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ryates

PURPOSE ^

Reverse Yates' algorithm to give estimated responses

SYNOPSIS ^

[y, id]=ryates(ef)

DESCRIPTION ^

 RYATES Reverse Yates' algorithm to give estimated responses
 
  CALL:  y = ryates(ef);
 
   y  = Estimated response given the effects.
   ef = vector of average response, main effects and interaction effects.
 
  RYATES applies the reverse Yates' algorithm to the effect EF to obtain 
  the estimated response. EF is assumed to
  be arranged in what is called standard order. (The order of the actual
  running should, of course, be random).  EF(1,:) is the
  average response and EF(2:end,:) contain the main effects and
  interaction effects.
 
  Example:
    D = ffd(3);                    % complete 2^3 design in standard order.
    y = [60 72 54 68 52 83 45 80]; % Responses to design D.
    [ef,id] = yates(y);
    y1 = ryates(ef);               % gives the same as Y
 
  See also  ffd

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [y, id]=ryates(ef)
002 %RYATES Reverse Yates' algorithm to give estimated responses
003 %
004 % CALL:  y = ryates(ef);
005 %
006 %  y  = Estimated response given the effects.
007 %  ef = vector of average response, main effects and interaction effects.
008 %
009 % RYATES applies the reverse Yates' algorithm to the effect EF to obtain 
010 % the estimated response. EF is assumed to
011 % be arranged in what is called standard order. (The order of the actual
012 % running should, of course, be random).  EF(1,:) is the
013 % average response and EF(2:end,:) contain the main effects and
014 % interaction effects.
015 %
016 % Example:
017 %   D = ffd(3);                    % complete 2^3 design in standard order.
018 %   y = [60 72 54 68 52 83 45 80]; % Responses to design D.
019 %   [ef,id] = yates(y);
020 %   y1 = ryates(ef);               % gives the same as Y
021 %
022 % See also  ffd
023 
024 
025 
026 % Reference 
027 % Box, G.E.P, Hunter, W.G. and Hunter, J.S. (1978)
028 % Statistics for experimenters, John Wiley & Sons, pp 342
029 
030 % Tested on: Matlab 5.3
031 % History:
032 % By Per A. Brodtkorb 16.03.2001
033 
034 error(nargchk(1,2,nargin))
035 sz = size(ef);
036 n  = length(ef); 
037 if prod(sz) == n, 
038   ef = ef(:);       % Make sure it is a column vector
039 else   
040   n = sz(1);        % Number of runs
041 end
042 
043 k = log2(n);      % Number of variables.
044 if round(k)~=k, error('The length of EF must be in power of two'), end
045 
046 % Reverse yates algorithm:
047 y      = ef*(n/2);
048 y(1,:) = y(1,:)*2;
049 if nargout>1,
050   [y,id] = yates(flipud(y));
051 else
052   y = yates(flipud(y));
053 end
054 y = flipud(y)/2;
055 y(end,:) = y(end,:)*2;
056 
057 
058 return
059 
060 
061 
062 
063

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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