Tally test statistics

Tally test statistics from data and from multiple draws from a simulated null distribution

statTally(
  sample,
  rdata,
  FUN,
  direction = NULL,
  alternative = c("default", "two.sided", "less", "greater"),
  sig.level = 0.1,
  system = c("gg", "lattice"),
  shade = "navy",
  alpha = 0.1,
  binwidth = NULL,
  bins = NULL,
  fill = "gray80",
  color = "black",
  center = NULL,
  stemplot = dim(rdata)[direction] < 201,
  q = c(0.5, 0.9, 0.95, 0.99),
  fun = function(x) x,
  xlim,
  quiet = FALSE,
  ...
)

Arguments

sample

sample data

rdata

a matrix of randomly generated data under null hypothesis.

FUN

a function that computes the test statistic from a data set. The default value does nothing, making it easy to use this to tabulate precomputed statistics into a null distribution. See the examples.

direction

1 or 2 indicating whether samples in rdata are in rows (1) or columns (2).

alternative

one of default, two.sided, less, or greater

sig.level

significance threshold for wilcox.test used to detect lack of symmetry

system

graphics system to use for the plot

shade

a color to use for shading.

alpha

opacity of shading.

binwidth

bin width for histogram.

bins

number of bins for histogram.

fill

fill color for histogram.

color

border color for histogram.

center

center of null distribution

stemplot

indicates whether a stem plot should be displayed

q

quantiles of sampling distribution to display

fun

same as FUN so you don't have to remember if it should be capitalized

xlim

limits for the horizontal axis of the plot.

quiet

a logicial indicating whether the text output should be suppressed

...

additional arguments passed to lattice::histogram() or ggplot2::geom_histogram()

Value

A lattice or ggplot showing the sampling distribution.

As side effects, information about the empirical sampling distribution and (optionally) a stem plot are printed to the screen.

Examples

# is my spinner fair?
x <- c(10, 18, 9, 15)   # counts in four cells
rdata <- rmultinom(999, sum(x), prob = rep(.25, 4))
statTally(x, rdata, fun = max, binwidth = 1)  # unusual test statistic
#> 
#> Null distribution appears to be asymmetric. (p = 0.00144) 
#> 
#> Test statistic applied to sample data =  18 
#> 
#> Quantiles of test statistic applied to random data: 
#> 50% 90% 95% 99% 
#>  17  20  21  23  
#> 
#> Of the  1000  samples (1 original +  999  random), 
#> 	 131 ( 13.1 % ) had test stats = 18 
#> 	 321 ( 32.1 % ) had test stats >= 18 

statTally(x, rdata, fun = var, shade = "red", binwidth = 2)  # equivalent to chi-squared test
#> 
#> Null distribution appears to be asymmetric. (p = 7.94e-06) 
#> 
#> Test statistic applied to sample data =  18 
#> 
#> Quantiles of test statistic applied to random data: 
#>      50%      90%      95%      99% 
#> 10.66667 28.00000 36.66667 51.33333  
#> 
#> Of the  1000  samples (1 original +  999  random), 
#> 	 24 ( 2.4 % ) had test stats = 18 
#> 	 261 ( 26.1 % ) had test stats >= 18 

# Can also be used with test stats that are precomputed.
if (require(mosaicData)) {
D <- diffmean( age ~ sex, data = HELPrct); D
nullDist <- do(999) * diffmean( age ~ shuffle(sex), data = HELPrct)
statTally(D, nullDist)
statTally(D, nullDist, system = "lattice")
}
#> Using parallel package.
#>   * Set seed with set.rseed().
#>   * Disable this message with options(`mosaic:parallelMessage` = FALSE)
#> 
#> Null distribution appears to be symmetric. (p =  0.894 ) 
#> 
#> Test statistic applied to sample data =  -0.7841 
#> 
#> Quantiles of test statistic applied to random data: 
#>         50%         90%         95%         99% 
#> -0.06220626  1.02679488  1.34615364  1.81014154  
#> 
#> Of the  1000  samples (1 original +  999  random), 
#> 	 9 ( 0.9 % ) had test stats = -0.7841 
#> 	 205 ( 20.5 % ) had test stats <= -0.7841 
#> 	 194 ( 19.4 % ) had test stats >= 0.6597 
#> 
#> Null distribution appears to be symmetric. (p =  0.894 ) 
#> 
#> Test statistic applied to sample data =  -0.7841 
#> 
#> Quantiles of test statistic applied to random data: 
#>         50%         90%         95%         99% 
#> -0.06220626  1.02679488  1.34615364  1.81014154  
#> 
#> Of the  1000  samples (1 original +  999  random), 
#> 	 9 ( 0.9 % ) had test stats = -0.7841 
#> 	 205 ( 20.5 % ) had test stats <= -0.7841 
#> 	 194 ( 19.4 % ) had test stats >= 0.6597