EXPERIMENTAL DESIGN STAT 706
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This 6 page Class Notes was uploaded by Shane Marks on Monday October 26, 2015. The Class Notes belongs to STAT 706 at University of South Carolina - Columbia taught by J. Grego in Fall. Since its upload, it has received 45 views. For similar materials see /class/229658/stat-706-university-of-south-carolina-columbia in Statistics at University of South Carolina - Columbia.
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Date Created: 10/26/15
Twolevel designs In this exercise we will focus on the analysis of an unreplicated full factorial two level design typically referred to as a 2k designik factors all crossed with two levels each I had discussed replicated designs as well but unreplicated designs have their own particular methods for inference that are quite different from methods used for replicated factorial completely randomized designs CRD7s and I would like to reinforce some of these differences with this exercise For our data set we will use a former statistics student7s Carla Padgett class project under Prof Don Edwards in which the loudness of a Violin7s note measured in deci bels was modelled as a function of 4 2 level factors This experiment was actually replicated 11 timesl but we will study the averages here and treat it as an unrepli cated experiment Table 1 Factors and Factor Levels Factor Factor Label 1 1 A Bow Speed Low High B Bow Angle Low High C Bow Placement Near Far D Pressure Low High Table 2 Responses and Runs ABCD Decibels Y 693 753 759 793 674 749 744 788 734 775 788 816 723 788 781 815 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Note that Table 2 has the data entered in the wrong77 order with the levels of Factor A varying the slowest while the levels of Factor D vary the quickest When creating the design in Minitab see Some notes on factorial designs in Minitab77 on the course website for a primer we could actually modify the way in which we specify the de sign using StatgtDDEgtFaCtorialgtCreate Customized Design lt7s easier however just to reverse the labels of the factors when using StatgtDDEgtFactoria1gtCreate Factorial Design so that we enter our Factor D as Minitab7s Factor A etc We do this by selecting the Factor button in the StatgtDDEgtFaCtoria1gtCreate Factorial Design interface after having selected a 4 factor full factorial design and then en tering information on labels and levels for our factors in reverse order After we have created the factorial design we can then enter the response variable in the Minitab worksheet in its orginal order Inspect the Minitab worksheet to make sure that both your labeling and run order are correct the Minitab worksheet should look something like this Table 3 Minitab Worksheet Bow Bow Angle Speed StdOrder RunOrder CenterPt Blocks Pressure Place Decibels With the responses entered remember to add a name to this column eg Decibels we can now analyze the design Again refer to the website for the basics on analysis be sure to select Effects li lot77 under Graphs I usually choose the Normal Effects Plot but for this demonstration I also selected the Half Normal Effects Plot You should get output in the Session window that looks like this Factorial Fit Decibels versus Pressure Bow Placement Estimated Effects and Coefficients for Decibels coded units Term Effect Coef Constant 760750 Pressure 33250 16625 Bow Placement 06250 03125 Bow Angle 9500 24750 Bow Speed 7500 23750 PressureBow Placement PressureBow Angle PressureBow Speed Bow PlacementBow Angle Bow PlacementBow Speed Bow AngleBow Speed PressureBow PlacementBow Angle 01500 00750 PressureBow PlacementBow Speed PressureBow AngleBow Speed Bow PlacementBow AngleBow Speed 02750 01375 PressureBow PlacementBow Angle 01500 00750 Bow Speed I I I I H o o o o o s 4s N U c I c N I N U 00 HO IO39I O39IO CO CO 00 DH IO39I O39IO S PRESS Analysis of Variance for Decibels coded units Source DF Seq SS Adj SS Adj MS Main Effects 4 234045 234045 585112 2 Way Interactions 6 10950 10950 18250 3 Way Interactions 4 0525 4 Way Interactions 1 0090 0090 00900 Residual Error 0 Total 15 245610 0 II M fl 0 I A I M Tj quotU Some ofthe information in the Session Window is not that interesting7 simply because we have a saturated unreplicated design With no degrees of freedom for errors7 Minitab will not produce individual standard errors and t tests for each effect7 and 3 the mom shls mu 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