Sample size or precision for a mean

prec_mean returns the sample size or the precision for the provided mean and standard deviation.

Usage

prec_mean(
  mean,
  sd,
  n = NULL,
  conf.width = NULL,
  conf.level = 0.95,
  ...,
  mu = NULL
)

Arguments

mean

hypothesized mean; not used in determining n or precision. Only needed to display a hypothetical confidence interval.

sd

standard deviation.

n

number of observations.

conf.width

precision (the full width of the confidence interval).

conf.level

confidence level.

...

other arguments to uniroot (e.g. tol).

mu

deprecated argument

Value

Object of class "presize", a list with mean mean, sd standard deviation, n sample size, conf.width precision (the width of the confidence interval), lwr lower bound of confidence interval, upr upper bound of confidence interval, augmented with method and note elements.

Details

Exactly one of the parameters n or conf.width must be passed as NULL, and that parameter is determined from the other.

The precision is defined as the full width of the confidence interval. The confidence interval calculated as \(t(n - 1) * sd / sqrt(n)\), with t(n-1) from the t-distribution with n-1 degrees of freedom.

This function is also suitable for a difference in paired means, as this reduces to a single value per individual - the difference.

uniroot is used to solve n.

Examples

# mean of 5, SD of 2.5, whats the confidence interval width with 20 participants?
prec_mean(mean = 5, sd = 2.5, n = 20)
#> 
#>      precision for mean 
#> 
#>   mean  sd  n conf.width conf.level      lwr      upr
#> 1    5 2.5 20   2.340072       0.95 3.829964 6.170036
# mean of 5, SD of 2.5, how many participants for CI width of 2.34?
prec_mean(mean = 5, sd = 2.5, conf.width = 2.34)  # approximately the inverse of above
#> 
#>      sample size for mean 
#> 
#>   mean  sd        n conf.width conf.level  lwr  upr
#> 1    5 2.5 20.00108       2.34       0.95 3.83 6.17

# The mean argument is hypothetical and only used to calculate lower and upper
# limits of a hypothesized CI. The estimated n or conf.width only depends on
# the standard deviation.

# same conf.width regardless of mean
prec_mean(mean = 25, sd = 2.5, n = 20)$conf.width
#> [1] 2.340072
prec_mean(mean = 250, sd = 2.5, n = 20)$conf.width
#> [1] 2.340072

# same n regardless of mean
prec_mean(mean = 25, sd = 2.5, conf.width = 2.34)$n
#> [1] 20.00108
prec_mean(mean = 250, sd = 2.5, conf.width = 2.34)$n
#> [1] 20.00108