From VOC to IPA: This Beer s For You! Joel Smith Statistician Minitab Inc. jsmith@minitab.com 2013 Minitab, Inc.
Image courtesy of amazon.com
The Data Online beer reviews Evaluated overall and: Appearance Aroma Palate Taste Focus on American Porters 2013 Minitab, Inc.
The Data Text counter for descriptive terms i.e. THICK, COFFEE, BLACK Most common became variables Initial cleansing 2013 Minitab, Inc.
Count Chart of Citations 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Citations
Descriptive Statistics: HEAD, DARK, BROWN, BLACK, COFFEE, TAN, LIGHT, LACING,... Variable Mean Minimum Q1 Median Q3 Maximum HEAD 0.88731 0.62500 0.86111 0.89189 0.92708 1.00000 DARK 0.62370 0.23077 0.57576 0.63043 0.68182 0.91667 BROWN 0.61144 0.23529 0.54545 0.61194 0.68421 0.94444 BLACK 0.48373 0.00000 0.35294 0.50000 0.60556 0.95000 COFFEE 0.3561 0.0000 0.2188 0.3500 0.4667 0.9474 TAN 0.43249 0.08333 0.37398 0.43478 0.48276 0.84615 BOURBON 0.03454 0.00000 0.00000 0.00000 0.00000 0.80556 FRUITx 0.06493 0.00000 0.02646 0.05634 0.08696 0.40000 SMOKEx 0.1412 0.0000 0.0323 0.0649 0.1250 0.8500 BITTERx 0.11349 0.00000 0.05882 0.10784 0.16197 0.36842 SWEETx 0.22135 0.00000 0.15217 0.21053 0.28049 0.65217
Are American Porters Homogenous? Image courtesy of drinks.seriouseats.com
2013 Minitab, Inc. Stat > Multivariate > Cluster K-Means
K-means Cluster Analysis: HEAD, DARK, BROWN, BLACK, COFFEE, TAN, LIGHT, LACING, THICK, CARAMEL, VANILLA, OPAQUE, WHITE, SMOOTH, STRO Standardized Variables Final Partition Number of clusters: 2 Average Maximum Within distance distance Number of cluster sum from from observations of squares centroid centroid Cluster1 194 7847.713 6.067 10.928 Cluster2 132 5557.371 6.141 12.055 Distances Between Cluster Centroids Cluster1 Cluster2 Cluster1 0.0000 3.3753 Cluster2 3.3753 0.0000
Cluster Centroids Grand Variable Cluster1 Cluster2 centroid HEAD 0.0031-0.0046 0.0000 DARK -0.1523 0.2238-0.0000 BROWN -0.3743 0.5501 0.0000 BLACK 0.5733-0.8426-0.0000 COFFEE 0.1443-0.2121-0.0000 DENSE 0.0573-0.0843 0.0000 BROWNISH -0.0066 0.0096 0.0000 SOUR 0.0407-0.0598 0.0000 BUBBLY 0.0975-0.1433-0.0000 WOOD 0.0039-0.0057 0.0000 HOPx -0.2007 0.2950 0.0000
Cluster 1 Cluster 2 BLACK MOCHA OPAQUE THICK ESPRESSO ALCOHOL COFFEE MILK LIGHT CLEAR BROWN AMBER MAHOGANY WHITE BEIGE HOPX NUTTY MILD CARAMEL DRY DARK TOASTED 2013 Minitab, Inc.
What Are Customers Differentiating? Image courtesy of finedininglovers.com
2013 Minitab, Inc. Stat > Multivariate > Principal Components
Variable PC1 PC2 PC3 PC4 PC5 HEAD 0.034 0.025 0.063-0.445-0.121 DARK 0.101-0.068-0.054-0.234-0.031 BROWN 0.254 0.047 0.103-0.250-0.069 BLACK -0.404 0.013 0.029-0.004-0.008 COFFEE -0.122-0.302-0.283-0.033-0.115 TAN 0.037 0.034-0.101-0.325 0.243 LIGHT 0.266-0.095-0.101 0.025-0.002 BROWNISH 0.068 0.042 0.206-0.156-0.106 SOUR 0.010 0.075 0.012 0.051 0.199 BUBBLY -0.022-0.126 0.048 0.099 0.146 WOOD -0.017 0.219 0.120 0.188 0.192 HOPx 0.134-0.287 0.135-0.025-0.039
Principal Component Analysis: HEAD, DARK, BROWN, BLACK, COFFEE, TAN, LIGHT, LACING, THICK, CARAMEL, VANILLA, OPAQUE, WHITE, SMOOTH, Eigenanalysis of the Correlation Matrix Eigenvalue 4.2617 2.5063 2.0396 1.7995 1.6684... Proportion 0.097 0.057 0.046 0.041 0.038... Cumulative 0.097 0.154 0.200 0.241 0.279...
