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Bread Example: nknw817.sas

This study investigates the effects of shelf display height (bottom, middle, top) and width (regular, wide) on bread sales using ANOVA and various statistical plots. Data is analyzed through multiple models to determine whether display height, width, and their interaction significantly affect sales performance. Residual diagnostics, normality checks, and interaction plots are also explored, providing comprehensive insights into consumer purchasing behaviors based on display strategies. This analysis is crucial for optimizing shelf space in retail environments.

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Bread Example: nknw817.sas

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  1. Bread Example: nknw817.sas Y = number of cases of bread sold (sales) Factor A = height of shelf display (bottom, middle, top) Factor B = width of shelf display (regular, wide) n = 2 (nT = 12)

  2. Bread Example: input data bread; infile'I:\My Documents\Stat 512\CH19TA07.DAT'; input sales height width; procprintdata=bread; run; title1h=3'Bread Sales'; axis1label=(h=2); axis2label=(h=2angle=90);

  3. Bread Example: input scatterplot data bread; set bread; if height eq1 and width eq1then hw='1_BR'; if height eq1 and width eq2then hw='2_BW'; if height eq2 and width eq1then hw='3_MR'; if height eq2 and width eq2then hw='4_MW'; if height eq3 and width eq1then hw='5_TR'; if height eq3 and width eq2then hw='6_TW'; title2h=2'Sales vs. treatment'; symbol1v=circle i=nonec=blue; procgplotdata=bread; plot sales*hw/haxis=axis1 vaxis=axis2; run;

  4. Bread Example: Scatterplot

  5. Bread Example: ANOVA procglmdata=bread; class height width; model sales=height width height*width; means height width height*width; outputout=diag r=resid p=pred; run;

  6. Bread Example: ANOVA means

  7. Bread Example: Means procmeansdata=bread; var sales; by height width; outputout=avbreadmean=avsales; procprintdata=avbread; run;

  8. ANOVA Table – One Way

  9. ANOVA Table – Two Way

  10. Bread Example: Scatterplot

  11. Bread Example: diagnostics procglmdata=bread; class height width; model sales=height width height*width; means height width height*width; outputout=diag r=resid p=pred run; title2h=2'residual plots'; procgplotdata=diag; plotresid * (pred height width)/vref=0 haxis=axis1 vaxis=axis2; run; title2'normality'; procunivariatedata=diagnoprint; histogramresid/normalkernel; qqplotresid/normal (mu=estsigma=est); run;

  12. Bread Example: Residual Plots

  13. Bread Example: Normality

  14. ANOVA Table – Two Way

  15. Strategy for Analysis

  16. Bread Example: nknw817.sas Y = number of cases of bread sold (sales) Factor A = height of shelf display (bottom, middle, top) Factor B = width of shelf display (regular, wide) n = 2 (nT = 12) Questions: • Does the height of the display affect sales? • Does the width of the display affect sales? • Does the effect on height on sales depend on width? • Does the effect of the width depend on height?

  17. Bread Example: Interaction Plots title2'Interaction Plot'; symbol1v=square i=join c=black; symbol2v=diamond i=join c=red; symbol3v=circle i=join c=blue; procgplotdata=avbread; plotavsales*height=width/haxis=axis1 vaxis=axis2; plotavsales*width=height/haxis=axis1 vaxis=axis2; run;

  18. Bread Example: Interaction Plots (cont)

  19. Bread Example: ANOVA table procglmdata=bread; class height width; model sales=height width height*width; means height width height*width; outputout=diag r=resid p=pred; run;

  20. Bread Example: ANOVA table

  21. Bread Example: Interaction Plots (cont)

  22. Bread Example: cell means model (MSE) procglmdata=bread; class height width; model sales=height width height*width; means height width height*width; outputout=diag r=resid p=pred; run;

  23. Bread Example: cell means model procglmdata=bread; class height width; model sales=height width height*width; means height width height*width; outputout=diag r=resid p=pred; run;

