Formula Used
For a two group continuous outcome, the expected difference is:
Δ = |Mean B − Mean A|
The standard error is:
SE = SD × √(1 / nA + 1 / nB)
For one sample or paired outcomes, the standard error is:
SE = SD / √n
The planning statistic is:
Zeffect = Δ / SE
For a two sided test, approximate power is:
Power = 1 − Φ(Zα − Zeffect) + Φ(−Zα − Zeffect)
The required sample size uses:
n = ((Zα + Zpower) × SD / Δ)²
For two unequal groups, this value is adjusted by the allocation ratio.
How to Use This Calculator
- Select the study design that matches your continuous outcome.
- Enter the two expected means from pilot data or assumptions.
- Enter the standard deviation for the measured outcome.
- Add group sizes, alpha, tails, and target power.
- Use allocation ratio for unequal group planning.
- Add dropout inflation when samples may be lost.
- Press Submit to view power and sample results.
- Download CSV or PDF for your records.
Example Data Table
| Physics Use Case |
Mean A |
Mean B |
SD |
nA |
nB |
Alpha |
Target Power |
| Sensor power reading |
15.2 W |
17.1 W |
3.4 W |
40 |
40 |
0.05 |
0.80 |
| Thermal loss test |
22.5 J |
19.8 J |
4.1 J |
55 |
55 |
0.05 |
0.90 |
| Material stretch trial |
8.4 mm |
9.2 mm |
1.6 mm |
70 |
90 |
0.01 |
0.80 |
Power Planning for Continuous Outcomes
A continuous outcome is a measured value. It may be voltage, force, heat loss, particle size, or time. Power shows the chance of detecting a real mean difference. A high power value reduces missed effects. It does not prove an effect exists. It supports better experiment design before data collection starts.
Why Power Matters
Physics studies often compare average readings. A lab may compare two sensors, two materials, or two calibration methods. Small effects need larger samples. Noisy measurements also need larger samples. The calculator links these ideas with standard deviation, alpha, tails, and sample size. This makes planning clearer and more repeatable.
Inputs That Control Results
The expected difference is the gap between two means. Standard deviation describes natural spread. Alpha is the allowed false positive risk. A two sided test checks both increase and decrease. A one sided test checks only the planned direction. Allocation ratio lets one group be larger than another. Dropout inflation protects the planned sample size.
Interpreting the Output
Achieved power uses the current sample size. Required sample size uses the target power. Minimum detectable difference gives the smallest mean gap that the design can detect at the target power. Effect size divides the mean difference by the standard deviation. This helps compare studies that use different units.
Practical Notes
Use realistic pilot data when possible. Avoid guessing a very small standard deviation. That can make the study look stronger than it is. Use two sided tests when the effect could move either way. Raise target power when missing a real effect is costly. Review assumptions with the measurement method, not only with statistics. Good planning also needs stable instruments, clear protocols, and controlled conditions. The calculator gives a planning estimate. Final decisions should also consider physics limits, safety, cost, and replication needs.
Common Use Cases
Use this tool before running thermal tests, material trials, sensor comparisons, or timing studies. Enter values from pilot runs. Then compare power, sample size, and detectable difference. Adjust the design until it matches the goal. Save the result for reports and method sections. Repeat the calculation when assumptions change. Document choices carefully, because transparent assumptions make later review much easier for research teams.
FAQs
What is a continuous outcome?
It is a measurement that can take many numeric values. Examples include voltage, force, time, mass, heat, length, and pressure.
What does statistical power mean?
Power is the chance of detecting a real difference when that difference truly exists. Higher power lowers the chance of a missed effect.
Which standard deviation should I enter?
Use the expected standard deviation of the measured outcome. Pilot data, previous experiments, or validated references are better than guesses.
Should I use one sided or two sided testing?
Use two sided testing when the outcome may increase or decrease. Use one sided testing only when one direction is scientifically justified.
What is minimum detectable difference?
It is the smallest mean difference your design can detect at the chosen power, alpha, sample size, and standard deviation.
Why does larger variation lower power?
Large variation hides the mean difference inside measurement noise. More samples are then needed to separate signal from spread.
What does allocation ratio mean?
It is group B sample size divided by group A sample size. A value of 1 means both groups are equal.
Can this replace expert study design?
No. It gives a planning estimate. Review assumptions, measurement limits, safety needs, and experimental constraints before final decisions.