UDT_power: Power calculator for UDT

In singcar: Comparing Single Cases to Small Samples

Power calculator for UDT

Description

Calculates exact power given sample size or sample size given power, using analytical methods for the frequentist test of deficit for a specified case scores, means and standard deviations for the control sample. The means and standard deviations defaults to 0 and 1 respectively, so if no other values are given, the case scores are interpreted as deviations from the mean in standard deviations. The returned value will approximate the power for the given parameters.

Usage

UDT_power(
  case_a,
  case_b,
  mean_a = 0,
  mean_b = 0,
  sd_a = 1,
  sd_b = 1,
  r_ab = 0.5,
  sample_size = NULL,
  power = NULL,
  alternative = c("two.sided", "greater", "less"),
  alpha = 0.05,
  spec = 0.005
)

Arguments

case_a	A single value from the expected case observation on task A.
case_b	A single value from the expected case observation on task B.
mean_a	The expected mean from the control sample on task A. Defaults to 0.
mean_b	The expected mean from the control sample on task B. Defaults to 0.
sd_a	The expected standard deviation from the control sample on task A. Defaults to 1.
sd_b	The expected standard deviation from the control sample on task B. Defaults to 1.
r_ab	The expected correlation between the tasks. Defaults to 0.5
sample_size	The size of the control sample, vary this parameter to see how the sample size affects power. One of sample size or power must be specified, not both.
power	A single value between 0 and 1 specifying desired power for calculating necessary sample size. One of sample size or power must be specified, not both.
alternative	The alternative hypothesis. A string of either "two.sided" (default) or "one.sided".
alpha	The specified Type I error rate. This can also be varied, with effects on power. Defaults to 0.05.
spec	A single value between 0 and 1. If desired power is given as input the function will utilise a search algorithm to find the sample size needed to reach the desired power. However, if the power specified is greater than what is actually possible to achieve the algorithm could search forever. Hence, when power does not increase substantially for any additional participant in the sample, the algorithm stops. By default the algorithm stops when power does not increase more than 0.5 participant, but by varying spec, this specificity can be changed.

Value

Either a single value of the exact power, if sample size is given. Or a dataframe consisting of both the sample size and the exact power such size would yield.

Examples

UDT_power(case_a = -3, case_b = -1, mean_a = 0, mean_b = 0,
          sd_a = 1, sd_b = 1, r_ab = 0.5, sample_size = 20)
UDT_power(case_a = -3, case_b = -1, power = 0.8)

singcar documentation built on March 31, 2023, 9:25 p.m.