# qqrank: Load-Deviance Ranking In phalen: Phalen Algorithms and Functions

## Description

Rank by size and deviance from the hypothesized mean.

## Usage

 ```1 2 3``` ```qqrank(X, INDEX, alternative = c("two.sided", "less", "greater"), absrank = TRUE, N = NA, b = NA, plotpenalty = TRUE, allowed.error = 0.005) ```

## Arguments

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

## 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.

## 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`.

## Author(s)

Robert P. Bronaugh

`glpenalty` `t.test` `binom.test`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ``` # 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) ```