample, and independent sample work. You can enter raw values or summary statistics. Raw values are best when you want the tool to compute the mean and sample standard deviation. Summary fields are useful when your report already gives n, mean, and standard deviation.
Confidence Level
The confidence level controls the width of the interval. A 95% interval is a common default. A higher confidence level gives a wider interval. A lower level gives a narrower interval. The choice should match your study risk and reporting standard.
Choosing the Right Method
For one sample tests, the point estimate is the sample mean. For paired tests, the estimate is the mean of the paired differences. For independent tests, the estimate is the difference between two sample means. Welch output is preferred when variances may differ. The pooled option is suitable when equal variance is reasonable.
Interpreting the Test
The t statistic compares the estimate with a hypothesized value. The p value measures how unusual the observed result is under that hypothesis. The confidence interval gives a practical range. Both views help interpretation. A result can be statistically significant yet still have a small practical effect.
Using the Chart and Exports
Use the chart to see the point estimate, the null value, and the confidence limits. A wide interval means more uncertainty. A narrow interval means the estimate is more precise. Larger samples and smaller variation usually produce tighter intervals.
Good Practice
Exports make reporting easier. The CSV file stores the main numerical results. The PDF button saves a clean summary for notes or client reports. Always check assumptions before relying on results. Values should be independent for independent tests. Paired tests need matched observations. Severe outliers can distort the mean. In such cases, review a plot or consider a robust method.
Data Quality
Keep units consistent across entries. Record the context for each sample. This makes later review easier and reduces reporting mistakes greatly overall.
FAQs
1. What is a t test confidence interval?
It is a calculated range for a true mean or mean difference. It uses sample data, standard error, degrees of freedom, and a t critical value.
2. When should I use a one sample t interval?
Use it when you have one sample and want to estimate the population mean. It is useful when the population standard deviation is unknown.
3. When should I use a paired t interval?
Use it when observations are matched. Common examples include before and after results, repeated measures, or two readings from the same subject.
4. What is the Welch option?
Welch is used for two independent samples when variances may not be equal. It adjusts the degrees of freedom for safer comparison.
5. What is the pooled option?
The pooled option assumes both independent groups have equal population variance. Use it only when that assumption is reasonable for your data.
6. Why is my confidence interval wide?
A wide interval often means high variation, small sample size, or high confidence level. More consistent data usually gives a narrower interval.
7. What does the p value show?
The p value shows how unusual your result is under the null hypothesis. Smaller values give stronger evidence against the null value.
8. Can I use summary statistics?
Yes. Leave raw data blank and enter sample size, mean, and standard deviation. For two samples, complete both summary sections.