`powerTOSTone.Rd`

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 This function is no longer maintained please use power_t_TOST.

```
powerTOSTone(alpha, statistical_power, N, low_eqbound_d, high_eqbound_d)
powerTOSTone.raw(alpha, statistical_power, N, sd, low_eqbound, high_eqbound)
```

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

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

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

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

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

- sd
standard deviation.

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

- high_eqbound
upper equivalence bounds (e.g., 0.5) expressed in raw 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, 90% power, equivalence bounds of
## Cohen's d = -0.3 and Cohen's d = 0.3, and assuming true effect = 0
powerTOSTone(alpha=0.05, statistical_power=0.9, low_eqbound_d=-0.3, high_eqbound_d=0.3)
#> The required sample size to achieve 90 % power with equivalence bounds of -0.3 and 0.3 is 121
#>
#> [1] 120.2464
## Power for sample size of 121, alpha = 0.05, equivalence bounds of
## Cohen's d = -0.3 and Cohen's d = 0.3, and assuming true effect = 0
powerTOSTone(alpha=0.05, N=121, low_eqbound_d=-0.3, high_eqbound_d=0.3)
#> The statistical power is 90.21 % for equivalence bounds of -0.3 and 0.3 .
#>
#> [1] 0.902106
## Equivalence bounds for sample size of 121, alpha = 0.05, statistical power of
## 0.9, and assuming true effect d = 0
powerTOSTone(alpha=0.05, N=121, statistical_power=.9)
#> The equivalence bounds to achieve 90 % power with N = 121 are -0.3 and 0.3 .
#>
#> [1] -0.2990643 0.2990643
#' ## Sample size for alpha = 0.05, 90% power, equivalence bounds of -0.3 and 0.3 in
## raw units, assuming pooled standard deviation of 1, and assuming true effect d = 0
powerTOSTone.raw(alpha=0.05, statistical_power=0.9, sd = 1, low_eqbound=-0.3, high_eqbound=0.3)
#> The required sample size to achieve 90 % power with equivalence bounds of -0.3 and 0.3 is 121
#>
#> [1] 120.2464
## Power for sample size of 121, alpha = 0.05, equivalence bounds of
## -0.3 and 0.3 in raw units, assuming pooled standard deviation of 1, and assuming true effect = 0
powerTOSTone.raw(alpha=0.05, N=121, sd = 1, low_eqbound=-0.3, high_eqbound=0.3)
#> The statistical power is 90.21 % for equivalence bounds of -0.3 and 0.3 .
#>
#> [1] 0.902106
## Power for sample size of 121, alpha = 0.05, statistical power of
## 0.9, and assuming true effect = 0
powerTOSTone.raw(alpha=0.05, N=121, statistical_power=.9, sd=1)
#> The equivalence bounds to achieve 90 % power with N = 121 are -0.3 and 0.3 .
#>
#> [1] -0.2990643 0.2990643
```