# powerLong: Power calculation for longitudinal study with 2 time point In powerMediation: Power/Sample Size Calculation for Mediation Analysis

## Description

Power calculation for testing if mean changes for 2 groups are the same or not for longitudinal study with 2 time point.

## Usage

 1 2 3 4 powerLong(es, n, rho = 0.5, alpha = 0.05) 

## Arguments

 es effect size of the difference of mean change. n sample size per group. rho correlation coefficient between baseline and follow-up values within a treatment group. alpha Type I error rate.

## Details

The power formula is based on Equation 8.31 on page 336 of Rosner (2006).

power=Φ≤ft(-Z_{1-α/2}+\frac{δ√{n}}{σ_d √{2}}\right)

where σ_d = σ_1^2+σ_2^2-2ρσ_1σ_2, δ=|μ_1 - μ_2|, μ_1 is the mean change over time t in group 1, μ_2 is the mean change over time t in group 2, σ_1^2 is the variance of baseline values within a treatment group, σ_2^2 is the variance of follow-up values within a treatment group, ρ is the correlation coefficient between baseline and follow-up values within a treatment group, and Z_u is the u-th percentile of the standard normal distribution.

We wish to test μ_1 = μ_2.

When σ_1=σ_2=σ, then formula reduces to

power=Φ≤ft(-Z_{1-α/2} + \frac{|d|√{n}}{2√{1-ρ}}\right)

where d=δ/σ.

## Value

power for testing for difference of mean changes.

## Note

The test is a two-sided test. For one-sided tests, please double the significance level. For example, you can set alpha=0.10 to obtain one-sided test at 5% significance level.

## Author(s)

Weiliang Qiu stwxq@channing.harvard.edu

## References

Rosner, B. Fundamentals of Biostatistics. Sixth edition. Thomson Brooks/Cole. 2006.

ssLong, ssLongFull, powerLongFull.
 1 2 3  # Example 8.34 on page 336 of Rosner (2006) # power=0.75 powerLong(es=5/15, n=75, rho=0.7, alpha=0.05)