qqrank: Load-Deviance Ranking

Description

Rank by size and deviance from the hypothesized mean.

Usage

qqrank(X, INDEX, alternative = c("two.sided", "less", "greater"),  absrank = TRUE, N = NA, b = NA, plotpenalty = TRUE,  allowed.error = 0.005)

Arguments

A numeric vector.

INDEX

A factor of length X.

alternative

The alternative hypothesis. Accepts "two.sided", "less", or "greater".

absrank

If TRUE, INDEX means greater than or less than the population mean will produce a positive qqscore. If FALSE, INDEX means greater than the population mean will have a positive qqscore and INDEX means less than the population mean will have a negative qqscore. The default is TRUE.

The number of observations below which a growth penalty is applied. N is passed to x1 argument of glpenalty.

A positive numeric value representing the growth rate of the glpenalty.

plotpenalty

If TRUE, the glpenalty is plotted. The default is TRUE.

allowed.error

The allowed difference between glpenalty and 1 at N. The default is 0.005.

Value

qqrankmatrix: A data frame containing the size, mean, standard deviation, and qqrank of each INDEX.
test.used: The statistical test used to measure deviance from the mean.
pop.mean: The mean of X.
pop.sd: The standard deviation of X.

Details

qqrank ranks by size and deviance from the hypothesized mean using either the Binomial Test or Welch's t-Test. Restated, qqrank is a function of a size penalty, test statistic or variant thereof, and p-value.

Examples

Run this code

  # which hospital has the "worst" readmissions? (note: the average
  # readmission rate is 17.13%
  data(ipadmits)
  attach(ipadmits)
  ip.ag = data.frame('sum' = tapply(ipadmits$isReadmission,ipadmits$HospID,sum),
                     'avg' = tapply(ipadmits$isReadmission,ipadmits$HospID,mean))
  
  # hospital 9 has the most readmissions (1,094), but the percent of readmissions
  # is low at 14%, less than the population average. 
  ip.ag[order(-ip.ag$sum),][1,]
  
  # hostpital 80 has the highest percentage of readmissions 87.5%, but only
  # 7 readmissions over all. 
  ip.ag[order(-ip.ag$avg),][1,]
  
  # using qqrank and penalizing samples less than N = 250 at a growth
  # rate of b = 0.05, Hospital 39 has 1606 readmissions with a readmission
  # percent of 38%. 
  qqr = qqrank(ipadmits$isReadmission,ipadmits$HospID
               ,alternative = "greater",N = 250, b = 0.05)
  round(qqr$rankmatrix,2)
  
  # relax sample penalty and rank on both sides of the mean
  # Hospital 21 has the "best" readmission track record.
  qqr = qqrank(ipadmits$isReadmission,ipadmits$HospID
               ,alternative = "two.sided",absrank = FALSE,N = 30, b = 0.1)
  round(qqr$rankmatrix,2)
  detach(ipadmits)

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