| Title: | Power and Sample Size Analysis for One-way and Two-way ANOVA Models |
|---|---|
| Description: | User friendly functions for power and sample size analysis at one-way and two-way ANOVA settings take either effect size or delta and sigma as arguments. They are designed for both one-way and two-way ANOVA settings. In addition, a function for plotting power curves is available for power comparison, which can be easily visualized by statisticians and clinical researchers. |
| Authors: | Pengcheng Lu, Junhao Liu, Devin Koestler |
| Maintainer: | Pengcheng Lu <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0 |
| Built: | 2024-12-16 06:50:50 UTC |
| Source: | CRAN |
User friendly functions for power and sample size analysis at one-way and two-way ANOVA settings take either effect size or delta and sigma as arguments. They are designed for both one-way and two-way ANOVA settings. In addition, a function for plotting power curves is available for power comparison, which can be easily visualized by statisticians and clinical researchers.
| Package: | SPA |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2017-05-01 |
| License: | GPL-2 |
There are major five functions in the package. The pwr.1way and pwr.2way functions provide the power analysis for one-way and two-way ANOVA models. The ss.1way and ss.2way functions provide the sample size calculation for one-way and two-way ANOVA models. The pwr.plot function illustrates drawing power curves for different parameter settings.
Pengcheng Lu, Junhao Liu, and Devin Koestler.
Maintainer:Pengcheng Lu <[email protected]>
[1] Angela Dean & Daniel Voss (1999). Design and Analysis of Experiments. Springer.
## Example 1 pwr.2way(a=3, b=3, alpha=0.05, size.A=4, size.B=5, f.A=0.8, f.B=0.4) pwr.2way(a=3, b=3, alpha=0.05, size.A=4, size.B=5, delta.A=4, delta.B=2, sigma.A=2, sigma.B=2) ## Example 2 ss.2way(a=3, b=3, alpha=0.05, beta=0.1, delta.A=1, delta.B=2, sigma.A=2, sigma.B=2, B=100) ## Example 3 n <- seq(2, 30, by=4) f <- seq(0.1, 1.0, length.out=10) pwr.plot(n=n, k=5, f=f, alpha=0.05)## Example 1 pwr.2way(a=3, b=3, alpha=0.05, size.A=4, size.B=5, f.A=0.8, f.B=0.4) pwr.2way(a=3, b=3, alpha=0.05, size.A=4, size.B=5, delta.A=4, delta.B=2, sigma.A=2, sigma.B=2) ## Example 2 ss.2way(a=3, b=3, alpha=0.05, beta=0.1, delta.A=1, delta.B=2, sigma.A=2, sigma.B=2, B=100) ## Example 3 n <- seq(2, 30, by=4) f <- seq(0.1, 1.0, length.out=10) pwr.plot(n=n, k=5, f=f, alpha=0.05)
Calculate power for one-way ANOVA models.
pwr.1way(k=k, n=n, alpha=alpha, f=NULL, delta=delta, sigma=sigma)pwr.1way(k=k, n=n, alpha=alpha, f=NULL, delta=delta, sigma=sigma)
k |
Number of groups |
n |
Sample size per group |
f |
Effect size |
alpha |
Significant level (Type I error probability) |
delta |
The smallest difference among k groups |
sigma |
Standard deviation, i.e. square root of variance |
If effect size f is known, plug it in to the function; If delta and sigma are known instead of effect size, put NULL to f.
Object of class "power.htest", a list of the arguments (including the computed one) augmented with "method" and "note" elements.
Pengcheng Lu, Junhao Liu, and Devin Koestler.
Angela Dean & Daniel Voss (1999). Design and Analysis of Experiments. Springer.
