Lecture 3
Download
1 / 19

Lecture 3 - PowerPoint PPT Presentation


  • 68 Views
  • Uploaded on

Lecture 3. Last Day: 1.4, 1.6, 1.7 and 1.9 Today: Finish notes from last day; Sections 2.1-2.3 Next Day: Finish 2.1-2.3 Please read these sections. You are responsible for all material in these sections…even those not discussed in class Assignment #1: Chapter 1: 11, 13, 16, 18(i).

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Lecture 3' - lucas-barnett


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Lecture 3
Lecture 3

  • Last Day: 1.4, 1.6, 1.7 and 1.9

  • Today: Finish notes from last day; Sections 2.1-2.3

  • Next Day: Finish 2.1-2.3

  • Please read these sections. You are responsible for all material in these sections…even those not discussed in class

  • Assignment #1:

    • Chapter 1: 11, 13, 16, 18(i)


Example boys shoes
Example (Boys Shoes)

  • Company wishes to run an experiment to determine if a new synthetic material is better than the existing one used for making the soles of boys' shoes

  • Experiment was run to see if the new, cheaper sole wears at the same rate at which the soles wear out

  • Have enough resources to make 10 pairs of shoes

  • How should one sun the experiment?


Are these the same

Experiment 1:

10 boys were selected at random

Each boy was given a pair of shoes

5 boys received a pair of shoes with the old sole (Sole A) and 5 boys received shoes with the the new sole (sole B)

Each boy wears the shoes for 1 month and the amount of wear is measured

Experiment 2

10 boys were selected at random

Each boy was given a pair of shoes

Each pair had 1 shoe with the old sole and 1 shoe with the new sole

For each pair of shoes, the sole type was randomly assigned to the right or left foot

Each boy wears the shoes for 1 month and the amount of wear is measured

Are These the Same?


Analysis
Analysis

  • How would you analyze the data from Experiment 1?


Completely random design
Completely Random Design

  • Objective: Comparing two treatments - A and B

  • Method:

    • N experimental units available for the experiment

    • randomly assign treatment A to n1 exp. units and treatment B to n2 units (N = n1 + n2)

    • Conduct experiment

    • results: A: yA1, yA2, …, yAn1; B: yB1, yB2, … yBn2

  • Analysis Objective:

    • Compare the average responses, A vs. B

    • Is there evidence that one treatment is better than other, on average? How much better?



Analysis1
Analysis

  • How would you analyze the data from Experiment 2?

  • Can we use a 2-sample t-test or ANOVA here?

  • Would the 2-sample t-test or ANOVA detect a significant difference?


Paired comparison designs
Paired Comparison Designs

  • Objective - Compare two treatments

  • Method

    • Select N experimental units

    • Each experimental unit receives both treatments

    • Conduct the experiment assigning the treatments in random order

    • Measure the responses

    • Results, N pairs: (yA1, yB1), (yA2, yB2), …, (yAN, yBN)



Benefits of paired experiment
Benefits of Paired Experiment

  • Paired experiment used to eliminate possible sources of variability (noise)

    • If one receives sole A and another sole B, then the experimental error (variability among experimental units that receive the same treatment) reflects variability between boys and the variability within each boy

    • If each boys receives both soles, then the comparison within boy eliminates the variability among boys from the reference noise. The variability of repeated measurements within each boy is the pertinent experimental error in this case

  • Can be cheaper





Comments
Comments

  • Experimental results must be interpreted and thought about in terms of the subject-matter, not just the statistical results

  • In a good experiment, the message should be reasonably clear in a good plot of the data

  • Formal statistical procedures quantify the impressions that good plots convey


Something to help you get to sleep
Something to Help You Get to Sleep

  • Read the following news item and in groups of 2-4 discuss the question below:

    Headline:Xeriscaping May Use Up More Water

    MESA, AZ – Desert landscaping (called xeriscaping), often planted by residents to conserve water, may actually be using more water. ASU botanist Chris Martin and two students have been measuring the amount of irrigation used in the yards of 18 homes in Tempe and Phoenix. Half have desert plantings; the others have conventional plantings. In the 18 months of the study so far, homeowners put an average of 2.24 gallons per square foot on the xeriscaped yards, compared with 1.67 gallons per square foot on the other yards.

  • What questions would you like to ask Prof. Martin to help you interpret and evaluate these results?


You should know
You should know …

  • how to design, conduct, and analyze:

    • completely randomized design

    • randomized paired comparison design

  • how to recognize design from description of experiment


Blocking and randomization
Blocking and Randomization

  • Blocking

    • eliminate sources of variability

  • Randomization

    • balance possible effects of uncontrolled sources of variability

    • provide fair estimate of noise variability

  • General Guidance:

    “Block what you can and randomize what you cannot”


ad