General Full Factorial Design

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Presentation transcript:

General Full Factorial Design Dedy Sugiarto

Case 2 : Time to boil water experiment For example, we may want to investigate the influence of pan size and cover on the time in minute to boil water. We use general full factorial design and completely randomize design or without blocking of experimental unit. Single. There are two-level for each factor and 3 replications for each combination. Dimensions of small pan is 14 cm for diameter and 10 cm for height. Dimensions of medium pan is 18 cm for diameter and 11 cm for height. Volume of water is 600 ml.

Randomization using Minitab : RunOrder pan size cover time (minutes) 1 medium no 2 small yes 3 4 5 6 7 8 9 10 11 12

Picture 5. Medium pan with cover on Picture 4. Small pan, medium pan and glass cover Picture 5. Medium pan with cover on stove

The results of experiment : RunOrder pan size cover time (minutes) 1 medium no 3.92 2 small yes 3.07 3 3.00 4 3.53 5 3.63 6 3.83 7 3.20 8 3.22 9 3.75 10 3.98 11 3.50 12 3.60

Minitab Output : General Linear Model: time (minutes) versus pan size, cover Factor Type Levels Values pan size fixed 2 small, medium cover fixed 2 yes, no Analysis of Variance for time (minutes), using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P pan size 1 0.29768 0.29768 0.29768 4.90 0.058 cover 1 0.22141 0.22141 0.22141 3.65 0.093 pan size*cover 1 0.20021 0.20021 0.20021 3.30 0.107 Error 8 0.48560 0.48560 0.06070 Total 11 1.20489 S = 0.246374 R-Sq = 59.70% R-Sq(adj) = 44.58% Unusual Observations for time (minutes) time Obs (minutes) Fit SE Fit Residual St Resid 7 3.20000 3.67000 0.14224 -0.47000 -2.34 R R denotes an observation with a large standardized residu

Interpreting the Results : The small p-values for the pan size (p = 0.058) and cover (p = 0.093) that lower than α (0.10) suggest there is enough significant effect of pan size and cover on time to boil water. Interaction of pan size and cover is not significant. Mean plot of rensponse suggests that small and cover (yes) give lower time to boil water .