## Example 1 pwr.1way(k=5, n=15, alpha=0.05, delta=1.5, sigma=1) pwr.1way(k=5, n=15, f=NULL, alpha=0.05, delta=1.5, sigma=1) ## Example 2 pwr.1way(k=5, n=15, f=0.4, alpha=0.05)## Example 1 pwr.1way(k=5, n=15, alpha=0.05, delta=1.5, sigma=1) pwr.1way(k=5, n=15, f=NULL, alpha=0.05, delta=1.5, sigma=1) ## Example 2 pwr.1way(k=5, n=15, f=0.4, alpha=0.05)
Calculate power for two-way ANOVA models.
pwr.2way(a=a, b=b, alpha=alpha, size.A=size.A, size.B=size.B, f.A=NULL, f.B=NULL, delta.A=NULL, delta.B=NULL, sigma.A=NULL, sigma.B=NULL)pwr.2way(a=a, b=b, alpha=alpha, size.A=size.A, size.B=size.B, f.A=NULL, f.B=NULL, delta.A=NULL, delta.B=NULL, sigma.A=NULL, sigma.B=NULL)
a |
Number of groups in Factor A |
b |
Number of groups in Factor B |
alpha |
Significant level (Type I error probability) |
size.A |
Sample size per group in Factor A |
size.B |
Sample size per group in Factor B |
f.A |
Effect size of Factor A |
f.B |
Effect size of Factor B |
delta.A |
The smallest difference among a groups in Factor A |
delta.B |
The smallest difference among b groups in Factor B |
sigma.A |
Standard deviation, i.e. square root of variance in Factor A |
sigma.B |
Standard deviation, i.e. square root of variance in Factor B |
If effect sizes f.A and f.B are known, plug them in to the function; If delta.A and sigma.A are known instead of f.A, put NULL to f.A. Similarly as delta.B and sigma.B.
Object of class "power.htest", a list of the arguments (including the computed one) augmented with "method" and "note" elements.
Pengcheng Lu, Junhao Liu, and Devin Koestler.
Angela Dean & Daniel Voss (1999). Design and Analysis of Experiments. Springer.
## Example 1 pwr.2way(a=3, b=3, alpha=0.05, size.A=4, size.B=5, f.A=0.8, f.B=0.4) ## Example 2 pwr.2way(a=3, b=3, alpha=0.05, size.A=4, size.B=5, delta.A=4, delta.B=2, sigma.A=2, sigma.B=2) pwr.2way(a=3, b=3, alpha=0.05, size.A=4, size.B=5, f.A=NULL, f.B=NULL, delta.A=4, delta.B=2, sigma.A=2, sigma.B=2)## Example 1 pwr.2way(a=3, b=3, alpha=0.05, size.A=4, size.B=5, f.A=0.8, f.B=0.4) ## Example 2 pwr.2way(a=3, b=3, alpha=0.05, size.A=4, size.B=5, delta.A=4, delta.B=2, sigma.A=2, sigma.B=2) pwr.2way(a=3, b=3, alpha=0.05, size.A=4, size.B=5, f.A=NULL, f.B=NULL, delta.A=4, delta.B=2, sigma.A=2, sigma.B=2)
Draw power curves for different parameter settings in balanced one-way ANOVA models.
pwr.plot(n=n, k=k, f=f, alpha=alpha)pwr.plot(n=n, k=k, f=f, alpha=alpha)
n |
Sample size per group |
k |
Number of groups |
f |
Effect size |
alpha |
Significant level (Type I error probability) |
This function demonstrates drawing power curves for different sample size and effect size settings. N and f can be either a single value or a sequence of values, but they cannot be single values simultaneously. The combination of them could be (a sequence of n, a sequence of f), (a sequence of n, a single f), or (a single n, a sequence of f).
Pengcheng Lu, Junhao Liu, and Devin Koestler.
Angela Dean & Daniel Voss (1999). Design and Analysis of Experiments. Springer.
## Example 1 n <- seq(2, 30, by=4) f <- 0.5 pwr.plot(n=n, k=5, f=f, alpha=0.05) ## Example 2 n <- 20 f <- seq(0.1, 1.0, length.out=10) pwr.plot(n=n, k=5, f=f, alpha=0.05) ## Example 3 n <- seq(2, 30, by=4) f <- seq(0.1, 1.0, length.out=10) pwr.plot(n=n, k=5, f=f, alpha=0.05)## Example 1 n <- seq(2, 30, by=4) f <- 0.5 pwr.plot(n=n, k=5, f=f, alpha=0.05) ## Example 2 n <- 20 f <- seq(0.1, 1.0, length.out=10) pwr.plot(n=n, k=5, f=f, alpha=0.05) ## Example 3 n <- seq(2, 30, by=4) f <- seq(0.1, 1.0, length.out=10) pwr.plot(n=n, k=5, f=f, alpha=0.05)
Calculate sample size for one-way ANOVA models.
