ss.power.pcm | R Documentation |

Returns power given the sample size, or sample size given the desired power, for polynomial change models (currently only linear, that is, straight-line, change models)

```
ss.power.pcm(beta, tau, level.1.variance, frequency, duration, desired.power = NULL,
N = NULL, alpha.level = 0.05, standardized = TRUE, directional = FALSE)
```

`beta` |
the level two regression coefficient for the group by time (linear) interaction; where "X" is coded -.5 and .5 for the two groups. |

`tau` |
the true variance of the individuals' slopes |

`level.1.variance` |
level one variance |

`frequency` |
frequency of measurements per unit of time duration of the study in the particular units (e.g., age, hours, grade level, years, etc.) |

`duration` |
time in some number of units (e.g., years) |

`desired.power` |
desired power |

`N` |
total sample size (one-half in each of the two groups) |

`alpha.level` |
Type I error rate |

`standardized` |
the standardized slope is the unstandardized slope divided by the square root of tau, the variance of the unique effects for beta. |

`directional` |
should a one ( |

Ken Kelley (University of Notre Dame; KKelley@ND.Edu)

Raudenbush, S. W., & X-F., Liu. (2001). Effects of study duration, frequency of observation,
and sample size on power in studies of group differences in polynomial change. *Psychological Methods, 6*, 387–401.

```
# Example from Raudenbush and Liu (2001)
ss.power.pcm(beta=-.4, tau=.003, level.1.variance=.0262, frequency=2, duration=2,
desired.power=.80, alpha.level=.05, standardized=TRUE, directional=FALSE)
ss.power.pcm(beta=-.4, tau=.003, level.1.variance=.0262, frequency=2, duration=2,
N=238, alpha.level=.05, standardized=TRUE, directional=FALSE)
# The standardized effect size is obtained as beta/sqrt(tau): -.4/sqrt(.003) = -.0219.
# ss.power.pcm(beta=-.0219, tau=.003, level.1.variance=.0262, frequency=2, duration=2,
# desired.power=.80, alpha.level=.05, standardized=FALSE, directional=FALSE)
ss.power.pcm(beta=-.0219, tau=.003, level.1.variance=.0262, frequency=2, duration=2,
N=238, alpha.level=.05, standardized=FALSE, directional=FALSE)
```

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