NPLOT Normal probability plot of effects CALL: nplot(ef,id) ef = vector of average response, main effects and interaction effects in the order given in id. id = identification vector of main and interaction effects. (default is standard order as given from the output of YATES) Two problems arise in the assessment of effects from unreplicated factorials: 1) occassionally real and meaningful high-order interactions occur, and 2) it is necessary to allow for selection. However, NPLOT by which effects are plotted on normal probability paper often provides an effective way of overcoming both difficulties. In the example below 3 effects with effects close to zero fit reasonably on a straight line. Those corresponding to A, B and AC do not. Conclusion: these effects are not easily explained as chance of occurences. Example: y = [60 72 54 68 52 83 45 80]; % Responses to design D. [ef,id] = yates(y); nplot(ef,id) See also yates

- range
- wnorminv
- yates
- cat
- cellstr
- deal
- diff
- error
- hold
- mean
- num2str
- plot
- text
- xlabel
- ylabel

Calculates the difference between the maximum and minimum values. | |

Inverse of the Normal distribution function | |

Calculates main and interaction effects using Yates' algorithm. | |

Concatenate arrays. | |

Create cell array of strings from character array. | |

Deal inputs to outputs. | |

Difference and approximate derivative. | |

Display message and abort function. | |

Hold current graph. | |

Average or mean value. | |

Convert number to string. (Fast version) | |

Linear plot. | |

Text annotation. | |

X-axis label. | |

Y-axis label. |

001 function h= nplot(ef,id,offset) 002 %NPLOT Normal probability plot of effects 003 % 004 % CALL: nplot(ef,id) 005 % 006 % ef = vector of average response, main effects and interaction effects 007 % in the order given in id. 008 % id = identification vector of main and interaction effects. 009 % (default is standard order as given from the output of YATES) 010 % 011 % Two problems arise in the assessment of effects from unreplicated 012 % factorials: 1) occassionally real and meaningful high-order 013 % interactions occur, and 2) it is necessary to allow for selection. 014 % However, NPLOT by which effects are plotted on normal probability paper 015 % often provides an effective way of overcoming both difficulties. 016 % 017 % In the example below 3 effects with effects close to zero fit 018 % reasonably on a straight line. Those corresponding to A, B and AC do 019 % not. Conclusion: these effects are not easily explained as chance of 020 % occurences. 021 % 022 % Example: 023 % y = [60 72 54 68 52 83 45 80]; % Responses to design D. 024 % [ef,id] = yates(y); 025 % nplot(ef,id) 026 % 027 % See also yates 028 029 % Reference 030 % Daniel, C. (1959) 031 % Use of half-normal plot in interpreting factorial two-level 032 % experiments, Technimetrics, Vol 1, No 149. 033 % Daniel, C. (1976) 034 % Applications of statistics to Industrial Experimentation. 035 036 error(nargchk(1,3,nargin)) 037 sz = size(ef); 038 n = length(ef); 039 if prod(sz)==n, 040 ef = ef(:); 041 else 042 n = sz(1); 043 end 044 045 046 if nargin<2|isempty(id) 047 % Make a list of all possible main effects and interaction effects 048 %------------------------------------------------------------------ 049 [y,id]= yates(ef); 050 end 051 % Secret option 052 if nargin<3|isempty(offset),offset = range(ef(2:end,:))/(3*n);end 053 [eff, ind] = sort(ef(2:end,:)); 054 055 id = id(ind,:); 056 F = (0.5:n-1.5)'/(n-1); 057 nscore = wnorminv(F); % Normal score 058 ind = (diff(eff)==0); 059 ind = find(([0;ind] | [ind; 0])==0); 060 h1 = plot(eff(ind),nscore(ind),'.'); 061 h2 = text(eff(ind)+offset,nscore(ind),id(ind,:),... 062 'HorizontalAlignment','left','VerticalAlignment','middle'); 063 eff(ind) = []; 064 065 if ~isempty(eff) 066 nscore(ind) = []; 067 id(ind,:) = []; 068 iy = 1; 069 ne = length(eff); 070 hold on 071 for ix=2:ne 072 iy = iy+1; 073 if ix==ne |eff(ix) ~= eff(ix+1), 074 tmp = mean(nscore(ix-iy+1:ix)); 075 h1 = [h1 ; plot(eff(ix),tmp,'k.')]; 076 %h1 = text(eff(ix),tmp,num2str(iy)); 077 tmp2 = cellstr(id(ix-iy+1:ix,:)).'; 078 [tmp2{2,1:iy-1}] = deal(', '); 079 tmp2{2,iy} = ' '; 080 h2 = [h2;text(eff(ix)+offset/2,tmp,cat(2,[num2str(iy) ' '],tmp2{:}),... 081 'HorizontalAlignment','left','VerticalAlignment','middle')]; 082 083 iy = 0; 084 end 085 end 086 hold off 087 end 088 if nargout>0, 089 h = [h1;h2]; 090 end 091 xlabel('Effect') 092 ylabel('Nscore') 093 094 095 096

Mathematical Statistics

Centre for Mathematical Sciences

Lund University with Lund Institute of Technology

Comments or corrections to the WAFO group

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