Eigenvalue Scree Plot of HEAD,..., HOPx 4 3 2 1 0 1 5 10 15 20 25 30 35 40 Component Number
Second Component Loading Plot of HEAD,..., HOPx 0.3 VANILLA 0.2 WOOD LACING SUGAR WHITE 0.1 0.0-0.1 BLACK SOUR ALCOHOL FLUFFY BROWNISH BUBBLES TAN BEIGE MAHOGANY BROWN HEAD STRONG CLEAR MOLASSES DENSE OPAQUE DARK AMBER MOCHA NUTTY EARTHY LIGHT THICK ESPRESSO HEAVY STICKY BUBBLY MILD MILK CARBONATION TOFFEE CARAMEL -0.2-0.3 BURNT SMOOTH COFFEE TOASTED DRY HOPx CHOCOLATE -0.4-0.5-0.4-0.3-0.2-0.1 0.0 First Component 0.1 0.2 0.3 0.4
2013 Minitab, Inc. Stat > Regression > Regression > Best Subsets
Best Subsets Regression: Overall versus Appearance, Aroma, Palate, Taste Response is Overall A p p e a P r A a T a r l a n o a s R-Sq R-Sq c m t t Vars R-Sq (adj) PRESS (pred) Mallows Cp S e a e e 1 91.2 91.2 2.5 91.1 13.8 0.087905 X 1 81.7 81.7 5.3 81.4 377.1 0.12684 X 1 68.8 68.7 9.0 68.4 870.3 0.16565 X 1 57.4 57.3 12.3 56.8 1305.9 0.19355 X 2 91.4 91.4 2.5 91.3 8.0 0.087015 X X 2 91.3 91.3 2.5 91.1 12.2 0.087565 X X 2 91.2 91.2 2.6 91.0 15.7 0.088033 X X 2 82.5 82.3 5.1 81.9 350.9 0.12444 X X 2 81.7 81.6 5.3 81.3 379.1 0.12703 X X 3 91.6 91.5 2.5 91.4 3.0 0.086214 X X X 3 91.4 91.4 2.5 91.2 8.9 0.086998 X X X 3 91.3 91.2 2.5 91.1 13.7 0.087640 X X X 3 82.5 82.3 5.2 81.8 352.0 0.12456 X X X 4 91.6 91.5 2.5 91.3 5.0 0.086349 X X X X
Regression Analysis: Overall versus Appearance, Aroma, Palate, Taste Stepwise Selection of Terms α to enter = 0.05, α to remove = 0.05 The stepwise procedure added terms during the procedure in order to maintain a hierarchical model at each step. Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 3 26.1102 8.70341 1170.93 0.000 Aroma 1 0.0832 0.08325 11.20 0.001 Palate 1 0.0522 0.05222 7.03 0.008 Taste 1 2.6086 2.60861 350.95 0.000 Error 322 2.3934 0.00743 Total 325 28.5036 Model Summary S R-sq R-sq(adj) R-sq(pred) 0.0862144 91.60% 91.52% 91.37%
What are the characteristics of the best porter? Image courtesy of beerandbrewing.com
2013 Minitab, Inc. Stat > Regression > Regression > Fit Regression Model
HI Individual Value Plot of HI 0.30 0.25 0.20 0.15 0.10 0.05 0.00
HI_2 Individual Value Plot of HI_2 0.12 0.10 0.08 0.06 0.04 0.02 0.00
Regression Analysis: Taste versus ABV, HEAD, DARK, BROWN, BLACK, COFFEE, TAN, LIGHT,... Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 6 11.4860 1.91433 31.40 0.000 ABV 1 2.1544 2.15437 35.33 0.000 BLACK 1 1.3679 1.36792 22.43 0.000 THICK 1 0.4965 0.49647 8.14 0.005 CARAMEL 1 0.3403 0.34030 5.58 0.019 SMOOTH 1 0.8143 0.81431 13.36 0.000 SOUR 1 0.6925 0.69250 11.36 0.001 Error 280 17.0725 0.06097 Total 286 28.5585 Model Summary S R-sq R-sq(adj) R-sq(pred) 0.246928 40.22% 38.94% 36.89%
