﻿ADJUSTMENT 
  FOR 
  SAMPLING 
  BIAS 
  

  

  The 
  design 
  for 
  sampling 
  contained 
  an 
  inherent 
  source 
  of 
  bias 
  inasmuch 
  as 
  skiers 
  

   who 
  skied 
  frequently 
  during 
  the 
  season 
  were 
  more 
  likely 
  to 
  be 
  selected 
  than 
  skiers 
  who 
  

   skied 
  only 
  occasionally. 
  To 
  the 
  extent 
  that 
  frequent 
  skiers 
  as 
  a 
  group 
  had 
  unique 
  

   characteristics, 
  the 
  sample 
  results 
  would 
  tend 
  to 
  exaggerate 
  these 
  characteristics 
  and 
  

   underestimate 
  the 
  characteristics 
  of 
  the 
  less 
  frequent 
  skier. 
  This 
  bias 
  can 
  be 
  elimi- 
  

   nated 
  by 
  using 
  the 
  method 
  proposed 
  by 
  Lucas 
  ."^^ 
  The 
  method 
  weights 
  the 
  number 
  of 
  

   skiers 
  and 
  the 
  number 
  of 
  visits 
  by 
  the 
  reciprocal 
  of 
  the 
  number 
  of 
  visits 
  per 
  skier. 
  

  

  The 
  following 
  examples 
  show 
  how 
  this 
  bias 
  can 
  influence 
  estimates 
  of 
  population 
  

   characteristics 
  and 
  how 
  the 
  bias 
  is 
  avoided 
  when 
  the 
  weighting 
  method 
  is 
  used. 
  

  

  Example 
  1: 
  

  

  A 
  known 
  population 
  of 
  400 
  skiers 
  has 
  the 
  following 
  participation 
  characteristics: 
  

   100 
  skiers 
  each 
  visiting 
  30 
  times 
  per 
  season 
  = 
  3, 
  000 
  skier 
  visits 
  

   300 
  skiers 
  each 
  visiting 
  5 
  times 
  per 
  season 
  = 
  1,500 
  skier 
  visits 
  

  

  The 
  average 
  number 
  of 
  visits 
  per 
  skier 
  is 
  11.25 
  (X= 
  4,500 
  / 
  400 
  = 
  11.25). 
  

   It 
  appears 
  that 
  there 
  would 
  be 
  three 
  times 
  as 
  many 
  5 
  -day 
  skiers 
  as 
  30 
  -day 
  skiers 
  on 
  

   any 
  given 
  day. 
  But 
  the 
  30 
  -day 
  skiers 
  made 
  twice 
  as 
  many 
  visits 
  as 
  the 
  5 
  -day 
  skiers 
  

   (3,000 
  / 
  1, 
  500). 
  Therefore, 
  theoretically 
  there 
  would 
  be 
  twice 
  as 
  many 
  30-day 
  skiers 
  

   as 
  5 
  -day 
  skiers 
  on 
  any 
  given 
  day. 
  K 
  a 
  10 
  -percent 
  sample 
  were 
  selected 
  on 
  a 
  particular 
  

   day 
  when 
  150 
  skiers 
  were 
  present, 
  the 
  sample 
  would 
  probably 
  consist 
  of 
  15 
  skiers 
  with 
  

   the 
  following 
  characteristics: 
  

  

  10 
  skiers 
  who 
  ski 
  30 
  times 
  per 
  season 
  

   5 
  skiers 
  who 
  ski 
  5 
  times 
  per 
  season 
  

  

  If 
  the 
  average 
  number 
  of 
  visits 
  per 
  season 
  were 
  estimated 
  from 
  this 
  sample, 
  it 
  

   would 
  be 
  biased 
  upward 
  as 
  shown 
  below: 
  

  

  10 
  skiers 
  visiting 
  30 
  times 
  per 
  season 
  - 
  300 
  visits 
  

   5 
  skiers 
  visiting 
  5 
  times 
  per 
  season 
  = 
  25 
  visits 
  

   X 
  = 
  325 
  / 
  15 
  = 
  21.7 
  visits 
  per 
  skier 
  per 
  season 
  

  

  The 
  considerable 
  difference 
  between 
  the 
  known 
  average 
  days 
  skied 
  per 
  season 
  

   (11.25) 
  and 
  the 
  average 
  estimated 
  from 
  the 
  sample 
  (21.7) 
  results 
  from 
  the 
  inevitable 
  

   biases. 
  By 
  applying 
  Lucas' 
  method, 
  an 
  unbiased 
  estimate 
  of 
  the 
  population 
  mean 
  rate 
  

   of 
  annual 
  participation 
  can 
  be 
  obtained 
  from 
  this 
  sample 
  as 
  shown 
  below: 
  

  

  ( 
  5 
  skiers) 
  ( 
  5 
  visits) 
  (f) 
  ~ 
  ^ 
  visits 
  by 
  ( 
  5) 
  (^) 
  or 
  1.000 
  skier 
  

  

  1 
  1 
  

   (10 
  skiers) 
  (30 
  visits) 
  (^) 
  = 
  10 
  visits 
  by 
  (10) 
  (-^) 
  or 
  .333 
  skier 
  

  

  X 
  = 
  15 
  / 
  1,333 
  = 
  11.25 
  visits 
  per 
  skier 
  

  

  Lucas, 
  Robert 
  C. 
  Bias 
  in 
  estimating 
  recreationists' 
  length 
  of 
  stay 
  from 
  sample 
  

   interviews. 
  J. 
  Forest. 
  61(12): 
  912-914. 
  1963. 
  

  

  53 
  

  

  