bayesics (version 2.0.2)

sign_test_b: Paired sign test

Description

Sign test for paired data.

Usage

sign_test_b(
  x,
  y,
  p0 = 0.5,
  prior = "jeffreys",
  prior_shapes,
  ROPE,
  CI_level = 0.95,
  plot = TRUE
)

Value

(returned invisible) A list with the following:

• posterior_mean: Posterior mean of the median difference

• CI: Credible interval for the median difference

• Pr_less_than_p: Posterior probability that the proportion of differences that are positive is less than the argument p0.

• ROPE_bounds: ROPE bounds for the proportion of differences that are positive

• ROPE: Posterior probability that the proportion of differences which are positive falls in the ROPE

• prop_plot: Prior and posterior plot

• posterior_parameters: Posterior beta shape parameters for the proportion of differences which are positive

Arguments

x

Either numeric vector or binary vector. If the former, \(z_i = 1_{[x_i > y_i]}\) if y is supplied, else \(z_i = 1_{[x_i > 0]}\). If the latter, then \(z_i = x_i\).

y

Optional numeric vector to pair with x.

p0

sign_test_b will return the posterior probability that \(p < p0\). Defaults to 0.5, as is most typical in the sign test.

prior

Either "jeffreys" (Beta(1/2,1/2)) or "uniform" (Beta(1,1)). This is ignored if prior_shapes is provided.

prior_shapes

Vector of length two, giving the shape parameters for the beta distribution that will act as the prior on the probability that \(z_i = 1\).

ROPE

positive numeric of length 1 or 2. If of length 1, then ROPE is taken to be \(p0\pm \)ROPE. Defaults to \(\pm 0.05\).

CI_level

The posterior probability to be contained in the credible interval for \(p\).

plot

logical. Should a plot be shown?

Details

The sign test looks at \(z_i:= 1_{[x_i > y_i]}\) rather than trying to model the distribution of \((x_i,y_i)\). sign_test_b then uses the fact that $$ z_i \overset{iid}{\sim} Bernoulli(p) $$ and then makes inference on \(p\). The prior on \(p\) is $$ p \sim Beta(a,b), $$ where \(a\) and \(b\) are given by the argument prior_shapes. If prior_shapes is missing and prior = "jeffreys", then a Jeffreys prior will be used (\(Beta(1/2,1/2)\)), and if prior = "uniform", then a uniform prior will be used (\(Beta(1,1)\)).

Examples

# \donttest{
# Single population
sign_test_b(x = rnorm(50))

## Change ROPE
sign_test_b(x = rnorm(50),
            ROPE = 0.1)

## Change the prior
sign_test_b(x = rnorm(50),
            prior = "uniform")
sign_test_b(x = rnorm(50),
            prior_shapes = c(2,2))

## Two populations
sign_test_b(x = rnorm(50,1),
            y = rnorm(50,0))

## Change reference probability
sign_test_b(x = rnorm(50,1),
            y = rnorm(50,0),
            p0 = 0.7)
# }