Spower (version 0.6)

p_t.test: p-value from independent/paired samples t-test simulation

Description

Generates one or two sets of continuous data group-level data according to Cohen's effect size 'd', and returns a p-value. The data and associated t-test assume that the conditional observations are normally distributed and have have equal variance by default, however these may be modified.

Usage

p_t.test(
  n,
  d,
  mu = 0,
  r = NULL,
  type = "two.sample",
  n2_n1 = 1,
  two.tailed = TRUE,
  var.equal = TRUE,
  means = NULL,
  sds = NULL,
  conf.level = 0.95,
  gen_fun = gen_t.test,
  return_analysis = FALSE,
  ...
)
gen_t.test(
  n,
  d,
  n2_n1 = 1,
  r = NULL,
  type = "two.sample",
  means = NULL,
  sds = NULL,
  ...
)

Value

a single p-value

Arguments

n

sample size per group, assumed equal across groups. For paired samples this corresponds to the number of pairs (hence, half the number of data points observed)

d

Cohen's standardized effect size d. For the generated data this standardized mean appears in the first group (two-sample)/first time point (paired samples)

mu

population mean to test against

r

(optional) instead of specifying d specify a point-biserial correlation. Internally this is transformed into a suitable d value for the power computations

type

type of t-test to use; can be 'two.sample', 'one.sample', or 'paired'

n2_n1

allocation ratio reflecting the same size ratio. Default of 1 sets the groups to be the same size. Only applicable when type = 'two.sample'

two.tailed

logical; should a two-tailed or one-tailed test be used?

var.equal

logical; use the classical or Welch corrected t-test?

means

(optional) vector of means for each group. When specified the input d is ignored

sds

(optional) vector of SDs for each group. If not specified and d is used then these are set to a vector of 1's

conf.level

confidence interval level passed to t.test

gen_fun

function used to generate the required two-sample data. Object returned must be a list containing one (one-sample) or two (independent samples/paired samples) elements, both of which are numeric vectors. Default uses gen_t.test to generate conditionally Gaussian distributed samples. User defined version of this function must include the argument ...

return_analysis

logical; return the analysis object for further extraction and customization?

...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Author

Phil Chalmers

See Also

gen_t.test

Examples

# sample size of 50 per group, "medium" effect size
p_t.test(n=50, d=0.5)

# point-biserial correlation effect size
p_t.test(n=50, r=.3)

# second group 2x as large as the first group
p_t.test(n=50, d=0.5, n2_n1 = 2)

# specify mean/SDs explicitly
p_t.test(n=50, means = c(0,1), sds = c(2,2))

# paired and one-sample tests
p_t.test(n=50, d=0.5, type = 'paired') # n = number of pairs
p_t.test(n=50, d=0.5, type = 'one.sample')

# return analysis object
p_t.test(n=50, d=0.5, return_analysis=TRUE)

# \donttest{
  # compare simulated results to pwr package

  pwr::pwr.t.test(d=0.2, n=60, sig.level=0.10,
             type="one.sample", alternative="two.sided")
  p_t.test(n=60, d=0.2, type = 'one.sample', two.tailed=TRUE) |>
         Spower(sig.level=.10)

  pwr::pwr.t.test(d=0.3, power=0.80, type="two.sample",
                  alternative="greater")
  p_t.test(n=interval(10, 200), d=0.3, type='two.sample', two.tailed=FALSE) |>
         Spower(power=0.80)

# }


###### Custom data generation function

# Generate data such that:
#   - group 1 is from a negatively distribution (reversed X2(10)),
#   - group 2 is from a positively skewed distribution (X2(5))
#   - groups have equal variance, but differ by d = 0.5

args(gen_t.test)   ## can use these arguments as a basis, though must include ...

# arguments df1 and df2 added; unused arguments caught within ...
my.gen_fun <- function(n, d, df1, df2, ...){
 	 group1 <- -1 * rchisq(n, df=df1)
	     group2 <- rchisq(n, df=df2)
	     # scale groups first given moments of the chi-square distribution,
	     #   then add std mean difference
	     group1 <- ((group1 + df1) / sqrt(2*df1))
	     group2 <- ((group2 - df2) / sqrt(2*df2)) + d
	     dat <- list(group1, group2)
	     dat
}

# check the sample data properties
dat <- my.gen_fun(n=10000, d=.5, df1=10, df2=5)
sapply(dat, mean)
sapply(dat, sd)

p_t.test(n=100, d=0.5, gen_fun=my.gen_fun, df1=10, df2=5)

# \donttest{

  # power given Gaussian distributions
  p_t.test(n=100, d=0.5) |> Spower(replications=30000)

  # estimate power given the customized data generating function
  p_t.test(n=100, d=0.5, gen_fun=my.gen_fun, df1=10, df2=5) |>
    Spower(replications=30000)

  # evaluate Type I error rate to see if liberal/conservative given
  # assumption violations (should be close to alpha/sig.level)
  p_t.test(n=100, d=0, gen_fun=my.gen_fun, df1=10, df2=5) |>
    Spower(replications=30000)

# }