Understanding One Sample T Testing
A one sample t test checks whether one sample mean differs from a chosen population mean. It is useful when the population standard deviation is unknown. The test uses sample variation, so it fits small and moderate samples. This calculator accepts raw observations or summary statistics.
When To Use It
Use this test when values are numeric and come from one group. The observations should be independent. The population should be normal, especially for small samples. Larger samples are more forgiving. Common uses include quality checks, exam score comparisons, production targets, measurements, and finance benchmarks.
What The Result Means
The t statistic measures how far the sample mean sits from the hypothesized mean. It counts that distance in standard error units. A large positive value supports a greater mean. A large negative value supports a lower mean. A two tailed test checks for any difference in either direction.
P Value And Decision
The p value shows how unusual the sample result is, assuming the null mean is true. If the p value is at or below alpha, the result is statistically significant. Then the null hypothesis is rejected. If it is above alpha, the evidence is not strong enough. This does not prove equality. It only means the sample did not show enough evidence.
Confidence Interval
The confidence interval gives a likely range for the true population mean. If a two sided interval excludes the hypothesized mean, it usually matches a significant two tailed test at the related confidence level. Wider intervals show more uncertainty. Larger samples and lower variation make intervals narrower.
Advanced Outputs
Effect size helps judge practical importance. Cohen's d compares the mean difference with the sample standard deviation. Hedges' g adjusts that effect for small samples. The standard error shows sampling precision. The approximate observed power gives a rough sensitivity check. It should not replace a planned power study.
Good Data Practice
Review data before testing. Look for entry errors, extreme outliers, and mixed units. Keep raw values when possible. Summary inputs are helpful when only n, mean, and standard deviation are available. Always report the tail choice, alpha level, confidence level, t statistic, degrees of freedom, p value, and interpretation.