1 / 33

330 likes | 449 Views

Chapter 6 The 2 k Factorial. The Essentials of 2-Cubed Designs. Methodology Cube Plots Estimating Main Effects Estimating Interactions (Interaction Tables and Graphs) Statistical Significance (Effects Probability Plots) Example With Interactions A U-Do-It Case Study.

Download Presentation
## Chapter 6 The 2 k Factorial

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**The Essentials of 2-Cubed Designs**• Methodology • Cube Plots • Estimating Main Effects • Estimating Interactions (Interaction Tables and Graphs) • Statistical Significance (Effects Probability Plots) • Example With Interactions • A U-Do-It Case Study**Methodology Example 2**• Looking For Patterns In The Data To Discover How The Factors Affect The Response, y.**Methodology Example 2 - Estimating the Main Effect of A**• Take the Difference of the Average Response for A+ and A- • Eliminate Those Edges of the Cube Where Going from One Cube Corner to Another Involves Changing A from- to + • Average the Corners on the Common Faces and Difference • A=[(70+71+72+73)/4] -[(66+66+68+66)/4] = 71.5-66.5 = 5**Methodology Example 2 - Signs Table**• The Signs of the Main Effects Give The Recipes For the 8 Runs in the Design • Actual Run Corresponds to the Order of the Experimental Runs (Recipes)**MethodologyExample 2 - Signs TableUsed to Calculate Effects**• To Estimate the Main Effects • Multiply the Response y by the Corresponding Sign Column • Sum the Column • Divide the Sum by the Divisor to Get the Estimated Main Effect • U-Do-It • Calculate the Main Effects Due to B and to C**Methodology Example 2 - Estimating the Effect of A Another**Way**Methodology Example 2 - Estimating the Effect of A Another**Way • Average the Differences of A+and A- Over All the Combinations of B and C. • Retain Those Edges of the Cube Where Going from One Cube Corner to Another Involves Changing A from - to + • Difference These Corners and Average • [(72-68)+(71-66)+(73-66) +(70-66)]/4 = 20/4 = 5**MethodologyExample 2 - Estimating the Effect of the AB**Interaction • Average • The Four Values in the Shaded Corners • The Four Values in the Unshaded Corners • Difference the Averages • [(71+72 +66+66)/4] -[(70+73+66+68)/4]=68.75-69.25=-.5**MethodologyExample 2 - Estimating the Effect of the AB**Interaction Another Way • The Second Way Shows that the AB Interaction is Comparing the Differences in going from A- to A+ at B- and B+. • If there is a “Significant” Difference, then A and B are said to Interact • [(71-66)+(72-68)-(73-66)-(70-66)]/4 = -0.5 • In this example, there are no significant interactions. Thus, the interpretation is straightforward. • WARNING: When a higher order interaction is “significant,” the direct interpretation of lower order interactions and main effects is misleading.**Methodology Example 2 - Signs TableCalculating the Signsand**the Effect of Interaction AB**MethodologyExample 2 - Signs TableU-Do-It**• Calculate the Signs for Interactions AC, BC and ABC • Calculate These Interaction Effects**MethodologyExample 2 - Discussion**• Only the Main Effect A is Significant • Set A Hi to Maximize y • Set A Lo to Minimize y • This Data is Real and Will be Considered in Later Sections • For This Data Minimizing y is the Objective**MethodologyExample 2 - Estimating the Response**• Since Only the Main Effect A is Significant The Estimated Mean Response (EMR) is given by EMR = y + (Sign of A)(Effect of A)/2 = 69 + (Sign of A)5/2 • For A Lo, EMR = 69 + (-1)(2.5) = 66.5 • For A Hi, EMR = 69 + (+1)(2.5) =71.5**MethodologyExample 2 - Estimating the ResponseWhy the**One-Half? • The Formula Gives You Just What You Expect: The Average Response at that Level of the A • For A Lo, EMR = 69 + (-1)(2.5) = 66.5 = (66 +66 +66 +68)/4 • For A Hi, EMR = 69 + (+1)(2.5) =71.5 = (70 + 71 + 73 +72)/4**II. SummaryKey Ideas**• Use Sign Tables to Estimate Effects • Use Probability Plots to Identify Significant Effects • Interaction Tables and Graphs are Used to Analyze Significant Interactions(To be explained later)**II. SummaryConcluding Comments**• A Main Effect Is Easy To Interpret When There Are No Significant Interactions Involving It • In The Presence of a Significant Higher-Order Interaction, the Lower-Order Interactions and Corresponding Main Effects Are Hard To Interpret by Themselves. (You Still Can Figure Out What to Do, Though) • The Size of the Effects You are Trying to Detect and the Noise of the Process (How Much Variation It Has) Will Dictate How Much Replication Is Needed

More Related