Understanding the One Sample T Test
A one sample t test checks one group mean. It compares the sample mean with a chosen population mean. The method is useful when the population standard deviation is unknown. That situation is common in research, quality control, learning analytics, and health studies.
Why This Calculator Helps
This calculator mirrors the logic used by R. You can paste raw values or enter summary statistics. It then reports the sample size, mean, standard deviation, standard error, degrees of freedom, t statistic, p value, confidence interval, and effect size. These outputs help you read the result before running code in R.
Role of the Hypothesized Mean
The hypothesized mean is the value tested by the null hypothesis. A value of zero is common in change scores. A target value is common in process testing. The test asks whether the sample evidence is strong enough to reject that value.
Choosing the Alternative
A two sided test checks for any difference. A greater test checks whether the sample mean is higher. A less test checks whether the sample mean is lower. Pick the direction before viewing results. This keeps the analysis fair and defensible.
Reading the P Value
The p value measures how unusual the observed t statistic is, assuming the null hypothesis is true. A small p value suggests the sample mean is not consistent with the hypothesized mean. Compare the p value with alpha. If it is smaller, reject the null hypothesis.
Confidence Intervals
The confidence interval estimates a reasonable range for the true mean. Wider intervals show less precision. Larger samples and lower variability usually create narrower intervals. For a two sided test, the interval gives both a lower and upper bound.
Effect Size
Cohen's d shows the difference in standard deviation units. Hedges' g adds a small sample correction. These values support practical interpretation. A result may be statistically significant but small in practical terms.
Using Results in Reports
Report the test direction, t statistic, degrees of freedom, p value, confidence interval, and mean difference. Add the R command when sharing reproducible work. Always explain the context. Numbers need a clear study question to be useful. Document assumptions and review outliers before final conclusions.