Question

c) Compute or find the average effect for each main efflect (factor) and each interaction (Data set is FADE)A manufacturer of telephones was experiencing difficulties with the ability of the shell of the telephone to resist fading of its color. A manufacturing engineer determined that three factors can be studied to determine their effect on color fading, as measured with a photoelectric spectrometer. (The lower the reading, the higher the stability of the color.) The three factors were color (red versus pink), temperature (100°F versus 300°F), and amount of light (obscure versus bright). The results are summarized in the following table: 1. Color (Factor A) Temperature (F (Factor B) Light (Factor C Spectrometer Reading 212 215 983 920 1,090 945 1,253 1,375 Obscure Obscure Obscure Bright 100 100 300 100 300 100 300 300 Red Pink Red Red Pink Pink Red Pink Obscure Bright Bright Bright How many treatment combinations are possible for this problem? a) Use MINITAB to obtain the ANOVA and using a 0.05 level of significance, determine which factors are significant. b) c) Compute or find the average effect for each main effect (factor) and each interaction. Use MINITAB to set up a normal probability plot of the main effects and interactions effects and determine which effects are significant. d)

Answer 1

a) We have 2 levels of each treatment, so we can have 2*2*2 =8 combinations of treatments.

b)

General Linear Model: Spectrometer versus Color(Factor, Temprature(, .. Factor Color (Factor A) Temprature(F) (Factor B) fixed Light (Factor C) Type Levels Values fixed 2 Pink, Red 2 100, 300 2 Bright, obscure fixed Analysis of Variance for Spectrometer Reading, using Adjusted SS for Tests Source Color (Factor A) Temprature("F) (Factor B) 1 725410 725410 725410 28.26 0.006 Light (Factor C) Error Total DF Seq SS Adj SS Adj MS 8256 8256 8256 0.32 0.601 1 496506 496506 496506 19.34 0.012 4 102688 102688 25672 7 1332861 S 160.225 R-Sq 92.30% R-Sq (adj ) -86.52% -

At 5% level of significance Light and Temperature are significant. Colour has p-value of 0.601 >0.05. So it is not significant.

c)

Analysis of Variance for Spectrometer Reading, using Adjusted SS for Tests Source Color (Factor A) Temprature("F) (Factor B) Light (Factor C) Color (Factor A)* DF Seq SS Adj SS Adj MS 8256 8256 8256 1347.94 0.017 1 725410 725410 725410 118434.31 0.002 1 496506 496506 496506 81062.22 0.002 824.51 0.022 5050 5050 5050 Temprature("F) (Factor B) Temprature("F) (Factor B) 1 97461 97461 97461 15912.02 0.005 Light (Factor C) Color (Factor A) *Light (Factor C) Error Total 1 27.94 0.119 7 1332861

d)

Interaction Plot for Spectrometer Reading Fitted Means 300 Bright Obscure uN) Color(Factor A) Pink 1200 Red 800 Color(Factor A) Temprature( F) (Factor B) 1200 800 300 TempratureF) (Factor B 400 Light(Factor C)

Main Effects Plot for Spectrometer Reading Fitted Means 1250 1000 750 Pink Red 100 300 1250 1000 750 500 Obscure Bright