# Roger Palay copyright 2021-04-12
# Saline, MI 48176
#
# in the goodfit function:
#    items   is a list of the item values (i.e., labels)
#    H_null  is a list of the hypothesized proportions
#    observed is a list of the observed counts of items
#    sig_level is the level at which the test is to be run
#    show_table if TRUE will cause the function to use
#               View to display a nice table of values
goodfit <- function( items, H_null, observed, 
                     sig_level,show_table=FALSE ) 
{
  #  there are a few  checks that we should make
  
  #  first, is the sum of the H_null proportions == 1
  sum_H0 <- sum( H_null )
  if( abs( sum_H0 - 1) > 0.00000001)
  { return("H_null proportions must add to 1")}
  
  #  second, all of the H_null values must be non-negative
  find_negs <- which( H_null < 0 )
  if( length( find_negs ) > 0 )
  {return( "cannot have negative proportions")}
  
  #  Third, we need the same number of items, 
  #       H_null proportions, and observed frequencies
  items_length <- length( items )
  H0_length <- length( H_null )
  obs_length <- length( observed )
  if( items_length != H0_length |
      items_length != obs_length)
  { return("Need same number of items, proportions, and observed frequencies")}
  
  obs_total <- sum(observed)
  expected <- H_null*obs_total
  #   Fourth, we need enough expected values
  num_too_small <- length( which( expected < 5))
  
  if( num_too_small > 0 )
  { cat( "expected values, some too small","\n")
    cat(expected,"\n")
    return("use larger sample")}
  diff <- observed - expected
  diff2 <- diff^2
  chi_component <- diff2/expected
  total = sum( chi_component )
  goff_table <<- data.frame( items, H_null, observed, expected,
                             diff, diff2, chi_component)
  colnames( goff_table ) <- c( "Items","H_null", "observed", "expected",
                               "diff", "diff^2", "chi component")
  print( goff_table)
  if( show_table ) {View( goff_table )}
  cat( "-----------------------------------\n")
  cat("total observations = ",obs_total,"\n")
  cat("Number of categories = ", obs_length,"\n")
  cat("Number of degrees of freedom = ", (obs_length-1),"\n")
  cat("Total of chi component =", total,"\n")
  cat("P(total >= ",total,") = ",
      pchisq(total, obs_length-1,lower.tail=FALSE), "\n")
  crit_value <- qchisq( sig_level, obs_length-1, lower.tail=FALSE)
  cat("For ",(sig_level*100),"% to the right, the ","\n")
  cat("    critical value  is ", crit_value, "\n")
  if( total > crit_value )
  { "reject H0"}
  else
  {" not enough evidence to reject H0"}
}