Test of percentiles by permutation test — percentileTest • rcompanion

Conducts a permutation test to compare two groups for medians, percentiles, or proportion below a threshold value.

Usage

percentileTest(
  formula = NULL,
  data = NULL,
  x = NULL,
  y = NULL,
  test = "median",
  tau = 0.5,
  type = 7,
  threshold = NA,
  comparison = "<",
  r = 1000,
  digits = 4,
  progress = "TRUE"
)

Arguments

formula: A formula indicating the response variable and the independent variable. e.g. y ~ group.
data: The data frame to use.
x: If no formula is given, the response variable for one group.
y: The response variable for the other group.
test: The statistic to compare between groups. Can be "median", "percentile", "iqr", "proportion", "mean", or "variance".
tau: If "percentile" is chosen as the test, tau indicates the percentile to test. Expressed as a quantile. That is, 0.5 indicates a test for medians. 0.75 indicates a test for 75th percentiles.
type: The type value passed to the quantile function.
threshold: If "proportion" is chosen as the test, threshold indicates the value of the dependent variable to use as the threshold. For example, to test if there is a different in the proportion of observations below $10,000, threshold = 10000 would be used.
comparison: If "proportion" is chosen as the test, comparison indicates the inequality to use. Options are "<", "<=", ">", ">=", or , "=="
r: The number of replicates in the permutation test.
digits: The number of significant digits in the output.
progress: If TRUE, prints a dot for every 1 percent of progress while conducting the test.

Value

A list of three data frames with the data used, a summary for each group, and the p-value from the test.

Details

The function will test for a difference in medians, percentiles, interquartile ranges, proportion of observations above or below some threshold value, means, or variances between two groups by permutation test.

The permutation test simply permutes the observed values over the two groups and counts how often the calculated statistic is at least as extreme as the original observed statistic.

The input should include either formula and data; or x and y.

The function removes cases with NA in any of the variables.

If the independent variable has more than two groups, only the first two levels of the factor variable will be used.

The p-value returned is a two-sided test.

Note

The parsing of the formula is simplistic. The first variable on the left side is used as the measurement variable. The first variable on the right side is used for the independent variable.

References

https://rcompanion.org/handbook/F_15.html

Author

Salvatore Mangiafico, mangiafico@njaes.rutgers.edu

Examples

data(BrendonSmall)
percentileTest(Sodium ~ Instructor, 
               data=BrendonSmall, 
               test="median")
#> ....................................................................................................
#> 
#> $Test
#>               Formula         Data   Test
#> 1 Sodium ~ Instructor BrendonSmall median
#> 
#> $Summary
#>                   n mean    sd  min  p25 median  p75  max iqr
#> 1   Brendon Small 9 1259 64.66 1164 1222   1271 1287 1377  65
#> 2 Jason Penopolis 9 1293 49.84 1199 1273   1281 1329 1368  56
#> 
#> $Result
#>           p.value
#> 1 p-value   0.579
#> 

percentileTest(Sodium ~ Instructor, 
               data=BrendonSmall, 
               test="percentile", 
               tau = 0.75)
#> ....................................................................................................
#> 
#> $Test
#>               Formula         Data       Test  tau
#> 1 Sodium ~ Instructor BrendonSmall percentile 0.75
#> 
#> $Summary
#>                   n mean    sd  min  p25 median  p75  max iqr
#> 1   Brendon Small 9 1259 64.66 1164 1222   1271 1287 1377  65
#> 2 Jason Penopolis 9 1293 49.84 1199 1273   1281 1329 1368  56
#> 
#> $Result
#>           p.value
#> 1 p-value   0.437
#> 

percentileTest(Sodium ~ Instructor, 
               data=BrendonSmall, 
               test="proportion", 
               threshold = 1300)
#> ....................................................................................................
#> 
#> $Test
#>               Formula         Data       Test
#> 1 Sodium ~ Instructor BrendonSmall proportion
#> 
#> $Summary
#>                   n mean    sd  min  p25 median  p75  max iqr comparison
#> 1   Brendon Small 9 1259 64.66 1164 1222   1271 1287 1377  65          <
#> 2 Jason Penopolis 9 1293 49.84 1199 1273   1281 1329 1368  56          <
#>   threshold proportion
#> 1      1300     0.8889
#> 2      1300     0.5556
#> 
#> $Result
#>           p.value
#> 1 p-value   0.302
#>