  24. Bread Example: factor effects model (overall mean)

  25. Bread Example: factor effects model (overall mean) (cont) procglmdata=bread; class height width; model sales=; outputout=pmu p=muhat; procprintdata=pmu;run;

  26. Bread Example: ANOVA means A (height)

  27. Bread Example: means A (cont) procglmdata=bread; class height width; model sales=height; outputout=pA p=Amean; procprintdata = pA; run;

  28. Bread Example: ANOVA means B (width)

  29. Bread Example: ANOVA means

  30. Bread Example: Factor Effects Model (zero-sum constraints) title2'overall mean'; procglmdata=bread; class height width; model sales=; outputout=pmu p=muhat; procprintdata=pmu; run; title2 'mean for height'; procglmdata=bread; class height width; model sales=height; outputout=pA p=Amean; procprintdata = pA; run; title2'mean for width'; procglmdata=bread; class height width; model sales=width; outputout=pB p=Bmean; run; title2'mean height/ width'; procglmdata=bread; class height width; model sales=height*width; outputout=pAB p=ABmean; run; dataparmest; merge bread pmupApBpAB; alpha=Amean-muhat; beta=Bmean-muhat; alphabeta=ABmean-(muhat+alpha+beta); run; procprint;run;

  31. Bread Example: Factor Effects Model (zero-sum constraints) (cont)

  32. Bread Example: nknw817b.sas Y = number of cases of bread sold (sales) Factor A = height of shelf display (bottom, middle, top) Factor B = width of shelf display (regular, wide) n = 2 (nT = 12 = 3 x 2)

  33. Bread Example: SAS constraints procglmdata=bread; class height width; model sales=height width height*width/solution; means height*width; run;

  34. Bread Example: SAS constraints (cont)

  35. Bread Example: Means

  36. Bread Example: nknw817b.sas Y = number of cases of bread sold (sales) Factor A = height of shelf display (bottom, middle, top) Factor B = width of shelf display (regular, wide) n = 2 (nT = 12 = 3 x 2)

  37. Bread Example: Pooling *factor effects model, SAS constraints, without pooling; procglmdata=bread; class height width; model sales=height width height*width; means height/tukeylines; run; *with pooling; procglmdata=bread; class height width; model sales=height width; means height / tukeylines; run;

  38. Bread Example: Pooling (cont)

  39. Bread Example: Pooling (cont)

  40. Bread Example: ANOVA table/Means

  41. Bread Example (nknw864.sas): contrasts and estimates procglmdata=bread; class height width; model sales=height width height*width; contrast'middle vs others' height -.51 -.5 height*width -.25 -.25.5.5 -.25 -.25; estimate'middle vs others' height -.51 -.5 height*width -.25 -.25.5.5 -.25 -.25; means height*width; run;

  42. Bread Example (nknw864.sas): contrasts and estimates (cont)

  43. ANOVA Table – Two Way, n = 1

  44. Car Insurance Example: (nknw878.sas) Y = 3-month premium for car insurance Factor A = size of the city small, medium, large Factor B = geographic region east, west

  45. Car Insurance: input datacarins; infile'I:\My Documents\Stat 512\CH20TA02.DAT'; input premium size region; if size=1thensizea='1_small '; if size=2thensizea='2_medium'; if size=3thensizea='3_large '; procprintdata=carins; run;

  46. Car Insurance: Scatterplot symbol1v='E'i=join c=green height=1.5; symbol2v='W'i=join c=blue height=1.5; title1h=3'Scatterplot of the Car Insurance'; procgplotdata=carins; plot premium*sizea=region/haxis=axis1 vaxis=axis2; run;

  47. Car Insurance: ANOVA procglmdata=carins; classsizea region; model premium=sizea region/solution; meanssizea region / tukey; outputout=preds p=muhat; run; procprintdata=preds; run;

  48. Car Insurance: ANOVA (cont)

  49. Car Insurance: ANOVA (cont)

  50. Car Insurance: ANOVA (cont)

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