Physics Use
A dependent t test is useful when the same physics item is measured twice. It may compare a sensor before and after calibration. It may compare paired readings from two instruments. Because the readings are paired, each item becomes its own control.
Planning Inputs
This calculator focuses on the difference score. First, estimate the mean paired difference you want to detect. Then estimate the standard deviation of the paired differences. A smaller spread needs fewer pairs. A larger spread needs more pairs. Strong paired correlation also reduces the difference spread when pre and post standard deviations are entered.
Power and Alpha
Power is the chance of detecting the planned effect. Higher power gives more dependable planning. It also increases sample needs. Alpha controls the false alarm risk. A two tailed test is safer when change could matter in either direction. A one tailed test is used only when the direction is justified before data collection.
Lab Reality
Physics experiments often face repeated trials, missing runs, noisy instruments, or unusable observations. The dropout field inflates the calculated number of pairs. This helps protect the final analysis. Use conservative inputs when the lab environment is uncertain. Good planning is cheaper than repeating a full experiment.
Effect Size
Effect size is shown as Cohen dz. It equals the expected mean difference divided by the standard deviation of the paired differences. The calculator can accept dz directly. It can also compute dz from a target difference and paired difference standard deviation. Another option derives the paired difference deviation from pre and post deviations and their correlation.
Formula Scope
The formula uses a normal approximation for the paired t test. It is best for planning and screening. Very small studies may need a specialist power package for exact noncentral t results. Still, the estimate is practical for many lab designs. Record every assumption with the study plan. Review pilot data whenever possible.
Final Guidance
Use the result as a planning guide, not a guarantee. Real data may show different spread, weaker correlation, or larger loss. Update the estimate after pilot measurements. Keep units consistent across every field. When assumptions are honest, the planned paired design becomes clearer, faster, and easier to defend well.