Regression Analysis: Taste versus ABV, BLACK, THICK, CARAMEL, SMOOTH, SOUR Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 7 12.0431 1.72044 29.06 0.000 ABV 1 1.8707 1.87071 31.60 0.000 BLACK 1 1.9144 1.91436 32.34 0.000 THICK 1 0.4240 0.42398 7.16 0.008 SMOOTH 1 0.8472 0.84720 14.31 0.000 SOUR 1 0.9757 0.97565 16.48 0.000 SOUR*SOUR 1 0.7480 0.74802 12.64 0.000 SMOOTH*SOUR 1 0.3530 0.35297 5.96 0.015 Error 279 16.5154 0.05920 Total 286 28.5585 Model Summary S R-sq R-sq(adj) R-sq(pred) 0.243300 42.17% 40.72% 38.29%
Coded Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 3.8227 0.0162 235.43 0.000 ABV 0.0903 0.0161 5.62 0.000 1.25 BLACK 0.0952 0.0167 5.69 0.000 1.35 THICK 0.0422 0.0158 2.68 0.008 1.20 SMOOTH 0.0564 0.0149 3.78 0.000 1.07 SOUR -0.1147 0.0283-4.06 0.000 3.86 SOUR*SOUR 0.02772 0.00780 3.55 0.000 4.05 SMOOTH*SOUR 0.0446 0.0183 2.44 0.015 1.51
Mean of Taste ABV Main Effects Plot for Taste Fitted Means BLACK THICK SMOOTH SOUR 4.1 4.0 3.9 3.8 3.7 3.6 4 8 12 0.0 0.5 1.00.0 0.2 0.40.00 0.15 0.30 0.00 0.15 0.30
Matrix Plot of ABV, BLACK, THICK, SMOOTH, SOUR 12 0.0 0.5 1.0 0.00 0.15 0.30 8 ABV 4 1.0 BLACK 0.5 0.4 0.0 0.2 THICK 0.0 0.30 SMOOTH 0.15 0.30 0.00 0.15 SOUR 0.00 4 8 12 0.0 0.2 0.4 0.00 0.15 0.30
Matrix Plot of ABV, BLACK, THICK, SMOOTH, SOUR 12 0.0 0.5 1.0 0.00 0.15 0.30 8 ABV 4 1.0 BLACK 0.5 0.4 0.0 0.2 THICK 0.0 0.30 SMOOTH 0.15 0.30 0.00 0.15 SOUR 0.00 4 8 12 0.0 0.2 0.4 0.00 0.15 0.30
2013 Minitab, Inc. Stat > Regression > Regression > Response Optimizer
Response Optimization: Taste Parameters Response Goal Lower Target Upper Weight Importance Taste Maximum 2.61628 4.65 1 1 Solution Taste Composite Solution ABV BLACK THICK SMOOTH SOUR Fit Desirability 1 12.2 0.95 0.392857 0.24 0 4.73742 1 95% Lower 95% Lower Confidence Prediction Response Fit SE Fit Bound Bound Taste 4.7374 0.0891 4.5903 4.3098
So what does a great porter taste like? Image courtesy of deschutesbrewery.com
Summary Data cleaning Graphical analysis, descriptive statistics + manual review Examine homogeneity Clustering + sensory test Differentiation Principal components, regression Optimization Regression Verification Beer drinking 2013 Minitab, Inc.
From VOC to IPA: This Beer s For You! Joel Smith Statistician Minitab Inc. jsmith@minitab.com 2013 Minitab, Inc.