`powerTOSTpaired.Rd`

Power analysis for TOST for dependent t-test (Cohen's dz). This function is no longer maintained please use power_t_TOST.

```
powerTOSTpaired(alpha, statistical_power, N, low_eqbound_dz, high_eqbound_dz)
powerTOSTpaired.raw(
alpha,
statistical_power,
low_eqbound,
high_eqbound,
sdif,
N
)
```

- alpha
alpha used for the test (e.g., 0.05)

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

- N
number of pairs (e.g., 96)

- low_eqbound_dz
lower equivalence bounds (e.g., -0.5) expressed in standardized mean difference (Cohen's dz)

- high_eqbound_dz
upper equivalence bounds (e.g., 0.5) expressed in standardized mean difference (Cohen's dz)

- low_eqbound
lower equivalence bounds (e.g., -0.5) expressed in raw mean difference

- high_eqbound
upper equivalence bounds (e.g., 0.5) expressed in raw mean difference

- sdif
standard deviation of the difference scores

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.

Chow, S.-C., Wang, H., & Shao, J. (2007). Sample Size Calculations in Clinical Research, Second Edition - CRC Press Book. Formula 3.1.9

```
## Sample size for alpha = 0.05, 80% power, equivalence bounds of
## Cohen's dz = -0.3 and Cohen's d = 0.3, and assuming true effect = 0
powerTOSTpaired(alpha=0.05,statistical_power=0.8,low_eqbound_dz=-0.3,high_eqbound_dz=0.3)
#> The required sample size to achieve 80 % power with equivalence bounds of -0.3 and 0.3 is 96 pairs
#>
#> [1] 95.15386
## Sample size for alpha = 0.05, N = 96 pairs, equivalence bounds of
## Cohen's dz = -0.3 and Cohen's d = 0.3, and assuming true effect = 0
powerTOSTpaired(alpha=0.05,N=96,low_eqbound_dz=-0.3,high_eqbound_dz=0.3)
#> The statistical power is 80.45 % for equivalence bounds of -0.3 and 0.3 .
#>
#> [1] 0.8045235
## Equivalence bounds for alpha = 0.05, N = 96 pairs, statistical power of
## 0.8, and assuming true effect = 0
powerTOSTpaired(alpha=0.05,N=96,statistical_power=0.8)
#> The equivalence bounds to achieve 80 % power with N = 96 are -0.3 and 0.3 .
#>
#> [1] -0.298675 0.298675
## Sample size for alpha = 0.05, 80% power, equivalence bounds of -3 and 3 in raw units
## and assuming a standard deviation of the difference scores of 10, and assuming a true effect = 0
powerTOSTpaired.raw(alpha=0.05,statistical_power=0.8,low_eqbound=-3, high_eqbound=3, sdif=10)
#> The required sample size to achieve 80 % power with equivalence bounds of -3 and 3 is 96 pairs
#>
#> [1] 95.15386
## Sample size for alpha = 0.05, N = 96 pairs, equivalence bounds of -3 and 3 in raw units
## and assuming a standard deviation of the difference scores of 10, and assuming a true effect = 0
powerTOSTpaired.raw(alpha=0.05,N=96,low_eqbound=-3, high_eqbound=3, sdif=10)
#> The statistical power is 80.45 % for equivalence bounds of -3 and 3 .
#>
#> [1] 0.8045235
## Equivalence bounds for alpha = 0.05, N = 96 pairs, statistical power of 0.8
## and assuming a standard deviation of the difference scores of 10, and assuming a true effect = 0
```