AB_permutation_distancing_test {pdt}

AB_permutation_distancing_test

Description

Performs a randomisation test for two phases (A and B) that corrects for dependency. The correcting is done through stepwise resampling the time series while varying the distance between observations. The required distance 0,1,2,3.. is determined based on repeated dependency testing while stepwise increasing the distance. The input x and y values should be equidistant (with NA's included) using insert_NA_and_try_to_shift. The distance per cycles = k-1. k_max should be max 25 If de_A_trend=TRUE, phase A will be first de_A_trended. If de_B_trend=TRUE, phase B will be first de_B_trended. If detrend_x_position = "first" : take predicted value for first valid observation. If detrend_x_position = "center": take predicted value for center observation. If detrend_x_position = "last" : take predicted value for last valid observation. The p-value returned corresponds with the lowest Ljung-Box test (minimal) p-value found. The statistic returned correspond with median chi-square k with p_box larger than alpha_p_box_test or statistic_box smaller than max_statistic_p_box_test (i.e., not dependent).

Usage

AB_permutation_distancing_test(
  x,
  y,
  test_statistic = "*",
  test_statistic_function = "mean",
  reps_max = 2000,
  k_max = NULL,
  alpha_p_box_test = 0.1,
  max_statistic_p_box_test = 2.7,
  no_duplicates = FALSE,
  remove_NA_series_above_k = TRUE,
  de_A_trend = FALSE,
  detrend_A_position = "center",
  de_B_trend = FALSE,
  detrend_B_position = "center",
  show_plot = FALSE,
  show_plot_header = ""
)

Arguments

x

factor vector to indicate conditions or phases (e.g., "A" and "B")

y

numerical vector with the observed y-values

test_statistic

character how to compute the test statistic c("A-B", "B-A", "*") *=two-sided

test_statistic_function

character compute and compare "mean" or "median" for A and B

reps_max

numerical maximum number of permutation replications (the theoretical number= n!)

k_max

numerical maximum k value

alpha_p_box_test

numerical see above

max_statistic_p_box_test

numerical see above

no_duplicates

boolean do a permutation test without duplicates (makes it much slower)

remove_NA_series_above_k

boolean first clean the data by skipping repeated NA's

de_A_trend

boolean de-trend A first (optional)

detrend_A_position

character c("first", "center", "last"), see detrend_A

de_B_trend

boolean de-trend B first (optional)

detrend_B_position

character c("first", "center", "last"), see detrend_B

show_plot

boolean show test plot of statistical test

show_plot_header

character header of test plot

Value

List with the permutation distancing test results: de_A_trend setting in call, detrend_A_position in call, de_B_trend setting in call, detrend_B_position in call, ar1 = vector of computed ar1 values per distancing step (0,1,2, etc), p_box = vector of computed box-test p-values per distancing step, statistic_box = vector of box-test statistics per distancing step, observed_test_statistic = computed overall AB test statistic (before distancing), effect_size_overall = computed overall effect size (before distancing), p = vector of computed permutation test p-values per distancing step, effect_size vector of computed permutation test effect-sizes per distancing step, p_fitted = vector of lm-fitted line p-values through p_box, k_max = k_max setting in call or computed based on the number of observations, k_selected_based_on_Box_test = selected k values, p_selected_based_on_Box_test = selected p-value, effect_size_selected_based_on_Box_test = selected effect-size values.

Examples

pdt::AB_permutation_distancing_test(
  as.factor(c(rep("A",20), rep("B",20))),
  c(rnorm(20), rnorm(20)+2),
  test_statistic="B-A",
  test_statistic_function="mean",
  reps_max=1000,
  k_max=NULL,
  alpha_p_box_test=0.1,
  max_statistic_p_box_test=2.7,
  no_duplicates=FALSE,
  remove_NA_series_above_k=TRUE,
  de_A_trend=FALSE,
  detrend_A_position="center",
  de_B_trend=FALSE,
  detrend_B_position="center",
  show_plot=FALSE,
  show_plot_header="")