Power Analysis T Test Calculator

Example Data Table

Formula Used

This calculator uses a normal approximation to t test power. For a two sample design, the noncentral signal is estimated as: delta = d / sqrt(1 / n1 + 1 / n2). For one sample and paired designs, it uses delta = d × sqrt(n).

For a two tailed test, the critical value is z(1 - alpha / 2). Power is estimated as P(Z > critical - delta) + P(Z < -critical - delta). For a one tailed greater test, power is P(Z > critical - delta). For a one tailed less test, power is P(Z < -critical - delta).

Raw means are converted into Cohen d. One sample d uses (mean - null mean) / SD. Paired d uses the standard deviation of the paired difference. Two sample d uses pooled standard deviation.

How To Use This Calculator

1. Select the goal: power, sample size, or minimum detectable effect.
2. Choose the t test design that matches your study.
3. Enter Cohen d directly, or select raw means and standard deviations.
4. Enter alpha, target power, tails, direction, and sample sizes.
5. Use allocation ratio when planning unequal two group studies.
6. Add dropout percent when solving for sample size.
7. Press Calculate to show results above the form.
8. Use CSV or PDF buttons to save the result.

Power Analysis For T Tests

Why Power Matters

Power analysis helps you plan a study before collecting data. It estimates the chance of detecting a real effect. A study with low power may miss useful findings. A study with too many participants may waste time and budget. This calculator gives a practical planning estimate for common t test designs.

Study Designs Covered

You can plan one sample, paired sample, and two independent sample tests. A one sample test compares one mean with a known value. A paired test compares matched observations, such as before and after scores. A two sample test compares two independent groups. Each design uses a different standard error.

Effect Size Choices

The calculator accepts Cohen d directly. It can also estimate d from raw means and standard deviations. Direct d is useful when prior research gives a standardized effect. Raw inputs are useful when your planning assumptions are expressed in original units, such as points, seconds, dollars, or scores.

Alpha, Power, And Tails

Alpha is the false positive rate you are willing to accept. Many studies use 0.05. Power is the chance of rejecting the null when the assumed effect is real. Many researchers target 0.80 or 0.90. A two tailed test checks both directions. A one tailed test checks one planned direction only.

Sample Size Planning

The sample size option searches for the smallest group size that reaches your target power. For two group studies, the allocation ratio controls unequal group sizes. A ratio of 1 gives balanced groups. A ratio of 2 makes group two twice as large. Dropout adjustment inflates the final recruitment target.

Minimum Detectable Effect

The minimum detectable effect option answers another planning question. It shows the smallest standardized effect your current sample can detect at the selected alpha and power. This is useful when the sample size is fixed. It helps decide whether a study can detect an effect that matters in practice.

Important Limits

Results are approximate. They are intended for planning, screening, and educational use. Exact software may use noncentral t distributions and slightly different rounding. For final clinical, regulatory, or grant decisions, compare results with specialist software and document every assumption clearly.

FAQs