﻿Report 
  on 
  the 
  Metabolism 
  of 
  Female 
  Munition 
  Workers. 
  69 
  

  

  under 
  (b) 
  and 
  those 
  inherent 
  in 
  any 
  method 
  of 
  gas 
  analysis 
  was 
  certainly 
  

   more 
  serious. 
  We 
  have 
  attempted 
  to 
  appraise 
  roughly 
  the 
  magnitude 
  of 
  such 
  

   error 
  in 
  the 
  following 
  way. 
  It 
  is 
  well 
  known 
  that 
  if 
  we 
  have 
  a 
  series 
  of 
  

   paired 
  readings 
  of 
  a 
  magnitude, 
  then 
  the 
  square 
  root 
  of 
  half 
  the 
  mean 
  square 
  

   of 
  the 
  differences 
  between 
  the 
  paired 
  readings 
  is 
  a 
  suitable 
  measure 
  of 
  the 
  

   error 
  of 
  observation, 
  provided 
  there 
  be 
  no 
  correlation 
  between 
  the 
  errors 
  of 
  

   paired 
  determinations 
  or 
  between 
  the 
  magnitude 
  of 
  the 
  error 
  and 
  that 
  of 
  the 
  

   quantity 
  measured. 
  The 
  former 
  assumption 
  cannot 
  be 
  strictly 
  accurate 
  

   because 
  of 
  secular 
  change, 
  that 
  is 
  to 
  say, 
  the 
  more 
  experienced 
  the 
  worker 
  the 
  

   smaller 
  his 
  error, 
  so 
  that 
  some 
  positive 
  correlation 
  surely 
  exists 
  between 
  

   errors 
  in 
  each 
  member 
  of 
  a 
  pair, 
  both 
  will 
  be 
  smaller 
  after 
  some 
  months' 
  

   work 
  than 
  at 
  the 
  beginning 
  of 
  the 
  research 
  ; 
  the 
  assumption 
  would 
  probably 
  

   be 
  quite 
  correct 
  if 
  the 
  analyst 
  had 
  had 
  years 
  of 
  experience 
  before 
  the 
  trial 
  

   period. 
  The 
  second 
  assumption 
  was 
  tested 
  by 
  correlating 
  the 
  difference 
  

   between 
  members 
  of 
  a 
  pair 
  with 
  the 
  mean 
  value 
  of 
  the 
  pair 
  and 
  it 
  was 
  found 
  

   that 
  the 
  correlation 
  in 
  the 
  series 
  tested 
  was 
  not 
  significant 
  with 
  respect 
  to 
  its 
  

   error 
  of 
  sampling. 
  The 
  first 
  assumption, 
  despite 
  its 
  unsound 
  theoretical 
  

   basis, 
  had 
  to 
  be 
  retained 
  owing 
  to 
  the 
  impossibility 
  of 
  estimating 
  satisfactorily 
  

   the 
  extent 
  of 
  the 
  correlation 
  mentioned. 
  In 
  the 
  case 
  before 
  us 
  we 
  have 
  two 
  

   variables, 
  viz., 
  the 
  CO2 
  readings 
  and 
  the 
  2 
  readings, 
  and 
  the 
  error 
  in 
  the 
  

   final 
  estimation 
  of 
  calories 
  expended 
  is 
  a 
  function 
  of 
  the 
  errors 
  in 
  each 
  

   reading 
  and 
  the 
  error 
  correlation 
  between 
  CO2 
  and 
  2 
  readings 
  (a 
  correlation 
  

   which 
  will 
  be 
  in 
  general 
  negative 
  for 
  if, 
  for 
  instance, 
  between 
  the 
  analyses 
  a 
  

   leak 
  has 
  occurred, 
  which 
  might 
  easily 
  happen, 
  the 
  C0 
  2 
  reading 
  will 
  go 
  down 
  

   and 
  the 
  2 
  reading 
  go 
  up). 
  The 
  square 
  roots 
  of 
  the 
  mean 
  square 
  errors 
  (calcu- 
  

   lated 
  on 
  the 
  above 
  assumptions) 
  and 
  the 
  correlation 
  in 
  error 
  of 
  oxygen 
  and 
  

   carbonic 
  acid 
  measurements 
  were 
  estimated 
  twice, 
  in 
  the 
  first 
  case 
  upon 
  23 
  

   paired 
  analyses 
  including 
  results 
  of 
  both 
  C. 
  H. 
  and 
  A. 
  E. 
  T., 
  in 
  the 
  second 
  case 
  

   upon 
  15 
  pairs 
  in 
  which 
  both 
  analyses 
  were 
  the 
  work 
  of 
  C. 
  H. 
  Since 
  the 
  

   majority 
  of 
  the 
  analyses 
  used 
  for 
  calculation 
  were 
  due 
  to 
  C. 
  H., 
  more 
  weight 
  

   was 
  assigned 
  to 
  the 
  latter 
  series 
  which 
  did 
  not, 
  however, 
  differ 
  very 
  greatly 
  

   from 
  the 
  former 
  except 
  in 
  giving 
  a 
  lower 
  value 
  for 
  the 
  standard 
  deviations 
  of 
  

   the 
  oxygen 
  errors 
  and 
  a 
  somewhat 
  lower 
  value 
  of 
  the 
  negative 
  correlation 
  

   between 
  errors 
  of 
  C0 
  2 
  and 
  errors 
  of 
  2 
  estimates. 
  We 
  reproduce 
  the 
  second 
  

   set 
  of 
  data 
  (Table 
  I). 
  From 
  these 
  errors, 
  the 
  errors 
  of 
  all 
  the 
  subsequently 
  

   computed 
  averages 
  (respiratory 
  quotient, 
  2 
  use, 
  etc.) 
  can 
  be 
  deduced 
  by 
  

   algebraical 
  reductions, 
  and 
  we 
  finally 
  reached 
  the 
  result 
  that 
  the 
  error 
  of 
  

   estimate 
  for 
  the 
  important 
  constant, 
  viz., 
  the 
  calorie 
  use 
  per 
  minute, 
  was 
  of 
  

   the 
  order 
  of 
  2 
  per 
  cent. 
  This 
  result 
  is 
  in 
  good 
  accord 
  with 
  the 
  estimate 
  

   of 
  C. 
  H.'s 
  working 
  error 
  reached 
  by 
  a 
  quite 
  different 
  route. 
  Two 
  samples 
  of 
  

  

  