One Sample T-Test Calculator
A one sample t-test calculator determines whether the mean of a single sample differs significantly from a known or hypothesized population mean. Researchers use it in hypothesis testing to assess statistical significance in fields like psychology, medicine, and market research.
Result:
T-Value:
Interpretation:
FAQs
What is a one sample t-test calculator?
A one sample t-test calculator is a statistical tool that compares a sample mean to a known population mean. It calculates the t-value and helps determine if observed differences are statistically significant, using sample size and standard deviation for calculations.
When should I use this calculator?
Use when you have one sample group and want to compare its mean to a population mean. Ideal for quality control, clinical trials, or any research comparing measured data to a standard value with unknown population variance.
What's the formula used?
The formula is t = (x̄ - μ)/(s/√n) where x̄=sample mean, μ=population mean, s=sample standard deviation, n=sample size. The calculator uses this to determine how many standard errors the sample mean is from population mean.
How to interpret results?
Compare calculated t-value with critical t-value from tables. If absolute t-value exceeds critical value, reject null hypothesis. Higher t-values indicate greater difference between sample and population means.
What's a good sample size?
Typically ≥30 for reliable results. Smaller samples increase Type II error risk. However, proper sample size depends on effect size and variability. Use power analysis to determine optimal size.
Can I use it for small samples?
Yes, the t-test is specifically designed for small samples (n <30) where population standard deviation is unknown. It uses t-distribution which accounts for sample size through degrees of freedom.
Difference between z-test and t-test?
Use z-test when population variance is known and sample size >30. Use t-test when population variance is unknown or small sample size. T-test uses t-distribution, z-test uses normal distribution.
What confidence levels are used?
Common confidence levels are 90%, 95%, and 99% (α=0.10, 0.05, 0.01). The calculator doesn't set confidence level but provides t-value for comparison with critical values at your chosen significance level.
How accurate is this calculator?
Accuracy depends on correct input values and meeting test assumptions (normal distribution, independent observations, continuous data). It performs exact calculations but always verify assumptions first.
Can I save results?
This calculator doesn't save results. Copy values manually or screenshot. For repeated use, consider spreadsheet integration or statistical software like SPSS/R for advanced analysis and data storage.