`power_twoprop.Rd`

```
powerTOSTtwo.prop(
alpha,
statistical_power,
prop1,
prop2,
N,
low_eqbound_prop,
high_eqbound_prop
)
power_twoprop(
p1,
p2,
n = NULL,
null = 0,
alpha = NULL,
power = NULL,
alternative = c("two.sided", "one.sided", "equivalence")
)
```

- alpha
a priori alpha-level (i.e., significance level).

- statistical_power
Deprecated. desired power (e.g., 0.8)

- prop1
Deprecated. expected proportion in group 1.

- prop2
Deprecated. expected proportion in group 2.

- N
Deprecated. sample size (e.g., 108)

- low_eqbound_prop
Deprecated. lower equivalence bounds (e.g., -0.05) expressed in proportion

- high_eqbound_prop
Deprecated. upper equivalence bounds (e.g., 0.05) expressed in proportion

- p1, p2
Proportions in each respective group.

- n
Sample size per group.

- null
the null hypothesis value.

- power
statistical power (1-beta).

- alternative
equivalence, one-sided, or two-sided test. Can be abbreviated.

Calculate either achieved power, equivalence bounds, or required N, assuming a true effect size of 0. Returns a string summarizing the power analysis, and a numeric variable for number of observations, equivalence bounds, or power.

Silva, G. T. da, Logan, B. R., & Klein, J. P. (2008). Methods for Equivalence and Noninferiority Testing. Biology of Blood and Marrow Transplantation: Journal of the American Society for Blood and Marrow Transplantation, 15(1 Suppl), 120-127. https://doi.org/10.1016/j.bbmt.2008.10.004

Julious, S. A. & Campell, M. J. (2012). Tutorial in biostatistics: sample sizes for parallel group clinical trials with binary data. Statistics in Medicine, 31:2904-2936.

Chow, S.-C., Wang, H., & Shao, J. (2007). Sample Size Calculations in Clinical Research, Second Edition (2 edition). Boca Raton: Chapman and Hall/CRC.

```
## Sample size for alpha = 0.05, 90% power, assuming true effect prop1 = prop 2 = 0.5,
## equivalence bounds of 0.4 and 0.6 (so low_eqbound_prop = -0.1 and high_eqbound_prop = 0.1)
#powerTOSTtwo.prop(alpha = 0.05, statistical_power = 0.9, prop1 = 0.5, prop2 = 0.5,
# low_eqbound_prop = -0.1, high_eqbound_prop = 0.1)
power_twoprop(alpha = 0.05, power = 0.9, p1 = 0.5, p2 = 0.5,
null = 0.1, alternative = "e")
#>
#> Power for Test of Differences in Two Proportions (z-test)
#>
#> n = 541.1074
#> proportions = 0.5, 0.5
#> alpha = 0.05
#> beta = 0.1
#> power = 0.9
#> null = 0.1, -0.1
#> alternative = equivalence
#> NOTE = Sample sizes for EACH group
#>
## Power for alpha = 0.05, N 542 , assuming true effect prop1 = prop 2 = 0.5,
## equivalence bounds of 0.4 and 0.6 (so low_eqbound_prop = -0.1 and high_eqbound_prop = 0.1)
#powerTOSTtwo.prop(alpha = 0.05, N = 542, prop1 = 0.5, prop2 = 0.5,
# low_eqbound_prop = -0.1, high_eqbound_prop = 0.1)
power_twoprop(alpha = 0.05, n = 542, p1 = 0.5, p2 = 0.5,
null = 0.1, alternative = "e")
#>
#> Power for Test of Differences in Two Proportions (z-test)
#>
#> n = 542
#> proportions = 0.5, 0.5
#> alpha = 0.05
#> beta = 0.09944181
#> power = 0.9005582
#> null = 0.1, -0.1
#> alternative = equivalence
#> NOTE = Sample sizes for EACH group
#>
#Example 4.2.4 from Chow, Wang, & Shao (2007, p. 93)
#powerTOSTtwo.prop(alpha=0.05, statistical_power=0.8, prop1 = 0.75, prop2 = 0.8,
# low_eqbound_prop = -0.2, high_eqbound_prop = 0.2)
power_twoprop(alpha = 0.05, power = 0.8, p1 = 0.75, p2 = 0.8,
null = 0.2, alternative = "e")
#>
#> Power for Test of Differences in Two Proportions (z-test)
#>
#> n = 132.2626
#> proportions = 0.75, 0.80
#> alpha = 0.05
#> beta = 0.2
#> power = 0.8
#> null = 0.2, -0.2
#> alternative = equivalence
#> NOTE = Sample sizes for EACH group
#>
# Example 5 from Julious & Campbell (2012, p. 2932)
#powerTOSTtwo.prop(alpha=0.025, statistical_power=0.9, prop1 = 0.8, prop2 = 0.8,
# low_eqbound_prop=-0.1, high_eqbound_prop=0.1)
power_twoprop(alpha = 0.025, power = 0.9, p1 = 0.8, p2 = 0.8,
null = 0.1, alternative = "e")
#>
#> Power for Test of Differences in Two Proportions (z-test)
#>
#> n = 415.8307
#> proportions = 0.8, 0.8
#> alpha = 0.025
#> beta = 0.1
#> power = 0.9
#> null = 0.1, -0.1
#> alternative = equivalence
#> NOTE = Sample sizes for EACH group
#>
# From Machin, D. (Ed.). (2008). Sample size tables for clinical studies (3rd ed).
# Example 9.4b equivalence of two proportions (p. 113) #
# powerTOSTtwo.prop(alpha=0.010, statistical_power=0.8, prop1 = 0.5, prop2 = 0.5,
# low_eqbound_prop = -0.2, high_eqbound_prop = 0.2)/2
power_twoprop(alpha = 0.01, power = 0.8, p1 = 0.5, p2 = 0.5,
null = 0.2, alternative = "e")
#>
#> Power for Test of Differences in Two Proportions (z-test)
#>
#> n = 162.7117
#> proportions = 0.5, 0.5
#> alpha = 0.01
#> beta = 0.2
#> power = 0.8
#> null = 0.2, -0.2
#> alternative = equivalence
#> NOTE = Sample sizes for EACH group
#>
```