One-Sample T-Test Effect Size Calculator

Understanding One-Sample T-Test Effect Size

Statistical significance demonstrates whether an observed effect exists, but effect size measures its magnitude. When performing a one-sample t-test, researchers often calculate Cohen's d to quantify how much the sample mean deviates from the hypothesized population mean in terms of standard deviation units. This metric bridges the gap between raw statistical outcomes and practical significance, ensuring that findings carry real-world weight.

Our advanced calculator supports multiple input methods, including raw data values, direct summary statistics, and existing t-statistics. It computes Cohen's d alongside Hedges' g for bias correction in smaller sample sizes. Analysts can easily customize confidence interval levels and alternative hypotheses to align with rigorous reporting standards across psychology, medicine, and social sciences.

Formula Used

The fundamental formula for Cohen's d in a one-sample context is defined as:

$$d = \frac{\bar{x} - \mu_0}{s}$$

Where $\bar{x}$ represents the sample mean, $\mu_0$ is the hypothesized population mean, and $s$ denotes the sample standard deviation. For small sample size adjustments, Hedges' g applies a correction factor $J(df)$: $$g \approx d \times \left(1 - \frac{3}{4n - 9}\right)$$

How to Use This Calculator

• Select your preferred input format under the input configuration options.
• Enter your specific sample statistics or raw comma-separated dataset values.
• Adjust variance parameters, confidence interval levels, and alternative hypothesis settings.
• Click the calculate button to review comprehensive metrics immediately displayed above the form.

Frequently Asked Questions