# powerLong.multiTime: Power calculation for testing if mean changes for 2 groups... 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 more than 2 time points.

## Usage

 1 powerLong.multiTime(es, m, nn, sx2, rho = 0.5, alpha = 0.05) 

## Arguments

 es effect size m number of subjects nn number of observations per subject sx2 within subject variance rho within subject correlation alpha type I error rate

## Details

We are interested in comparing the slopes of the 2 groups A and B:

β_{1A} = β_{1B}

where

Y_{ijA}=β_{0A}+β_{1A} x_{jA} + ε_{ijA}, j=1, …, nn; i=1, …, m

and

Y_{ijB}=β_{0B}+β_{1B} x_{jB} + ε_{ijB}, j=1, …, nn; i=1, …, m

The power calculation formula is (Equation on page 30 of Diggle et al. (1994)):

power=Φ≤ft[ -z_{1-α} + √{\frac{m nn s_x^2 es^2}{2(1-ρ)}} \right]

where es=d/σ, d is the meaninful differnce of interest, sigma^2 is the variance of the random error, ρ is the within-subject correlation, and s_x^2 is the within-subject variance.

power

## 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

Diggle PJ, Liang KY, and Zeger SL (1994). Analysis of Longitundinal Data. page 30. Clarendon Press, Oxford

ssLong.multiTime
 1 2  # power=0.8 powerLong.multiTime(es=0.5/10, m=196, nn=3, sx2=4.22, rho = 0.5, alpha = 0.05)