ss.1way(k=k, alpha=alpha, beta=beta, f=NULL, delta=delta, sigma=sigma, B=B)ss.1way(k=k, alpha=alpha, beta=beta, f=NULL, delta=delta, sigma=sigma, B=B)
k |
Number of groups |
alpha |
Significant level (Type I error probability) |
beta |
Type II error probability (Power=1-beta) |
f |
Effect size |
delta |
The smallest difference among k group |
sigma |
Standard deviation, i.e. square root of variance |
B |
Iteration times, default number is 100 |
Beta is the type II error probability which equals 1-power. For example, if the target power is 85% (=0.85), the corresponding beta equals 0.15. If effect size f is known, plug it in to the function; If delta and sigma are known instead of effect size, put NULL to f, or just miss f argument.
Object of class "power.htest", a list of the arguments (including the computed one) augmented with "method" and "note" elements.
Pengcheng Lu, Junhao Liu, and Devin Koestler.
Angela Dean & Daniel Voss (1999). Design and Analysis of Experiments. Springer.
## Example 1 ss.1way(k=5, alpha=0.05, beta=0.1, f=1.5, B=100) ## Example 2 ss.1way(k=5, alpha=0.05, beta=0.1, delta=1.5, sigma=1, B=100) ss.1way(k=5, alpha=0.05, beta=0.1, f=NULL, delta=1.5, sigma=1, B=100)## Example 1 ss.1way(k=5, alpha=0.05, beta=0.1, f=1.5, B=100) ## Example 2 ss.1way(k=5, alpha=0.05, beta=0.1, delta=1.5, sigma=1, B=100) ss.1way(k=5, alpha=0.05, beta=0.1, f=NULL, delta=1.5, sigma=1, B=100)
Calculate sample size for two-way ANOVA models.
ss.2way(a=a, b=b, alpha=alpha, beta=beta, f.A=NULL, f.B=NULL, delta.A=NULL, delta.B=NULL, sigma.A=NULL, sigma.B=NULL, B=B)ss.2way(a=a, b=b, alpha=alpha, beta=beta, f.A=NULL, f.B=NULL, delta.A=NULL, delta.B=NULL, sigma.A=NULL, sigma.B=NULL, B=B)
a |
Number of groups in Factor A |
b |
Number of groups in Factor B |
alpha |
Significant level (Type I error probability) |
beta |
Type II error probability (Power=1-beta) |
f.A |
Effect size of Factor A |
f.B |
Effect size of Factor B |
delta.A |
The smallest difference among a groups in Factor A |
delta.B |
The smallest difference among b groups in Factor B |
sigma.A |
Standard deviation, i.e. square root of variance in Factor A |
sigma.B |
Standard deviation, i.e. square root of variance in Factor B |
B |
Iteration times, default number is 100 |
Beta is the type II error probability which equals 1-power. For example, if the target power is 85% (=0.85), the corresponding beta equals 0.15. If effect size f is known, plug it in to the function; If delta and sigma are known instead of effect size, put NULL to f.
Object of class "power.htest", a list of the arguments (including the computed one) augmented with "method" and "note" elements.
Pengcheng Lu, Junhao Liu, and Devin Koestler.
Angela Dean & Daniel Voss (1999). Design and Analysis of Experiments. Springer.
## Example 1 ss.2way(a=3, b=3, alpha=0.05, beta=0.1, f.A=0.4, f.B=0.2, B=100) ss.2way(a=3, b=3, alpha=0.05, beta=0.1, f.A=0.4, f.B=0.2, delta.A=NULL, delta.B=NULL, sigma.A=NULL, sigma.B=NULL, B=100) ## Example 2 ss.2way(a=3, b=3, alpha=0.05, beta=0.1, delta.A=1, delta.B=2, sigma.A=2, sigma.B=2, B=100)## Example 1 ss.2way(a=3, b=3, alpha=0.05, beta=0.1, f.A=0.4, f.B=0.2, B=100) ss.2way(a=3, b=3, alpha=0.05, beta=0.1, f.A=0.4, f.B=0.2, delta.A=NULL, delta.B=NULL, sigma.A=NULL, sigma.B=NULL, B=100) ## Example 2 ss.2way(a=3, b=3, alpha=0.05, beta=0.1, delta.A=1, delta.B=2, sigma.A=2, sigma.B=2, B=100)