One-Sample T-Test Calculator
The one-sample t-test calculator lets you quickly compute the t-statistic and determine whether the difference between the sample mean and the hypothesized value is statistically significant. Just enter the mean, standard deviation, and sample size.
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How to Use the Calculator
Enter the sample mean, expected value (null hypothesis), standard deviation, and sample size. The calculator automatically computes the t-statistic, degrees of freedom, and displays a significance interpretation.
T-Test Calculation Example
Suppose the sample mean is 5.2, the expected value is 5.0, the standard deviation is 0.5, and n=30. T-statistic = (5.2−5.0)/(0.5/√30) ≈ 2.191. Since |t|>1.96 the result is significant at α=0.05.
Frequently Asked Questions
What is the Student's t-test?
The t-test is a parametric statistical test used to determine whether the sample mean differs significantly from an expected value. It was developed by William Sealy Gosset under the pseudonym "Student".
When should I use a one-sample t-test?
Use it when you want to compare the mean of a single sample against a known or hypothesized population mean. The test assumes normality or a sufficiently large sample (n≥30).
What does the t-statistic measure?
The t-statistic measures how many standard errors the observed mean is away from the expected value. A larger absolute t indicates a stronger departure from the null hypothesis.
What are degrees of freedom?
Degrees of freedom (df=n−1) define the shape of the t-distribution used to assess significance. More degrees of freedom bring the t-distribution closer to the normal distribution.
What does "significant at 0.05 level" mean?
It means that the probability of observing such an extreme t-statistic, assuming H₀ is true, is less than 5%. We reject the null hypothesis.
What is the difference between 0.01 and 0.05 significance levels?
The 0.01 level is more stringent and requires a stronger effect. The 0.05 level is the standard threshold in most scientific research.
What is the minimum recommended sample size?
At least 30 observations are recommended. With smaller samples, the data should be approximately normally distributed.
Is the t-test sensitive to outliers?
Yes — outliers can distort the mean and standard deviation. Check your data before testing and consider non-parametric alternatives if extreme values are present.
What are the assumptions of the t-test?
Random sampling, independent observations, and normality of the variable (or n≥30). Violating these assumptions reduces the reliability of results.
Does the calculator provide the p-value?
The calculator provides an interpretation based on critical thresholds (1.96 and 2.576). For the exact p-value, consult t-distribution tables or statistical software.
Results are indicative only and do not constitute statistical or scientific advice. Consult a statistician before making research decisions.