Score Grade Transformation

This document can be found on RPubs http://rpubs.com/ShKlinkenberg/225952

Set parameters

min.score         = 0
min.grade         = 1
min.grade         = min.grade/10
max.score         = 100
cutoff.precentage = .5
guess.score       = 20
non.guess.score   = max.score - guess.score
guess.percentage  = guess.score / max.score
score = min.score:max.score
score

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 [83]  82  83  84  85  86  87  88  89  90  91  92  93  94  95  96  97  98  99 100

Create Score Grade transformation function

ScoreGradeTransformation <- function(score, guess.score, min.grade, cutoff.precentage, max.score) {
    # Computes the grade corrected for guessing.
    #
    # Args:
    #   score             : Value or vector with raw exam scores
    #   guess.score       : Total amount of raw guessing score
    #   min.grade         : Minimal grate to be given
    #   cutoff.precentage : Raw cut-off score for a pass mark
    #   max.score         : Maximum raw score to be given
    #
    # Returns:
    #   Grade expressed as a number between minimal grade and 10
    
    # Setup vector to store grades
    grade = vector()
    
    # Determine cut-off score based on percentage and guessing score
    cutoff.score = guess.score + ( cutoff.precentage * (non.guess.score) )
    
    # Grade when guessing
      grade[score <= guess.score] = min.grade
    # Grade between guessing and cutoff
    
    ## Slope of transformation function
    a.tot.cutoff = (cutoff.precentage - min.grade) / (cutoff.score - guess.score); a.tot.cutoff
    
    grade[score > guess.score & score < cutoff.score] = (a.tot.cutoff * (score[score > guess.score & score < cutoff.score]-guess.score)) + min.grade
    
    # Grade between cutoff and max score
    
    ## Slope of transformation function
    a.na.cutoff = (1 - cutoff.precentage) / (max.score - cutoff.score); a.na.cutoff   
             
    grade[score >= cutoff.score] = (a.na.cutoff * (score[score >= cutoff.score]-cutoff.score)) + cutoff.precentage
    
    return(grade * 10)   
}   

Apply Score Grade Transformation function

grade <- ScoreGradeTransformation(score, guess.score, min.grade, cutoff.precentage, max.score) 

Plot score grade transformation