﻿Table 
  3. 
  — 
  Recomputed 
  and 
  bias 
  of 
  the 
  cube 
  root 
  transformation 
  for 
  several 
  quantiles 
  of 
  the 
  sample 
  

   distribution 
  

  

  VVIUIIIC 
  CL|UClllWll 
  

  

  Rl 
  M 
  Hi^trirt 
  

  

  

  n 
  

  

  uuaniiie 
  ot 
  

   sample 
  

  

  rreaictea 
  

   volume 
  

  

  Trans- 
  

   formation 
  

   Dias 
  

  

  

  

  

  

  Ft^/tree 
  

  

  Percent 
  

  

  Great 
  Basin 
  States 
  

  

  Western 
  juniper 
  

  

  0.76 
  

  

  25th 
  

  

  1.8 
  

  

  -5 
  

  

  

  

  

  50th 
  

  

  5.8 
  

  

  -2 
  

  

  

  

  

  75th 
  

  

  14.1 
  

  

  -1 
  

  

  

  

  

  95th 
  

  

  51.6 
  

  

  -1 
  

  

  

  Utah 
  juniper 
  

  

  .76 
  

  

  25th 
  

  

  .9 
  

  

  -7 
  

  

  

  

  

  50th 
  

  

  2.6 
  

  

  -3 
  

  

  

  

  

  75th 
  

  

  6.3 
  

  

  -2 
  

  

  

  

  

  95th 
  

  

  17.9 
  

  

  -1 
  

  

  

  SIngleleaf 
  pinyon 
  

  

  .82 
  

  

  25th 
  

  

  .8 
  

  

  -4 
  

  

  

  

  

  50th 
  

  

  2.5 
  

  

  -2 
  

  

  

  

  

  75th 
  

  

  6.5 
  

  

  -1 
  

  

  

  

  

  95th 
  

  

  20.6 
  

  

  

  

  Ely 
  BLM 
  

  

  Utah 
  juniper 
  

  

  .72 
  

  

  25th 
  

  

  .4 
  

  

  -9 
  

  

  

  

  

  50th 
  

  

  1.2 
  

  

  -4 
  

  

  

  

  

  75th 
  

  

  3.5 
  

  

  -2 
  

  

  

  

  

  95th 
  

  

  13.9 
  

  

  -1 
  

  

  Winnemucca 
  BLM 
  

  

  Utah 
  juniper 
  

  

  .60 
  

  

  25th 
  

  

  .8 
  

  

  -11 
  

  

  

  

  

  50th 
  

  

  2.5 
  

  

  -5 
  

  

  

  

  

  75th 
  

  

  7.2 
  

  

  -3 
  

  

  - 
  

  

  

  

  95th 
  

  

  25.7 
  

  

  -1 
  

  

  Colorado 
  Plateau 
  States 
  

  

  Oneseed 
  juniper 
  

  

  .88 
  

  

  25th 
  

  

  .9 
  

  

  -8 
  

  

  

  

  

  50th 
  

  

  2.3 
  

  

  -4 
  

  

  

  

  

  75th 
  

  

  6.6 
  

  

  -2' 
  

  

  

  

  

  95th 
  

  

  21.5 
  

  

  -1 
  

  

  

  Utah 
  juniper 
  

  

  .77 
  

  

  25th 
  

  

  .9 
  

  

  -7 
  

  

  

  

  

  50th 
  

  

  3.0 
  

  

  -3 
  

  

  

  

  

  75th 
  

  

  7.4 
  

  

  -2 
  

  

  

  

  

  95th 
  

  

  19.9 
  

  

  -1 
  

  

  

  Rocky 
  Mountain 
  juniper 
  

  

  .70 
  

  

  25th 
  

  

  .8 
  

  

  -7 
  

  

  

  

  

  50th 
  

  

  2.1 
  

  

  -4 
  

  

  

  

  

  75th 
  

  

  5.5 
  

  

  -2 
  

  

  

  

  

  95th 
  

  

  13.6 
  

  

  -1 
  

  

  

  Pinyon 
  

  

  .84 
  

  

  25th 
  - 
  

  

  .8 
  

  

  -6 
  

  

  

  

  

  50th 
  

  

  2.6 
  

  

  -3 
  

  

  

  

  

  75th 
  

  

  6.4 
  

  

  -2 
  

  

  

  

  

  

  

  i 
  

  

  Central 
  Rocky 
  Mountain 
  

  

  Gambel 
  oak 
  

  

  .86 
  

  

  

  

  

  States 
  

  

  

  

  

  

  

  

  Bur 
  oak 
  

  

  .70 
  

  

  

  

  

  

  Mountain-mahogany 
  

  

  .77 
  

  

  

  

  

  

  Hardwoods 
  

  

  .77 
  

  

  

  

  

  ''Bias 
  Is 
  the 
  cube 
  root 
  inverse 
  transformation 
  of 
  the 
  volume 
  prediction 
  

  

  (from 
  regression) 
  minus 
  the 
  smearing 
  esti- 
  

  

  mator 
  divided 
  by 
  the 
  smearing 
  estimator. 
  

  

  Data 
  from 
  emother 
  study 
  were 
  available 
  for 
  checking 
  

   some 
  of 
  the 
  equations 
  for 
  the 
  Great 
  Basin 
  States 
  (Born 
  

   and 
  Chojnacky, 
  in 
  preparation). 
  More 
  than 
  300 
  P-J 
  trees 
  

   were 
  destructively 
  sampled 
  for 
  volume. 
  Table 
  4 
  shows 
  

   the 
  percentage 
  error 
  for 
  predicting 
  volume 
  of 
  individual 
  

   trees 
  grouped 
  in 
  diameter 
  class 
  intervals. 
  The 
  error 
  was 
  

   large: 
  20 
  percent 
  or 
  more 
  in 
  about 
  half 
  of 
  the 
  diameter 
  

   classes. 
  

  

  In 
  summary, 
  the 
  cube 
  root 
  transformation 
  injected 
  a 
  

   negligible 
  bias 
  and 
  most 
  of 
  the 
  volume 
  equations 
  had 
  a 
  

   reasonable 
  R^. 
  However, 
  considerable 
  volume 
  prediction 
  

   errors 
  are 
  Ukely 
  to 
  result 
  from 
  application 
  of 
  these 
  equa- 
  

   tions 
  in 
  local 
  areas. 
  

  

  8 
  

  

  