Developing New Products

Analysis for a Field Test of Laundry Soaps

Loading required packages and data:

Examine data frame

'data.frame':   1008 obs. of  4 variables:
 $ choice: Factor w/ 2 levels "M","X": 2 2 2 2 2 2 2 2 2 2 ...
 $ muser : Factor w/ 2 levels "NO","YES": 1 1 1 1 1 1 1 1 1 1 ...
 $ wtemp : Factor w/ 2 levels "HIGH","LOW": 2 2 2 2 2 2 2 2 2 2 ...
 $ wtype : Factor w/ 3 levels "HARD","MEDIUM",..: 1 1 1 1 1 1 1 1 1 1 ...
NULL

Output of first few observations:

Peek at last few observations:

, , muser = NO, choice = M

      wtype
wtemp  HARD MEDIUM SOFT
  HIGH   30     23   27
  LOW    42     50   53

, , muser = YES, choice = M

      wtype
wtemp  HARD MEDIUM SOFT
  HIGH   43     47   29
  LOW    52     55   49

, , muser = NO, choice = X

      wtype
wtemp  HARD MEDIUM SOFT
  HIGH   42     33   29
  LOW    68     66   63

, , muser = YES, choice = X

      wtype
wtemp  HARD MEDIUM SOFT
  HIGH   24     23   19
  LOW    37     47   57

Summary of fit model of experimental design with interactions:

Call:  glm(formula = soaps_model, family = binomial, data = soaps)

Coefficients:
                  (Intercept)                       muserYES                       wtempLOW  
                      0.33647                       -0.91962                        0.14537  
                  wtypeMEDIUM                      wtypeSOFT              muserYES:wtempLOW  
                      0.02454                       -0.26501                        0.09745  
         muserYES:wtypeMEDIUM             muserYES:wtypeSOFT           wtempLOW:wtypeMEDIUM  
                     -0.15605                        0.42530                       -0.22875  
           wtempLOW:wtypeSOFT  muserYES:wtempLOW:wtypeMEDIUM    muserYES:wtempLOW:wtypeSOFT  
                     -0.04398                        0.54339                        0.37525  

Degrees of Freedom: 1007 Total (i.e. Null);  996 Residual
Null Deviance:      1397 
Residual Deviance: 1364     AIC: 1388

Analysis of deviance (ANOVA) for experimental factors

Analysis of Deviance Table

Model: binomial, link: logit

Response: choice

Terms added sequentially (first to last)

                  Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
NULL                               1007     1397.3              
muser              1  20.5815      1006     1376.7 5.715e-06 ***
wtemp              1   3.8002      1005     1372.9   0.05125 .  
wtype              2   0.2160      1003     1372.7   0.89763    
muser:wtemp        1   2.7328      1002     1370.0   0.09831 .  
muser:wtype        2   4.5961      1000     1365.4   0.10045    
wtemp:wtype        2   0.1618       998     1365.2   0.92228    
muser:wtemp:wtype  2   0.7373       996     1364.5   0.69166    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Generating an interaction plot for brand X choice as a percentage